Forces, Kinematics, and Dynamics

Frames of Reference help us describe motion correctly. A frame of reference is the point of view from which an observer measures and describes where something is and how it moves.

In everyday life, we often say things like “the car is moving” or “the book is still.” But in science, motion depends on what you compare the object to. That comparison is called the object’s frame of reference.

This means an object can seem to be moving in one frame of reference and not moving in another. Both descriptions can be correct, depending on who is observing.

Why does this matter? If we do not say what frame of reference we are using, descriptions of motion can be confusing. Scientists use frames of reference to make motion clear and accurate.

Main Idea: Motion is described relative to something else.

For example:

• If you are sitting on a bus, the seat under you may seem still.
• But to a person standing on the sidewalk, you and the seat are moving down the road.

So, are you moving? Yes and no—it depends on the frame of reference.

What is a frame of reference?

A frame of reference is the background or viewpoint used to describe motion. It is often based on:

• an observer’s position
• an observer’s own motion
• a nearby object used for comparison

Common frames of reference include:

• the ground
• a car
• a train
• a classroom
• another person

Rest and motion depend on the frame of reference.

An object is at rest if its position does not change compared with its frame of reference.

An object is in motion if its position changes compared with its frame of reference.

So, to decide if something is moving, ask:

1. What object am I observing?
2. What am I comparing it to?
3. Does its position change compared with that reference?

Example: Sitting in a moving car

Imagine you are sitting in a car that is moving at a steady speed.

• Compared to the car seat, you are at rest.
• Compared to the road, you are moving.
• Compared to a tree on the sidewalk, you are moving.

The same person can be described in different ways because the frame of reference changes.

Example: Walking on a train

Suppose a train is moving forward. Inside the train, a student walks toward the front.

• To another student sitting on the train, the walking student is moving slowly.
• To a person standing outside, the walking student is moving faster because the train is also moving.

This shows that motion can look different to different observers.

How distance and speed connect to frames of reference

In 7th Grade science, speed is often found using:

$$\text{speed} = \frac{\text{distance}}{\text{time}}$$

But even distance and speed depend on the frame of reference being used. If two observers measure motion from different frames of reference, they may get different descriptions.

For example, if a student walks 2 meters across a bus in 4 seconds, then in the bus frame of reference the student’s speed is:

$$\text{speed} = \frac{2\text{ m}}{4\text{ s}} = 0.5\text{ m/s}$$

But to a person outside the bus, the student is not only moving across the bus. The whole bus is moving too. So the student’s motion looks different from outside.

Important note: At this level, the key idea is not doing hard calculations. The key idea is understanding that motion depends on the observer.

Frames of reference in everyday life

• Playground: A child sitting on a merry-go-round may seem still compared to the seat, but moving compared to the ground.
• Airplane: A cup on a tray table seems still to a passenger, but it is moving very fast compared to the ground.
• Escalator: A person standing still on an escalator is not moving compared to the escalator step, but is moving compared to the floor below.
• Classroom: A backpack on the floor is at rest compared to the classroom, but because Earth moves through space, the backpack is not truly still compared to everything.

This last example shows something important: there is not always one “perfect” frame of reference for every situation. Scientists choose the one that is most useful.

Worked Example 1: A student on a bicycle

A student rides a bicycle past a mailbox.

Question: Is the student moving?

Step 1: Choose a frame of reference.

• If the frame of reference is the mailbox, the student’s position changes.

Conclusion: The student is moving relative to the mailbox.

Step 2: Try a different frame of reference.

• If the frame of reference is the bicycle seat, the student’s position does not change very much.

Conclusion: The student is at rest relative to the bicycle seat.

Big idea: The answer changes based on the frame of reference.

Worked Example 2: Walking inside a bus

A bus moves down the street. Inside the bus, Maya walks 3 meters toward the front in 6 seconds.

Question 1: What is Maya’s speed relative to the bus?

Use the speed formula:

$$\text{speed} = \frac{\text{distance}}{\text{time}}$$

Substitute the values:

$$\text{speed} = \frac{3\text{ m}}{6\text{ s}} = 0.5\text{ m/s}$$

Answer: Maya’s speed is \(0.5\text{ m/s}\) relative to the bus.

Question 2: Does a person on the sidewalk describe Maya the same way?

Answer: No. The sidewalk observer sees both Maya and the bus moving. So Maya’s motion looks different in that frame of reference.

Worked Example 3: Standing on an escalator

Jordan stands still on an escalator that is carrying him upward.

Question: Is Jordan moving?

Relative to the escalator step:

• Jordan stays in the same place.
• He is at rest.

Relative to the ground floor:

• Jordan changes position as he rises.
• He is moving.

Conclusion: Jordan can be at rest in one frame of reference and moving in another.

Worked Example 4: Two observers and a ball

A girl drops a ball while riding in a smoothly moving bus.

Observer 1: Inside the bus

• The ball appears to fall mostly straight down.

Observer 2: Standing outside the bus

• The ball moves forward with the bus while also falling down.

Conclusion: The path of the ball can look different depending on the observer’s frame of reference.

Common mistakes to avoid

• Mistake 1: Saying an object is “moving” without saying compared to what.
• Mistake 2: Thinking only one observer can be correct.
• Mistake 3: Forgetting that “at rest” also depends on a frame of reference.

How to answer questions about frames of reference

1. Identify the object whose motion is being described.
2. Identify the observer or reference point.
3. Ask whether the object’s position changes compared to that reference point.
4. State your answer clearly: “The object is moving relative to ___” or “The object is at rest relative to ___.”

Check Your Understanding

• If you sit in a parked car, are you moving relative to the seat? relative to the school building?
• If you ride past the school in that car, are you moving relative to the seat? relative to the school building?
• If a friend walks down the aisle of a moving train, how might the motion look different to someone on the train and someone outside?

Brief Summary

A frame of reference is the point of view used to describe motion. An object’s motion depends on what it is compared to. Because of this, the same object can be at rest in one frame of reference and moving in another. In science, always describe motion relative to a chosen observer or reference point.

Displacement and Distance are two ways to talk about motion.

When something moves, we can ask two different questions:

• How far did it travel altogether? This is called distance.
• How far is it from where it started to where it ended? This is called displacement.

These ideas sound alike, but they are not the same.

Distance means the total path traveled. It tells us how much ground was covered.

Displacement means the shortest straight line from the starting place to the ending place.

Think of it this way: distance is the whole trip, and displacement is the straight shortcut from start to finish.

Let’s learn each one step by step.

1. Distance

Distance is how far something moves along its path.

If you walk 3 steps forward and then 2 more steps forward, your distance is:

$$3 + 2 = 5$$

So the distance is 5 steps.

To find distance, we add all the parts of the trip.

2. Displacement

Displacement compares the starting point and the ending point.

It does not matter if the path was twisty or curvy. It only matters where the trip began and where it ended.

If you start at one spot and end 5 steps away in a straight line, then your displacement is 5 steps.

If you walk around a lot but end only 2 steps away from where you started, then your displacement is 2 steps.

A helpful way to remember:

• Distance = the whole path
• Displacement = start to finish in a straight line

Why can they be different?

Sometimes an object moves in more than one part. It may go forward, turn, or even come back.

When that happens, the distance keeps adding up because it counts every part of the trip.

But the displacement may be smaller because it only looks at how far the ending place is from the starting place.

Worked Example 1: Straight path

A toy car rolls 4 meters straight forward.

Distance: The car traveled 4 meters.

Displacement: The car started at one place and ended 4 meters away in a straight line.

So:

$$\text{Distance} = 4 \text{ m}$$

$$\text{Displacement} = 4 \text{ m}$$

When the motion is one straight path, distance and displacement can be the same.

Worked Example 2: Forward, then back

A child walks 6 steps forward, then 2 steps back.

Step 1: Find the distance.

Add all the walking parts:

$$6 + 2 = 8$$

Distance = 8 steps.

Step 2: Find the displacement.

The child went 6 steps away, then came back 2 steps.

$$6 - 2 = 4$$

Displacement = 4 steps.

So:

$$\text{Distance} = 8 \text{ steps}$$

$$\text{Displacement} = 4 \text{ steps}$$

The distance is bigger because it counts the whole trip.

Worked Example 3: Around the playground

A student runs around a small playground and comes back to the exact place where the run started. The total path around the playground is 20 meters.

Distance: The student ran all 20 meters.

So distance is 20 meters.

Displacement: The student ended at the same place where the run started.

The shortest straight line from start to finish is 0 meters.

So:

$$\text{Distance} = 20 \text{ m}$$

$$\text{Displacement} = 0 \text{ m}$$

This is an important idea: if you end where you started, your displacement is 0.

Worked Example 4: Turn and stop

A robot moves 5 squares to the right, then 3 squares to the left.

Distance:

Add both parts:

$$5 + 3 = 8$$

Distance = 8 squares.

Displacement:

The robot is 2 squares to the right of where it started.

$$5 - 3 = 2$$

Displacement = 2 squares.

So:

$$\text{Distance} = 8 \text{ squares}$$

$$\text{Displacement} = 2 \text{ squares}$$

How to tell which one to find

• If the question asks, “How far did it travel?” find distance.
• If the question asks, “How far is it from where it started?” find displacement.

Clues in questions

• Distance clues: total, altogether, traveled, path
• Displacement clues: start, finish, straight line, how far away now

Important ideas to remember

• Distance is always the total path.
• Displacement is the shortest straight line from start to finish.
• Distance can be the same as displacement if the motion is straight in one direction.
• Distance is often greater than displacement.
• If you end where you started, displacement is 0.

Let’s compare them one more time.

1. Start at one place.
2. Move along a path.
3. For distance, add the whole path.
4. For displacement, look only at the starting place and ending place.

Quick check

If a dog runs 7 meters to a tree and then 7 meters back to its owner:

• Distance: $$7 + 7 = 14$$ meters
• Displacement: back at the start, so $$0$$ meters

This shows again that distance and displacement are different ideas.

Summary

Distance tells the whole length of the trip. Displacement tells the straight-line change from start to finish.

When you solve motion problems, ask yourself: Am I finding the whole path, or am I finding how far away the ending place is from the starting place?

If you can answer that question, you can tell the difference between distance and displacement.

Scalars vs. Vectors is an important idea in science because it helps us describe motion clearly and correctly.

Some measurements tell us only how much. Other measurements must tell us how much and which way. That is the difference between a scalar and a vector.

When scientists talk about speed, distance, velocity, force, or displacement, they must be careful to use the right type of quantity. Understanding this makes motion and forces much easier to describe.

What is a scalar?

A scalar is a quantity that has magnitude only. Magnitude means the size or amount of something.

For a scalar, you do not need a direction. You only need a number and a unit.

• Examples of scalars: distance, speed, time, mass, temperature
• Examples: 5 meters, 12 seconds, 20°C, 3 kg, 8 m/s

If someone says, “I ran 200 meters,” that is a scalar. It tells how far, but not which direction.

What is a vector?

A vector is a quantity that has magnitude and direction.

For a vector, a number and unit are not enough. You must also include which way the quantity points or moves.

• Examples of vectors: displacement, velocity, force, acceleration
• Examples: 5 meters east, 10 m/s north, 20 N downward

If someone says, “I walked 50 meters north,” that is a vector. It tells both the amount and the direction.

The big difference

The easiest way to tell them apart is to ask this question:

Do I need a direction for this quantity to be complete?

• If the answer is no, it is a scalar.
• If the answer is yes, it is a vector.

Comparing common scalar and vector quantities

• Distance is a scalar because it tells how much ground was covered.
• Displacement is a vector because it tells how far something is from where it started and in what direction.
• Speed is a scalar because it tells how fast something moves.
• Velocity is a vector because it tells speed with direction.
• Force is a vector because a push or pull must act in a direction.

Distance vs. displacement

These two words can sound similar, but they are different.

Distance is the total path traveled. It does not matter which direction you went. That makes distance a scalar.

Displacement is the change from starting point to ending point, including direction. That makes displacement a vector.

For example, imagine you walk 3 meters east and then 3 meters west. Your total distance is:

$$3 + 3 = 6 \text{ meters}$$

But you end where you started, so your displacement is:

$$0 \text{ meters}$$

The distance is 6 meters, but the displacement is 0 meters because there is no overall change in position.

Speed vs. velocity

Speed tells how fast something moves. It does not include direction, so it is a scalar.

Velocity tells how fast something moves and in what direction, so it is a vector.

For example:

• Speed: 10 m/s
• Velocity: 10 m/s south

Both use the same number and unit, but only velocity includes direction.

How vectors are often shown

In science, vectors are often represented with arrows. The length of the arrow shows the magnitude, and the arrowhead shows the direction.

A longer arrow means a bigger vector. An arrow pointing right might mean east. An arrow pointing down might mean south.

This makes vectors very useful when describing motion and forces.

Worked Example 1: Identify scalar or vector

Classify each quantity as a scalar or vector:

1. 15 seconds
2. 8 m/s west
3. 12 kilograms
4. 25 N upward

Step-by-step:

1. 15 seconds has only an amount of time, no direction. It is a scalar.
2. 8 m/s west has a magnitude and a direction. It is a vector.
3. 12 kilograms has only mass, no direction. It is a scalar.
4. 25 N upward has a size and a direction. It is a vector.

Answer: scalar, vector, scalar, vector.

Worked Example 2: Distance or displacement?

A student walks 4 meters north and then 2 meters south.

Find the distance.

Distance is the total path traveled:

$$4 + 2 = 6 \text{ meters}$$

Find the displacement.

The student went 4 meters north, then came back 2 meters south. The overall change is 2 meters north.

$$4 - 2 = 2 \text{ meters north}$$

Answer:

• Distance = 6 meters (scalar)
• Displacement = 2 meters north (vector)

Worked Example 3: Speed or velocity?

A car travels at 20 m/s east.

What is the car's speed? What is its velocity?

Step-by-step:

Speed uses only magnitude, so we leave off the direction.

$$\text{Speed} = 20 \text{ m/s}$$

Velocity uses magnitude and direction.

$$\text{Velocity} = 20 \text{ m/s east}$$

Answer:

• Speed = 20 m/s
• Velocity = 20 m/s east

Worked Example 4: Is direction necessary?

Decide whether each quantity needs direction to make sense in science.

1. Temperature
2. Force
3. Displacement
4. Time

Step-by-step:

1. Temperature does not need direction. 18°C is complete. It is a scalar.
2. Force does need direction. A push must act in some direction. It is a vector.
3. Displacement needs direction because it describes change in position. It is a vector.
4. Time does not need direction. 30 seconds is complete. It is a scalar.

Why this matters in science

Scalars and vectors help scientists avoid confusion.

Imagine two students say they moved 5 meters. One went east and one went west. If we only use a scalar, we miss important information. A vector gives the full picture.

This is especially important when studying motion and forces. A force to the left and a force to the right do not affect an object in the same way, even if they have the same size.

Helpful clues

• If a quantity uses words like north, south, east, west, up, down, left, right, it is probably a vector.
• If a quantity is complete with just a number and unit, it is probably a scalar.
• Distance and speed are scalars.
• Displacement, velocity, and force are vectors.

Quick check

Decide whether each is a scalar or a vector:

• 9 m
• 9 m north
• 14 s
• 14 m/s west
• 22°C
• 5 N downward

Answers:

• 9 m → scalar
• 9 m north → vector
• 14 s → scalar
• 14 m/s west → vector
• 22°C → scalar
• 5 N downward → vector

Summary

A scalar has magnitude only. A vector has magnitude and direction.

Distance, speed, time, mass, and temperature are scalars. Displacement, velocity, force, and acceleration are vectors.

When you are unsure, ask: Does this quantity need a direction? If it does, it is a vector. If it does not, it is a scalar.

Distance vs. Displacement

When something moves, scientists can describe that motion in different ways. Two important ideas are distance and displacement. These words sound similar, but they do not mean the same thing.

Understanding the difference helps you describe motion correctly. It also helps you solve problems about how far something traveled and where it ended up compared to where it started.

Distance is the total length of the path traveled. It tells how much ground an object covered.

Displacement is the change in position from the starting point to the ending point. It tells how far and in what direction an object is from where it began.

Here is the simplest way to think about it:

• Distance = "How much did you travel altogether?"
• Displacement = "Where are you compared to where you started?"

Why are they different?

Imagine you walk around your school hallway. You may travel many meters as you move. That total path is your distance. But if you end up close to where you started, your displacement may be small.

If you return exactly to your starting point, your displacement is zero. Even if you walked a long way, your ending position is the same as your starting position.

Main idea: Distance depends on the path. Displacement depends only on the starting and ending positions.

Important features of distance

• Distance is a total amount.
• Distance does not include direction.
• Distance is always zero or positive.
• You find distance by adding all parts of the path.

Important features of displacement

• Displacement compares the ending position to the starting position.
• Displacement does include direction.
• Displacement can be zero.
• When motion is in one straight line, displacement can be written with a positive or negative sign to show direction.

For example, if we say right is positive:

• moving 5 m to the right can be written as \(+5\text{ m}\)
• moving 5 m to the left can be written as \(-5\text{ m}\)

A useful formula for displacement in a straight line

When motion happens in one straight line, displacement can be found with:

In symbols, this is often written as:

Here:

• \(x_f\) means final position
• \(x_i\) means initial position

Distance and displacement can sometimes be the same

If an object moves in one direction without turning around, then the total path and the change in position are equal in size.

For example, if a runner goes 20 m straight east and stops, then:

• Distance = 20 m
• Displacement = 20 m east

Distance and displacement can also be different

If the object changes direction, the distance usually becomes greater than the displacement.

For example, if a person walks 10 m east and then 4 m west:

• Distance = \(10 + 4 = 14\text{ m}\)
• Displacement = \(6\text{ m east}\)

The person traveled 14 m in total, but ended only 6 m east of the starting point.

Worked Example 1: Moving in one direction

A student walks 12 m forward down a hallway.

Step 1: Find the distance.

The student traveled only one path of 12 m.

Distance = \(12\text{ m}\)

Step 2: Find the displacement.

The student started at one point and ended 12 m forward from that point.

Displacement = \(12\text{ m forward}\)

Answer:

• Distance = \(12\text{ m}\)
• Displacement = \(12\text{ m forward}\)

Because the student never turned around, the distance and displacement are the same in size.

Worked Example 2: Turning around

A dog runs 15 m east, then 5 m west.

Step 1: Find the distance.

Add all parts of the path:

Distance = \(20\text{ m}\)

Step 2: Find the displacement.

The dog went 15 m east, then came back 5 m west.

So its final position is:

Displacement = \(10\text{ m east}\)

Answer:

• Distance = \(20\text{ m}\)
• Displacement = \(10\text{ m east}\)

Worked Example 3: Returning to the start

A girl walks 8 m north to a tree, then 8 m south back to where she started.

Step 1: Find the distance.

Add the total path:

Distance = \(16\text{ m}\)

Step 2: Find the displacement.

She ended exactly where she began.

Displacement = \(0\text{ m}\)

Answer:

• Distance = \(16\text{ m}\)
• Displacement = \(0\text{ m}\)

This is a very important example. An object can travel a distance greater than zero while having zero displacement.

Worked Example 4: Using positions on a number line

A toy car starts at \(2\text{ m}\) on a straight track and ends at \(11\text{ m}\).

Step 1: Find the displacement using the formula.

Displacement = \(9\text{ m}\) to the right

Step 2: Find the distance.

If the toy car moved straight from \(2\text{ m}\) to \(11\text{ m}\) without turning, then the path length is also 9 m.

Distance = \(9\text{ m}\)

Answer:

• Distance = \(9\text{ m}\)
• Displacement = \(9\text{ m}\) to the right

How to decide whether a problem is asking for distance or displacement

1. Look for words about the total path, such as "how far traveled" or "total distance."
2. Look for words about starting and ending position, such as "change in position" or "how far from the start."
3. If direction matters, the problem is often asking for displacement.
4. If you need to add every part of the trip, the problem is asking for distance.

Common mistakes to avoid

• Mistake 1: Thinking distance and displacement are always the same.
  They are only the same when the object moves in one direction without turning around.
• Mistake 2: Forgetting direction for displacement.
  Displacement needs direction, such as east, west, left, right, north, or south.
• Mistake 3: Adding movement for displacement when the object changes direction.
  For displacement, compare where the object ended to where it started.
• Mistake 4: Thinking displacement cannot be zero unless there was no motion.
  An object can move and still have zero displacement if it returns to its starting point.

Quick comparison

• Distance: total path traveled
• Displacement: straight-line change from start to end
• Distance: no direction needed
• Displacement: direction matters
• Distance: add all path lengths
• Displacement: look only at start and finish

Try thinking about this real-life situation

You walk from your front door to the kitchen, then to the living room, and finally back to the front door. You definitely traveled some distance because you moved through your house.

But your displacement is zero because you finished at the same place where you started.

Summary

Distance tells the total length of the path an object travels. Displacement tells the change in position from the starting point to the ending point.

If an object moves straight in one direction, distance and displacement can be the same in size. If it turns around or returns to the start, distance and displacement will be different, and displacement may even be zero.

Whenever you solve a motion problem, ask yourself: Am I finding the whole path, or am I comparing the start and end? That question will help you choose between distance and displacement.

Speed and Velocity are both ways to describe motion. They tell us how fast something moves, but they are not exactly the same.

In this lesson, you will learn what speed means, what velocity means, how to calculate each one, and why direction matters for velocity.

Understanding these ideas helps us describe real-life motion, like a car driving down a road, a runner moving around a track, or a student walking across a classroom.

What is speed?

Speed tells how much distance an object travels in a certain amount of time. Distance means how much ground an object covers.

The formula for speed is:

$$\text{speed} = \frac{\text{distance}}{\text{time}}$$

This means you divide the total distance traveled by the total time it took.

Speed does not include direction. If a bike moves at 5 meters per second, speed tells us how fast it is going, but not whether it is going north, south, left, or right.

Common units for speed are:

• meters per second \((m/s)\)
• kilometers per hour \((km/h)\)
• miles per hour \((mph)\)

What is velocity?

Velocity tells the speed of an object and its direction. Velocity uses displacement instead of distance.

Displacement is how far an object is from its starting point and in what direction. It is the straight-line change from start to finish.

The formula for velocity is:

$$\text{velocity} = \frac{\text{displacement}}{\text{time}}$$

Velocity must include a direction, such as:

• 3 m/s east
• 12 km/h north
• 5 m/s to the left

Distance and displacement are different.

This is one of the most important ideas in this lesson.

• Distance is the total path traveled.
• Displacement is the change in position from start to finish, including direction.

Imagine you walk 10 meters east and then 10 meters west. Your distance is 20 meters because you traveled 20 meters total.

But your displacement is 0 meters because you ended where you started.

That means your speed could be greater than 0, but your velocity could be 0 if your final position is the same as your starting position.

Average speed

Sometimes an object changes how fast it moves. It may go fast for a while and slow down later. In that case, we often calculate average speed.

The formula is still:

$$\text{average speed} = \frac{\text{total distance}}{\text{total time}}$$

You add all the distance traveled and divide by all the time used.

Average velocity

Average velocity is based on total displacement and total time.

$$\text{average velocity} = \frac{\text{total displacement}}{\text{total time}}$$

Remember: average velocity must include direction.

How to solve speed and velocity problems

1. Read the problem carefully.
2. Find the numbers for distance or displacement and time.
3. Decide whether the problem is asking for speed or velocity.
4. Use the correct formula.
5. Check your units.
6. If it is velocity, include the direction.

Worked Example 1: Finding speed

A student walks 30 meters in 6 seconds. What is the student's speed?

Use the formula:

$$\text{speed} = \frac{\text{distance}}{\text{time}}$$

Substitute the values:

$$\text{speed} = \frac{30\text{ m}}{6\text{ s}} = 5\text{ m/s}$$

Answer: The student's speed is 5 m/s.

Worked Example 2: Finding velocity

A bird flies 40 meters north in 8 seconds. What is the bird's velocity?

Use the formula:

$$\text{velocity} = \frac{\text{displacement}}{\text{time}}$$

Substitute the values:

$$\text{velocity} = \frac{40\text{ m north}}{8\text{ s}} = 5\text{ m/s north}$$

Answer: The bird's velocity is 5 m/s north.

Notice that the answer includes both the number and the direction.

Worked Example 3: Distance compared with displacement

A runner goes 100 meters east, then 40 meters west, in 20 seconds.

Step 1: Find distance.

Distance is the total path traveled:

$$100\text{ m} + 40\text{ m} = 140\text{ m}$$

Step 2: Find average speed.

$$\text{average speed} = \frac{140\text{ m}}{20\text{ s}} = 7\text{ m/s}$$

Step 3: Find displacement.

The runner moved 100 meters east, then 40 meters west. That means the final position is 60 meters east of the start.

$$100\text{ m east} - 40\text{ m west} = 60\text{ m east}$$

Step 4: Find average velocity.

$$\text{average velocity} = \frac{60\text{ m east}}{20\text{ s}} = 3\text{ m/s east}$$

Answer:

• Average speed = 7 m/s
• Average velocity = 3 m/s east

This example shows that speed and velocity can have different values.

Worked Example 4: Returning to the starting point

A student walks 15 meters south and then 15 meters north in 10 seconds total.

Step 1: Find distance.

$$15\text{ m} + 15\text{ m} = 30\text{ m}$$

Step 2: Find average speed.

$$\text{average speed} = \frac{30\text{ m}}{10\text{ s}} = 3\text{ m/s}$$

Step 3: Find displacement.

The student ended at the starting point, so:

$$\text{displacement} = 0\text{ m}$$

Step 4: Find average velocity.

$$\text{average velocity} = \frac{0\text{ m}}{10\text{ s}} = 0\text{ m/s}$$

Answer:

• Average speed = 3 m/s
• Average velocity = 0 m/s

This is a very important idea: an object can move and still have an average velocity of 0 if it ends where it started.

Comparing speed and velocity

• Speed uses distance.
• Velocity uses displacement.
• Speed does not include direction.
• Velocity must include direction.
• Speed tells how fast.
• Velocity tells how fast and which way.

Helpful tips

• If the problem asks only “how fast,” it is usually asking for speed.
• If the problem asks “how fast and in what direction,” it is asking for velocity.
• If an object turns around, the distance keeps adding, but the displacement may get smaller.
• If the object ends where it started, displacement is 0.

Why this matters in real life

Scientists use speed and velocity to study motion. Drivers, athletes, pilots, and engineers also use these ideas.

For example, a car's speedometer shows speed. But if you want to know how quickly a storm is moving toward the east, you need velocity because direction matters.

Summary

Speed is the rate at which distance is covered. It is found by dividing distance by time.

Velocity is the rate at which displacement happens. It is found by dividing displacement by time, and it must include direction.

When solving problems, always ask yourself: Am I using distance or displacement? That will help you decide whether to calculate speed or velocity.

Acceleration is how quickly an object's velocity changes. Velocity means both speed and direction, so acceleration happens any time an object speeds up, slows down, or changes direction.

For example, a car going from 10 meters per second to 20 meters per second is accelerating. A bike slowing down to a stop is also accelerating. Even a runner moving at the same speed around a curve is accelerating, because the runner's direction is changing.

Acceleration helps scientists describe motion more clearly. It tells us not just how fast something is moving, but how its motion is changing over time.

The formula for acceleration is:

$$a = \frac{v_f - v_i}{t}$$

In this formula:

• \(a\) = acceleration
• \(v_f\) = final velocity
• \(v_i\) = initial velocity
• \(t\) = time

You can also think of it as:

$$\text{acceleration} = \frac{\text{change in velocity}}{\text{time}}$$

The most common unit for acceleration is meters per second squared, written as \(m/s^2\). This means how many meters per second the velocity changes each second.

For example, an acceleration of \(3\, m/s^2\) means the velocity changes by 3 meters per second every second.

There are three common ways acceleration can happen:

• Speeding up: the object's speed increases
• Slowing down: the object's speed decreases
• Turning: the object's direction changes

When an object speeds up, its acceleration is often called positive acceleration. When an object slows down, it can have negative acceleration, which is also called deceleration.

Negative acceleration does not always mean “bad” or “backward.” It just means the change in velocity is in the opposite direction from the positive direction you chose.

How to calculate acceleration

1. Find the initial velocity.
2. Find the final velocity.
3. Subtract: final velocity minus initial velocity.
4. Divide by the time it took for the change to happen.
5. Include the correct unit, usually \(m/s^2\).

Worked Example 1: Speeding up

A scooter starts at \(2\, m/s\) and speeds up to \(8\, m/s\) in \(3\) seconds. What is its acceleration?

Step 1: Write the formula.

$$a = \frac{v_f - v_i}{t}$$

Step 2: Substitute the values.

$$a = \frac{8 - 2}{3}$$

Step 3: Solve.

$$a = \frac{6}{3} = 2\, m/s^2$$

Answer: The scooter's acceleration is \(2\, m/s^2\).

This means the scooter's velocity increases by 2 meters per second every second.

Worked Example 2: Slowing down

A ball rolls at \(10\, m/s\) and slows to \(4\, m/s\) in \(2\) seconds. What is its acceleration?

Step 1: Use the formula.

$$a = \frac{v_f - v_i}{t}$$

Step 2: Substitute the values.

$$a = \frac{4 - 10}{2}$$

Step 3: Solve.

$$a = \frac{-6}{2} = -3\, m/s^2$$

Answer: The ball's acceleration is \(-3\, m/s^2\).

The negative sign shows that the ball is slowing down.

Worked Example 3: Starting from rest

A skateboarder starts from rest, which means the initial velocity is \(0\, m/s\). After \(5\) seconds, the skateboarder is moving at \(15\, m/s\). What is the acceleration?

Step 1: Identify the values.

• \(v_i = 0\, m/s\)
• \(v_f = 15\, m/s\)
• \(t = 5\, s\)

Step 2: Use the formula.

$$a = \frac{15 - 0}{5}$$

Step 3: Solve.

$$a = \frac{15}{5} = 3\, m/s^2$$

Answer: The skateboarder's acceleration is \(3\, m/s^2\).

Worked Example 4: Finding final velocity from acceleration

A toy car has an acceleration of \(4\, m/s^2\) for \(3\) seconds. It starts at \(1\, m/s\). What is its final velocity?

We can rearrange the acceleration idea:

$$a = \frac{v_f - v_i}{t}$$

Multiply both sides by \(t\):

$$at = v_f - v_i$$

Add \(v_i\) to both sides:

$$v_f = v_i + at$$

Step 1: Substitute the values.

$$v_f = 1 + (4)(3)$$

Step 2: Solve.

$$v_f = 1 + 12 = 13\, m/s$$

Answer: The toy car's final velocity is \(13\, m/s\).

Acceleration and direction

Remember that velocity includes direction. If a car goes around a corner, its direction changes even if the speed stays the same. Because the velocity changed, the car is accelerating.

This idea is important because many students think acceleration only means speeding up. In science, acceleration means any change in velocity.

Acceleration and forces

Acceleration happens when there is an unbalanced force on an object. A force is a push or a pull.

For example:

• Pushing a wagon makes it speed up.
• Friction can make a sliding box slow down.
• A steering force can make a car turn.

If the forces on an object are balanced, the object will not change its velocity. That means it will not accelerate.

Common mistakes to avoid

• Mixing up speed and velocity: velocity includes direction.
• Forgetting to subtract correctly: always do final velocity minus initial velocity.
• Ignoring the negative sign: a negative answer usually shows slowing down or acceleration in the opposite direction.
• Forgetting units: acceleration should usually be written in \(m/s^2\).
• Thinking acceleration only means speeding up: slowing down and turning are also acceleration.

Quick check for understanding

• If a runner goes from \(6\, m/s\) to \(9\, m/s\), is the runner accelerating? Yes, because the velocity changed.
• If a bus goes from \(12\, m/s\) to \(12\, m/s\) in a straight line, is it accelerating? No, because the velocity stayed the same.
• If a bike moves at the same speed but turns left, is it accelerating? Yes, because the direction changed.

Summary

Acceleration is the rate at which velocity changes. An object can accelerate by speeding up, slowing down, or changing direction. To calculate acceleration, use $$a = \frac{v_f - v_i}{t}$$ and write the answer in \(m/s^2\).

Motion Graphs are pictures that show how an object moves over time. Instead of only using words, scientists use graphs to quickly understand whether something is standing still, moving slowly, moving fast, speeding up, or slowing down.

In this lesson, you will learn how to read two important kinds of motion graphs:

• Position-time graphs, which show where an object is at different times
• Velocity-time graphs, which show how fast an object is moving and in what direction

You will also learn a very important idea: the slope of a graph tells us useful information about motion.

For a position-time graph, the slope tells us velocity.

For a velocity-time graph, the slope tells us acceleration.

1. Review: position, velocity, and acceleration

Before reading motion graphs, it helps to remember what these words mean.

• Position: where an object is
• Velocity: how fast an object moves and in what direction
• Acceleration: how velocity changes over time

If velocity changes, then the object is accelerating. That can mean it is speeding up, slowing down, or changing direction.

2. What is slope?

Slope tells how steep a line is. On a graph, slope compares the change up or down to the change across.

We can write slope as:

$$\text{slope} = \frac{\text{change in vertical axis}}{\text{change in horizontal axis}}$$

Many students remember this as rise over run.

In motion graphs, the meaning of slope depends on what the axes represent.

3. Position-time graphs

On a position-time graph:

• The horizontal axis shows time
• The vertical axis shows position

This graph answers the question: Where is the object at each moment?

The most important rule is:

The slope of a position-time graph is velocity.

That means:

$$\text{velocity} = \frac{\text{change in position}}{\text{change in time}}$$

This is the same as:

$$v = \frac{\Delta x}{\Delta t}$$

Here, \(\Delta x\) means change in position, and \(\Delta t\) means change in time.

How to read a position-time graph

• Flat line: the object is not moving, because position is not changing
• Upward sloping line: the object is moving in the positive direction
• Downward sloping line: the object is moving in the negative direction, or back toward the starting point
• Steeper line: faster velocity
• Less steep line: slower velocity

Important note: A high point on the graph does not mean high speed. It only means the object is far from the starting position. To know speed or velocity, look at the slope, not just the height of the line.

4. Velocity-time graphs

On a velocity-time graph:

• The horizontal axis shows time
• The vertical axis shows velocity

This graph answers the question: How is the object’s velocity changing over time?

The most important rule is:

The slope of a velocity-time graph is acceleration.

That means:

$$\text{acceleration} = \frac{\text{change in velocity}}{\text{change in time}}$$

This is the same as:

$$a = \frac{\Delta v}{\Delta t}$$

Here, \(\Delta v\) means change in velocity.

How to read a velocity-time graph

• Flat line above zero: constant positive velocity, so acceleration is zero
• Flat line at zero: the object is stopped
• Line sloping upward: positive acceleration
• Line sloping downward: negative acceleration
• Steeper slope: greater acceleration

Important note: A point high on a velocity-time graph means high velocity, not high acceleration. To find acceleration, look at the slope.

5. Positive and negative motion

In motion graphs, positive and negative numbers often show direction.

For example, if a person walks 3 meters to the right, that might be positive. If the person walks 3 meters to the left, that might be negative. The graph depends on which direction was chosen as positive.

A negative velocity does not mean the object is moving slowly. It means the object is moving in the negative direction.

6. Constant motion and changing motion

If a graph is a straight line with the same slope the whole time, the motion is constant.

• On a position-time graph, a straight line means constant velocity.
• On a velocity-time graph, a straight line means constant acceleration.

If the graph changes steepness, then the motion is changing too.

Worked Example 1: Finding velocity from a position-time graph

A toy car moves from 0 meters at 0 seconds to 10 meters at 5 seconds. Find the velocity.

Step 1: Use the slope formula.

$$v = \frac{\Delta x}{\Delta t}$$

Step 2: Find the change in position.

$$\Delta x = 10 - 0 = 10\text{ m}$$

Step 3: Find the change in time.

$$\Delta t = 5 - 0 = 5\text{ s}$$

Step 4: Divide.

$$v = \frac{10}{5} = 2\text{ m/s}$$

Answer: The toy car’s velocity is 2 m/s.

This means the car moves 2 meters every second.

Worked Example 2: Reading a flat line on a position-time graph

A student stands still at 4 meters from 2 seconds to 6 seconds. What is the velocity during that time?

Step 1: Notice that the position does not change.

The graph would be a flat line at 4 meters.

Step 2: Use the slope idea.

$$v = \frac{\Delta x}{\Delta t}$$

Since the position stays at 4 meters,

$$\Delta x = 0\text{ m}$$

Step 3: Divide.

$$v = \frac{0}{4} = 0\text{ m/s}$$

Answer: The velocity is 0 m/s.

A flat line on a position-time graph means the object is not moving.

Worked Example 3: Finding acceleration from a velocity-time graph

A bicycle’s velocity changes from 2 m/s at 1 second to 8 m/s at 4 seconds. Find the acceleration.

Step 1: Use the slope formula for a velocity-time graph.

$$a = \frac{\Delta v}{\Delta t}$$

Step 2: Find the change in velocity.

$$\Delta v = 8 - 2 = 6\text{ m/s}$$

Step 3: Find the change in time.

$$\Delta t = 4 - 1 = 3\text{ s}$$

Step 4: Divide.

$$a = \frac{6}{3} = 2\text{ m/s}^2$$

Answer: The bicycle’s acceleration is 2 m/s².

This means the velocity increases by 2 meters per second every second.

Worked Example 4: Negative slope on a velocity-time graph

A skateboarder’s velocity changes from 6 m/s at 0 seconds to 0 m/s at 3 seconds. Find the acceleration.

Step 1: Use the acceleration formula.

$$a = \frac{\Delta v}{\Delta t}$$

Step 2: Find the change in velocity.

$$\Delta v = 0 - 6 = -6\text{ m/s}$$

Step 3: Find the change in time.

$$\Delta t = 3 - 0 = 3\text{ s}$$

Step 4: Divide.

$$a = \frac{-6}{3} = -2\text{ m/s}^2$$

Answer: The skateboarder’s acceleration is -2 m/s².

The negative sign tells us the velocity is decreasing over time.

7. Common mistakes to avoid

• Mixing up the graph types: On a position-time graph, slope means velocity. On a velocity-time graph, slope means acceleration.
• Looking at height instead of slope: The value on the vertical axis is important, but slope tells the change.
• Ignoring negative values: A negative slope or value can show motion in the opposite direction or slowing down.
• Forgetting units: Velocity is often in meters per second \((\text{m/s})\). Acceleration is often in meters per second squared \((\text{m/s}^2)\).

8. Quick comparison chart

• Position-time graph
  • Shows where an object is
  • Slope = velocity
  • Flat line = stopped
• Velocity-time graph
  • Shows how velocity changes
  • Slope = acceleration
  • Flat line = constant velocity

9. How to solve motion graph questions

1. Look at the axes carefully.
2. Ask: Is this a position-time graph or a velocity-time graph?
3. Decide what the slope represents.
4. Find the change in the vertical value.
5. Find the change in time.
6. Divide to find slope.
7. Include the correct units.

Summary

Motion graphs help us understand movement in a clear visual way. On a position-time graph, the slope tells velocity. On a velocity-time graph, the slope tells acceleration.

If you remember to check the axes first, then use slope as change over time, you can read motion graphs with confidence. Always pay attention to whether the line is flat, rising, falling, steep, or gentle, because each of these gives clues about how an object is moving.

Projectile motion happens when an object is thrown, kicked, launched, or dropped and then moves through the air while gravity pulls it downward.

You see projectile motion in real life when someone throws a basketball, kicks a soccer ball, or tosses a set of keys. Even though the object is moving forward, gravity is also pulling it down at the same time.

The big idea is that projectile motion has two kinds of motion happening together:

• Horizontal motion: movement forward or sideways
• Vertical motion: movement up and down

These two motions happen at the same time, but they are independent. That means the horizontal motion does not control the vertical motion, and the vertical motion does not control the horizontal motion.

For 7th Grade science, it helps to think of projectile motion as a combination of:

• a steady push forward
• gravity pulling downward

This is why a projectile usually follows a curved path instead of a straight line.

Important idea: After the object leaves the thrower or launcher, gravity is the main force changing its motion downward. If we ignore air resistance, the object keeps moving horizontally while falling vertically.

1. Horizontal and vertical motion

Imagine throwing a ball straight forward from a certain height.

The ball keeps moving forward because of its starting motion. At the same time, gravity pulls it downward. The result is a curved path.

We can describe the motion like this:

• Horizontal direction: the ball keeps moving forward
• Vertical direction: the ball speeds up downward because of gravity

If there is very little air resistance, the horizontal speed stays nearly the same.

But in the vertical direction, gravity changes the speed the whole time:

• If the object is going up, gravity slows it down.
• At the top, the vertical speed becomes zero for a moment.
• Then the object starts moving down, and gravity makes it fall faster.

2. Why the path is curved

A projectile does not move in a straight line because only one part of its motion stays steady.

The horizontal part stays nearly constant, but the vertical part keeps changing because of gravity. Since one direction stays steady and the other changes, the path bends into a curve.

This curve is often called an arc.

3. Launching horizontally vs. launching upward

There are different ways an object can become a projectile.

Launched horizontally: An object can roll off a table or be pushed straight forward. It starts with horizontal motion, and gravity immediately pulls it down.

Launched upward at an angle: An object can be thrown up and forward at the same time. Then it has both horizontal motion and upward vertical motion at the start.

In both cases, gravity still pulls downward during the entire trip.

4. A very important comparison

Suppose two balls start at the same height at the same time:

• one ball is dropped straight down
• the other ball is thrown forward horizontally

Which one hits the ground first?

If we ignore air resistance, they hit the ground at the same time.

This surprises many students. The reason is that both balls have the same vertical motion. The forward-moving ball is not held up by its horizontal motion. Moving forward does not stop gravity from pulling downward.

5. Key terms

• Projectile: an object moving through the air after being launched
• Gravity: the force that pulls objects toward Earth
• Horizontal motion: movement parallel to the ground
• Vertical motion: movement up and down
• Trajectory: the path the projectile follows

6. Simple math ideas for projectile motion

In 7th Grade, we can describe motion using basic speed and distance ideas.

For horizontal motion, if the speed stays constant, then:

$$\text{distance} = \text{speed} \times \text{time}$$

Or in symbols:

$$d = vt$$

Here:

• \(d\) = horizontal distance
• \(v\) = horizontal speed
• \(t\) = time

This formula works well for the horizontal part when air resistance is small.

For vertical motion, gravity changes the motion. You may not need a difficult formula yet, but you should know this:

• the object falls more and more each second
• gravity always pulls downward

So when we solve simple projectile motion problems in middle school, we often focus on:

• how far forward the object travels
• how gravity changes its up-and-down motion

7. What affects projectile motion?

Several things can change how a projectile moves:

• Starting speed: A faster object usually travels farther.
• Launch angle: Throwing upward changes how high and how far the object goes.
• Starting height: An object launched from a higher place stays in the air longer.
• Gravity: Gravity pulls the object downward the whole time.
• Air resistance: Air can slow the object, but we often ignore it in simple problems.

8. Common mistakes to avoid

• Mistake: Thinking forward motion cancels gravity.
  Correct idea: Gravity still pulls down no matter how fast the object moves forward.
• Mistake: Thinking the object keeps rising because it was thrown upward.
  Correct idea: Gravity slows the upward motion until the object stops rising and begins to fall.
• Mistake: Thinking a dropped object falls faster than a horizontally thrown object from the same height.
  Correct idea: Their vertical motion is the same, so they hit at the same time if air resistance is ignored.

9. Worked examples

Example 1: A ball rolls off a table

A ball rolls off a table with a horizontal speed of \(3\text{ m/s}\). It stays in the air for \(2\text{ s}\). How far does it travel horizontally?

Step 1: Use the horizontal motion formula.

$$d = vt$$

Step 2: Substitute the values.

$$d = 3 \times 2$$

Step 3: Solve.

$$d = 6\text{ m}$$

Answer: The ball travels 6 meters horizontally.

What this shows: While gravity pulls the ball downward, the ball still keeps moving forward.

Example 2: Two balls released at the same time

One ball is dropped straight down. Another ball is thrown straight forward from the same height at the same time. Which lands first?

Think about the vertical motion.

Both balls:

• start at the same height
• are pulled by the same gravity
• begin falling at the same time

Answer: They land at the same time if air resistance is ignored.

What this shows: Horizontal motion and vertical motion are independent.

Example 3: A ball is thrown upward and forward

A student throws a ball upward and forward. What happens to the ball during its flight?

Step-by-step description:

1. The ball moves forward because it was thrown forward.
2. The ball rises at first because it was also thrown upward.
3. Gravity pulls downward the whole time.
4. The upward motion slows down.
5. At the highest point, the vertical speed is \(0\) for a moment.
6. Then the ball starts falling.
7. It continues moving forward while falling.

Answer: The ball follows a curved path because it has forward motion and downward pull from gravity at the same time.

Example 4: Comparing two horizontal speeds

Two balls roll off the same table at the same time. Ball A moves at \(2\text{ m/s}\), and Ball B moves at \(5\text{ m/s}\). They are in the air for the same amount of time. Which ball lands farther from the table?

Use the idea \(d = vt\).

If the time is the same, the ball with the greater horizontal speed travels farther.

Since \(5\text{ m/s}\) is greater than \(2\text{ m/s}\), Ball B travels farther.

Answer: Ball B lands farther from the table.

What this shows: Greater horizontal speed means greater horizontal distance, as long as the air time is the same.

10. How to think through projectile motion problems

When you see a projectile motion question, use these steps:

1. Picture the motion. Is the object moving forward, upward, downward, or some combination?
2. Separate the motion into two parts. Think about horizontal motion and vertical motion separately.
3. Ask what gravity is doing. Gravity always pulls downward.
4. Check the horizontal motion. If air resistance is ignored, the object keeps moving forward at a steady rate.
5. Put the two parts together. This helps explain the curved path.

11. Real-world examples

• a basketball shot toward the hoop
• a soccer ball kicked through the air
• a water balloon thrown across a yard
• a rock tossed from a cliff
• a book sliding off a desk and falling

In each case, the object has horizontal motion, vertical motion, or both. Gravity affects all of them.

12. Brief summary

Projectile motion is the motion of an object moving through the air after it is launched.

The most important idea is that horizontal motion and vertical motion are independent. The object keeps moving forward while gravity pulls it downward.

This is why projectiles move in a curved path. To understand any projectile, think about the forward motion and the up-and-down motion separately.

Contact vs. Non-Contact Forces

Forces are pushes or pulls that can change an object’s motion. A force can make something start moving, stop moving, speed up, slow down, or change direction.

In science, forces are often grouped into two main types: contact forces and non-contact forces. Understanding the difference helps us explain many everyday events, from kicking a soccer ball to a magnet attracting a paper clip.

This lesson will show you what each type of force is, how to recognize them, and how to tell them apart in real-life situations.

1. What is a force?

A force is a push or pull acting on an object. If you push a shopping cart, pull open a door, or drop a book, forces are involved.

Forces are measured in units called newtons, written as N. Sometimes we show force with a simple equation:

$$F = ma$$

This means force equals mass times acceleration. You do not need to use this equation all the time to understand forces, but it reminds us that forces are what cause changes in motion.

2. Contact forces

A contact force happens when two objects touch. The force is passed from one object to another through direct contact.

In other words, if the objects are not touching, a contact force cannot happen.

Common examples of contact forces include:

• Pushes and pulls by your hand
• Friction, which happens when surfaces rub against each other
• Tension in a rope or string
• Support force from a table holding up a book
• Air resistance, when air pushes against a moving object

Examples of contact forces in daily life:

• Kicking a ball
• Pushing a chair
• Riding a bike and feeling the brakes slow the wheels through friction
• A parachute slowing a skydiver because of air resistance

3. Non-contact forces

A non-contact force acts on an object without touching it. These forces work across a distance.

That may seem strange at first, but we see it happen all the time. For example, Earth pulls objects downward even though it is not “touching” them with hands or ropes. That pull is gravity.

The main non-contact forces you should know are:

• Gravity — pulls objects toward each other
• Magnetic force — magnets can attract or repel certain materials and other magnets
• Electric force — charged objects can attract or repel each other

Examples of non-contact forces in daily life:

• An apple falling from a tree because of gravity
• A refrigerator magnet sticking to the fridge
• A rubbed balloon attracting small bits of paper

4. The biggest difference: touching vs. acting at a distance

The easiest way to tell the two types apart is to ask one question:

Are the objects touching?

• If yes, the force is usually a contact force.
• If no, the force is a non-contact force.

This simple rule works well for most 7th Grade science examples.

5. Comparing contact and non-contact forces

• Contact force: requires direct touch
• Non-contact force: does not require touch
• Contact force examples: friction, push, pull, tension, air resistance
• Non-contact force examples: gravity, magnetic force, electric force

6. More about common contact forces

Friction is a contact force that opposes motion between surfaces that touch. If you slide a book across a desk, friction acts between the book and the desk and slows the book down.

Air resistance is also a contact force. Even though air is hard to see, it is made of particles. When an object moves through air, it bumps into those particles, and the air pushes back.

Tension happens in ropes, strings, or cables when they pull on an object. If you pull a wagon with a rope, the rope provides tension.

Support force happens when a surface holds something up. A table pushes upward on a book resting on it so the book does not fall through the table.

7. More about common non-contact forces

Gravity is the force that pulls objects toward Earth. It gives objects weight and causes dropped objects to fall downward.

Gravity acts between all objects with mass, but Earth is so large that its pull is the one we notice most often.

Magnetic force comes from magnets. Magnets can attract some objects, like iron, or repel other magnets. This happens without direct contact.

Electric force happens between charged objects. For example, when you rub a balloon on your hair, the balloon can become electrically charged and then attract light objects such as tiny paper pieces.

8. Can more than one force act at the same time?

Yes. In fact, objects often have more than one force acting on them at once.

For example, when you push a box across the floor:

• Your push is a contact force.
• Friction from the floor is also a contact force.
• Gravity pulls the box downward as a non-contact force.
• The floor pushes upward on the box as a contact force.

This shows that contact and non-contact forces can act on the same object at the same time.

9. Worked Examples

Example 1: Kicking a soccer ball

Question: Is the force from your foot on the soccer ball a contact or non-contact force?

Step 1: Ask if the objects are touching.

Your foot touches the ball.

Step 2: Classify the force.

Because the foot and the ball are touching, this is a contact force.

Answer: The kick is a contact force.

Example 2: A magnet pulling a paper clip

Question: Is the force from the magnet on the paper clip a contact or non-contact force?

Step 1: Ask if the objects must touch for the force to happen.

The magnet can begin pulling the paper clip even before they touch.

Step 2: Classify the force.

Because the force happens across a distance, it is a non-contact force.

Answer: Magnetic force is a non-contact force.

Example 3: Sliding a book across a table

Question: What forces act on the book, and which are contact or non-contact?

Step 1: Identify the push.

Your hand pushes the book while touching it, so that push is a contact force.

Step 2: Identify friction.

The table rubs against the book and slows it down. Friction needs touching surfaces, so friction is a contact force.

Step 3: Identify gravity.

Earth pulls the book downward without touching it directly, so gravity is a non-contact force.

Step 4: Identify the table’s upward support.

The table touches the book and pushes up on it, so this is a contact force.

Answer:

• Push by hand: contact
• Friction: contact
• Gravity: non-contact
• Support from table: contact

Example 4: Comparing two situations

Question: Which situation shows a contact force, and which shows a non-contact force?

1. A student pulls a backpack with a strap.
2. A dropped pencil falls to the floor.

Step 1: Look at the backpack.

The strap is touching the backpack, so the pulling force is a contact force.

Step 2: Look at the pencil.

The pencil falls because of gravity. Gravity acts without touching, so it is a non-contact force.

Answer:

• Backpack with strap: contact force
• Pencil falling: non-contact force

10. Tips for telling the difference on a test

• Look for words like push, pull, rub, drag, or hold. These often describe contact forces.
• Look for words like gravity, magnet, or charge. These usually describe non-contact forces.
• Ask: Do the objects need to touch?
• Remember that invisible does not always mean non-contact. Air resistance is invisible, but it is still a contact force because air touches the object.

11. Common mistakes to avoid

• Mistake: Thinking all invisible forces are non-contact.
  Fix: Air resistance and friction can be hard to see, but they are contact forces.
• Mistake: Thinking gravity only works when something is falling.
  Fix: Gravity acts on objects all the time, even when they are sitting still.
• Mistake: Forgetting that more than one force can act on an object.
  Fix: Always think about all pushes and pulls in the situation.

12. Quick review

• A force is a push or pull.
• Contact forces happen when objects touch.
• Non-contact forces happen across a distance.
• Friction, tension, pushes, pulls, support force, and air resistance are contact forces.
• Gravity, magnetic force, and electric force are non-contact forces.

Summary

Contact forces require objects to touch, like when you push a box or friction slows a moving object. Non-contact forces act across a distance, like gravity pulling objects downward or a magnet attracting metal.

To tell the difference, ask whether the objects are touching. If they touch, it is a contact force. If the force happens without touching, it is a non-contact force.

Newton's First Law is often called the law of inertia. It explains what happens to an object when no unbalanced force acts on it.

The law says: An object at rest stays at rest, and an object in motion stays in motion at the same speed and in the same direction, unless acted on by a net external force.

This means objects do not change their motion by themselves. If something starts moving, stops moving, speeds up, slows down, or turns, a force caused that change.

To understand this law, we need to know two important ideas: motion and force.

Motion means a change in position over time. An object can be:

• At rest - not moving compared to its surroundings
• In motion - moving at a certain speed in a certain direction

Force is a push or a pull. Forces can make objects start moving, stop moving, speed up, slow down, or change direction.

But Newton's First Law does not say that every force changes motion. It says a change happens only when there is a net external force.

Net force means the overall force after combining all the pushes and pulls on an object.

If forces are balanced, the net force is:

$$0 \text{ N}$$

When the net force is zero, the object's motion does not change.

• If it is resting, it stays resting.
• If it is moving, it keeps moving in a straight line at the same speed.

If forces are unbalanced, the net force is not zero. Then the object's motion changes.

This law helps explain a very important idea called inertia.

Inertia is an object's tendency to resist changes in its motion. In simple words, objects like to keep doing what they are already doing.

• A book on a desk tends to stay still.
• A rolling ball tends to keep rolling.

In both cases, the object resists change unless a force acts on it.

Objects with more mass usually have more inertia. That means they are harder to start moving, harder to stop, and harder to change direction.

For example, pushing an empty shopping cart is easier than pushing a full shopping cart. The full cart has more mass, so it has more inertia.

Many students think that moving objects must always have a force pushing them forward. That seems true in everyday life, but it is not exactly correct.

In real life, moving objects often slow down because of friction or air resistance. These are forces that act against motion. If those forces were not there, the object would keep moving.

For example, if you slide a book across a table, it stops after a while. That does not mean Newton's First Law is wrong. It stops because friction acts on the book.

If friction were removed, the book would keep moving much longer.

Balanced and Unbalanced Forces

Let's look more closely at balanced and unbalanced forces.

Balanced forces are equal in size and opposite in direction. They cancel each other out.

Example: A book resting on a table has gravity pulling it downward and the table pushing upward. These forces balance, so the book stays at rest.

Unbalanced forces do not cancel out. One side is stronger, so the motion changes.

Example: If you kick a soccer ball, your foot applies a force. That unbalanced force changes the ball from rest to motion.

We can write net force as:

$$\text{Net force} = \text{all forces added together}$$

If a force of \(10\text{ N}\) pushes right and a force of \(10\text{ N}\) pushes left, then:

$$10 + (-10) = 0\text{ N}$$

The forces are balanced.

If a force of \(12\text{ N}\) pushes right and \(5\text{ N}\) pushes left, then:

$$12 + (-5) = 7\text{ N}$$

The net force is \(7\text{ N}\) to the right, so the motion changes.

Everyday Examples of Newton's First Law

• Seat belts in a car: When a car stops suddenly, your body keeps moving forward because of inertia. The seat belt provides the force that stops your body safely.
• A coin and a card trick: If a card is quickly pulled from under a coin, the coin tends to stay at rest and drops straight down into the cup because of inertia.
• Riding a bus: If the bus starts moving suddenly, your body seems to lean backward. Your feet move with the bus, but the rest of your body resists the change in motion.
• Rolling a skateboard: A skateboard keeps moving until friction and other forces slow it down.

Worked Example 1: A Book on a Desk

Question: A book is resting on a desk. Is Newton's First Law happening here?

Step 1: Look at the motion. The book is at rest.

Step 2: Think about forces. Gravity pulls the book downward. The desk pushes upward.

Step 3: Compare the forces. These forces are balanced, so the net force is \(0\text{ N}\).

Answer: Yes. Newton's First Law says the book will stay at rest because there is no net external force changing its motion.

Worked Example 2: A Soccer Ball Is Kicked

Question: A soccer ball is sitting still on the field. A player kicks it, and it starts moving. What caused the change?

Step 1: Start with the ball's original motion. The ball was at rest.

Step 2: Identify the force. The player's foot pushes on the ball.

Step 3: Decide if the force is balanced or unbalanced. The kick is an unbalanced force.

Answer: The unbalanced force from the kick changed the ball's motion, so it started moving.

Worked Example 3: Why Does a Rolling Ball Stop?

Question: A ball rolls across the floor and then stops. Does this break Newton's First Law?

Step 1: Think about what the law says. If no net external force acts, the ball should keep moving at the same speed and direction.

Step 2: Look for outside forces. Friction from the floor and air resistance act against the ball's motion.

Step 3: Decide what happens. These forces are unbalanced and slow the ball down.

Answer: No, the law is not broken. The ball stops because friction and air resistance act on it.

Worked Example 4: Finding Net Force

Question: A box is pushed with \(15\text{ N}\) to the right. Friction pushes with \(6\text{ N}\) to the left. What is the net force, and what happens to the box?

Step 1: Choose a direction to be positive. Let right be positive.

Step 2: Add the forces.

$$15 + (-6) = 9\text{ N}$$

Step 3: Interpret the result. The net force is \(9\text{ N}\) to the right.

Answer: The forces are unbalanced, so the box's motion changes. It will move or speed up to the right.

Important Ideas to Remember

• Objects do not change motion on their own.
• If the net force is zero, motion stays the same.
• If the net force is not zero, motion changes.
• Inertia is resistance to a change in motion.
• More mass means more inertia.
• Friction often causes moving objects to slow down in everyday life.

Common Mistakes

• Mistake: "If an object is moving, there must be a force pushing it forward."
  Correction: A moving object can keep moving without a forward push if no unbalanced force acts on it.
• Mistake: "If an object is not moving, there are no forces on it."
  Correction: It may have balanced forces acting on it, like gravity and support from a table.
• Mistake: "Heavier objects fall faster because they have more inertia."
  Correction: Inertia means resisting changes in motion. It does not mean an object must fall faster.

Brief Summary

Newton's First Law explains that objects keep their current motion unless a net external force changes it.

An object at rest stays at rest, and an object in motion stays in motion with the same speed and direction if forces are balanced.

Inertia is the tendency to resist change in motion, and objects with more mass have more inertia.

Understanding this law helps explain many everyday events, from seat belts to rolling balls to pushing heavy objects.

Newton’s Second Law explains how force, mass, and acceleration are connected. It is one of the main ideas scientists use to describe why objects speed up, slow down, or change direction.

You may have noticed that an empty shopping cart is easy to push, but a full cart is harder to get moving. You may also have noticed that pushing harder makes the cart speed up more quickly. Newton’s Second Law helps explain both of these observations.

The law is often written as:

$$F = ma$$

This formula means that the net force on an object equals its mass times its acceleration.

• 2.force: a push or a pull
• Mass (2m2): the amount of matter in an object
• Acceleration (2a2): how quickly an object’s speed or direction changes

In simple words, Newton’s Second Law says:

• If you push harder, the object gets a greater acceleration.
• If the object has more mass, it gets a smaller acceleration from the same force.

This means acceleration is directly proportional to force and inversely proportional to mass.

We can also rewrite the formula to solve for acceleration:

$$a = \frac{F}{m}$$

This version makes the relationships easier to see. If force increases, acceleration increases. If mass increases, acceleration decreases.

What does “net force” mean?

Net force is the total force after combining all the pushes and pulls acting on an object. If forces act in the same direction, you add them. If they act in opposite directions, you subtract them.

Newton’s Second Law uses net force, not just one single force by itself. This is important because an object’s motion depends on the overall effect of all forces together.

Units in Newton’s Second Law

• Force is measured in newtons (N).
• Mass is measured in kilograms (kg).
• Acceleration is measured in meters per second squared or 2m/s^22.

So if force is in newtons and mass is in kilograms, acceleration will be in 2m/s^22.

How to think about the law

Imagine kicking two balls with the same force: a soccer ball and a bowling ball. The soccer ball speeds up a lot more because it has less mass. The bowling ball has much more mass, so the same force causes much less acceleration.

Now imagine using a stronger kick on the soccer ball. Because the force is bigger, the ball accelerates more. This matches Newton’s Second Law perfectly.

Main ideas to remember

1. An object accelerates when there is a net force acting on it.
2. More force causes more acceleration.
3. More mass causes less acceleration, if the force stays the same.
4. The equation for this law is $$F = ma$$.

Worked Example 1: Finding force

A toy car has a mass of 22 kg2 and accelerates at 23 m/s^22. What force is acting on it?

Step 1: Write the formula.

$$F = ma$$

Step 2: Put in the numbers.

$$F = 2 \times 3$$

Step 3: Multiply.

$$F = 6\text{ N}$$

Answer: The force acting on the toy car is 6 N.

Worked Example 2: Finding acceleration

A box has a mass of 24 kg2. A force of 220 N2 pushes it forward. What is its acceleration?

Step 1: Use the formula for acceleration.

$$a = \frac{F}{m}$$

Step 2: Substitute the values.

$$a = \frac{20}{4}$$

Step 3: Divide.

$$a = 5\text{ m/s}^2$$

Answer: The box accelerates at 5 m/s^2.

Worked Example 3: Comparing mass

Two wagons are pushed with the same force of 212 N2. Wagon A has a mass of 23 kg2. Wagon B has a mass of 26 kg2. Which wagon has greater acceleration?

For Wagon A:

$$a = \frac{F}{m} = \frac{12}{3} = 4\text{ m/s}^2$$

For Wagon B:

$$a = \frac{F}{m} = \frac{12}{6} = 2\text{ m/s}^2$$

Answer: Wagon A has the greater acceleration because it has less mass.

This example shows the inverse relationship between mass and acceleration. When mass doubles from 3 kg to 6 kg, the acceleration is cut in half from 4 m/s^2 to 2 m/s^2, if the force stays the same.

Worked Example 4: Using net force

A sled is pulled to the right with 215 N2. Friction pushes to the left with 25 N2. The sled’s mass is 22 kg2. What is the sled’s acceleration?

Step 1: Find the net force.

The forces act in opposite directions, so subtract:

$$F_{\text{net}} = 15 - 5 = 10\text{ N}$$

Step 2: Use Newton’s Second Law.

$$a = \frac{F_{\text{net}}}{m}$$

Step 3: Substitute the numbers.

$$a = \frac{10}{2} = 5\text{ m/s}^2$$

Answer: The sled’s acceleration is 5 m/s^2 to the right.

This example is important because it shows that we must use the net force, not just the biggest force.

Common mistakes to avoid

• Forgetting to use net force: Always combine all forces first.
• Mixing up mass and weight: In this formula, use mass, usually in kilograms.
• Using the wrong formula form: If you need acceleration, use 2a = F/m2. If you need force, use 2F = ma2.
• Ignoring units: Include N, kg, and 2m/s^22 in your answer.

Real-life connections

• A lighter bicycle speeds up faster than a heavier one when pushed with the same force.
• A stronger engine can make a car accelerate more.
• A football moves faster when kicked harder.
• It takes more force to move a heavy couch than a small chair.

Quick check for understanding

Ask yourself these questions:

• If force increases and mass stays the same, what happens to acceleration?
• If mass increases and force stays the same, what happens to acceleration?
• Why do we use net force instead of just one force?

The answers should be:

• Acceleration increases.
• Acceleration decreases.
• Because all forces together determine how the object moves.

Brief Summary

Newton’s Second Law tells us that force, mass, and acceleration are connected by the equation $$F = ma$$. A larger force causes more acceleration, while a larger mass causes less acceleration if the force stays the same. To solve problems correctly, always pay attention to the net force and use the correct units.

Predictive Kinematics means guessing what will happen next when something moves.

That is a very big name, but the idea is simple. We watch how an object moves, and then we make a smart prediction about where it will go and where it will stop.

For 1st Grade, we can think about this with toy cars, balls, and blocks. If we give a push, the object moves. If the push is big, it may go farther. If the floor is rough, it may stop sooner.

We can ask questions like these:

• What will happen if I push softly?
• What will happen if I push hard?
• Will the object go far or not far?
• Where do I think it will stop?

When we make these kinds of smart guesses before we test, we are learning about motion.

Main Idea 1: A push or a pull can make things move.

Objects do not usually start moving by themselves. A push or a pull can start the motion.

If you push a toy car, it rolls. If you pull a wagon, it moves. The stronger the push or pull, the more the object may move.

We can think of a small push like this: \(1\) small push.

We can think of a bigger push like this: \(2\) pushes or a stronger push.

That is not a real measuring tool. It is just a simple way to compare smaller and bigger pushes.

Main Idea 2: Some surfaces make things slow down.

Not every floor feels the same. A smooth floor helps a toy car roll more easily. A rug or carpet can make it slow down faster.

This happens because some surfaces rub more against the object. For 1st Grade, we can just say: rough places slow things down more.

So if we want to predict where something will stop, we should look at the ground too.

• Smooth floor: may let it go farther
• Rough rug: may make it stop sooner

Main Idea 3: Heavier and lighter things may move differently.

Some things are light, like a ping-pong ball. Some things are heavier, like a big book or a heavy toy truck.

If you use the same push, a lighter object may move more easily. A heavier object may need a bigger push to go as far.

You do not need to memorize hard words. Just remember this: light things and heavy things may not move the same way.

Main Idea 4: We can predict before we test.

To make a prediction, we look at what we know:

1. What object is moving?
2. How big is the push?
3. Is the surface smooth or rough?
4. Where do I think it will stop?

Then we say our idea before we try it.

For example: “I think the toy car will stop by the chair because I pushed it hard on the smooth floor.”

How to Make a Good Prediction

You can use this easy plan:

1. Look at the object.
2. Think about the push.
3. Look at the floor or ground.
4. Guess where it will go.
5. Test and see what happens.

This helps us be careful thinkers.

Worked Example 1: Soft push, smooth floor

Sam puts a toy car on a smooth floor. Sam gives it a soft push.

Question: Will the car go a short way or a long way?

Think: The push is soft. Smooth floor helps it roll, but the push is still small.

Prediction: The car will go a short way.

Why? A small push usually makes an object move less far than a big push.

Worked Example 2: Hard push, smooth floor

Ava puts the same toy car on the same smooth floor. Ava gives it a hard push.

Question: Will it go farther than in Example 1?

Think: This time the push is bigger, and the floor is still smooth.

Prediction: Yes, the car will go farther.

Why? A bigger push can make the car move farther before it stops.

We can compare the two pushes like this:

Soft push: \(1\)

Hard push: \(2\)

Since \(2 > 1\), the harder push is bigger.

Worked Example 3: Same push, different floors

Leo rolls a ball with the same gentle push two times.

• First on a smooth floor
• Then on a rug

Question: Where will the ball go farther?

Think: The push is the same both times. Only the floor changes.

Prediction: The ball will go farther on the smooth floor.

Why? The rug slows the ball down sooner.

Worked Example 4: Light object and heavier object

Mia pushes two things with the same push:

• a light ball
• a heavier toy truck

Question: Will they always move the same?

Think: The objects are different. One is lighter, and one is heavier.

Prediction: They may not move the same.

Why? Different objects can move differently, even with the same push.

Let’s Practice Thinking

Here are some simple prediction ideas:

• If you push harder, the object may go farther.
• If the ground is rough, the object may stop sooner.
• If the object is different, it may move differently.

Words to Remember

• Move — to go from one place to another
• Push — to press something away
• Pull — to bring something closer
• Predict — to make a smart guess about what will happen
• Stop — to not move anymore

Try It in Real Life

You can practice with a toy car or ball.

1. Put it on the floor.
2. Guess where it will stop.
3. Give it a soft push.
4. Watch what happens.
5. Try again with a harder push.

You can also try a smooth floor and then a rug. Ask: “What changed?”

Important Thing to Remember

We do not have to be right every time. Scientists learn by predicting and then testing.

If your guess is different from what happened, that is okay. You can learn from it and make a better guess next time.

Summary

Objects move when they get a push or a pull. Bigger pushes can make objects go farther. Rough surfaces can make objects stop sooner, and different objects may move in different ways.

When we look at the object, the push, and the floor, we can make a smart prediction about where something will go and where it will stop.

Newton's Third Law helps explain what happens when two objects interact. It is often called the action-reaction law.

The law says: For every action force, there is an equal and opposite reaction force.

In simpler words, when one object pushes or pulls on a second object, the second object pushes or pulls back on the first object with the same size force, but in the opposite direction.

This idea is important because forces are not lonely. They always come in pairs.

Newton's Third Law statement:

$$\text{Force of A on B} = -\text{Force of B on A}$$

The negative sign means the forces point in opposite directions.

Introduction: What does “action-reaction” mean?

Imagine you press your hand against a wall. Your hand pushes on the wall. At the same time, the wall pushes back on your hand.

You may not see the wall move, but you can feel the push back. That push back is the reaction force.

This does not mean one force happens first and the other happens later. The two forces happen at the same time.

Also, the words “action” and “reaction” can be confusing. They do not mean “first” and “second.” They are just names for the two forces in the pair.

Main Teaching Point 1: Forces always come in pairs

Any time two objects interact, each object exerts a force on the other.

• If you push a shopping cart, the cart pushes back on you.
• If your foot pushes on the ground, the ground pushes back on your foot.
• If a book rests on a table, the book pushes down on the table, and the table pushes up on the book.

These are all examples of force pairs.

Each pair has two important features:

• Equal magnitude: the forces are the same size.
• Opposite direction: the forces point in opposite ways.

We can write this as:

$$F_{A\ on\ B} = F_{B\ on\ A}$$

for size, and

$$\text{directions are opposite}$$

Together, this means:

$$F_{A\ on\ B} = -F_{B\ on\ A}$$

Main Teaching Point 2: The two forces act on different objects

This is the most important part students often miss.

The action force and reaction force do not act on the same object. They act on different objects.

For example, if you kick a soccer ball:

• Your foot pushes on the ball.
• The ball pushes back on your foot.

These two forces are equal and opposite, but they act on different things: one acts on the ball, and one acts on the foot.

Because they act on different objects, they do not cancel each other out.

Forces cancel only when they act on the same object and are in opposite directions.

Main Teaching Point 3: Why objects can still move

A common question is: if the forces are equal, why does anything move?

The answer is that the equal and opposite forces are on different objects.

Suppose you push a skateboard. You push the skateboard forward, and the skateboard pushes you backward. If the skateboard can roll easily, it moves forward. You may not move much because your shoes grip the ground.

The two forces are equal, but they affect different objects, so motion can still happen.

Another example is walking. When you walk, your foot pushes backward on the ground. Then the ground pushes forward on your foot. That forward push helps move you ahead.

So, in many situations, Newton's Third Law helps explain how movement begins.

Main Teaching Point 4: Common examples of Newton's Third Law

1. Walking

   Your foot pushes backward on the ground. The ground pushes forward on you.

2. Swimming

   A swimmer pushes water backward. The water pushes the swimmer forward.

3. Rocket launch

   The rocket pushes gas downward. The gas pushes the rocket upward.

4. Sitting in a chair

   Your body pushes down on the chair. The chair pushes up on your body.

5. Jumping

   You push down on the ground. The ground pushes up on you, helping you rise.

Main Teaching Point 5: Avoiding a common mistake

Students sometimes say that gravity pulling an object down and the ground pushing it up are an action-reaction pair. That is not correct.

Why not? Because both of those forces act on the same object.

For example, for a book resting on a table:

• Earth pulls the book downward because of gravity.
• The table pushes the book upward.

These two forces may balance, but they are not a Third Law pair.

The actual Third Law pairs are:

• Earth on book and book on Earth
• table on book and book on table

This is an important difference:

• Balanced forces can act on the same object.
• Third Law pairs act on different objects.

Worked Example 1: Pushing on a wall

Situation: A student pushes on a wall with a force of \(20\text{ N}\).

Question: What force does the wall exert on the student?

Step 1: Identify the interaction.

The student pushes on the wall. The wall pushes back on the student.

Step 2: Use Newton's Third Law.

The force pair must be equal in size and opposite in direction.

Answer: The wall exerts a force of \(20\text{ N}\) on the student in the opposite direction.

Conclusion: If the student pushes right on the wall, the wall pushes left on the student with \(20\text{ N}\).

Worked Example 2: Kicking a ball

Situation: A soccer player kicks a ball with a force of \(35\text{ N}\).

Question: What is the reaction force?

Step 1: Find the two objects.

The two objects are the foot and the ball.

Step 2: Name both forces.

• Force of foot on ball = \(35\text{ N}\)
• Force of ball on foot = ?

Step 3: Apply Newton's Third Law.

The ball pushes back on the foot with the same force in the opposite direction.

Answer: The ball pushes on the foot with \(35\text{ N}\) in the opposite direction.

Important note: The ball may fly away, but the foot may only move a little. Equal forces do not always cause equal motion because the forces act on different objects.

Worked Example 3: Walking forward

Situation: A student is walking across the classroom.

Question: What action-reaction pair helps the student move?

Step 1: Think about the foot and the ground.

When the student steps, the foot pushes backward on the ground.

Step 2: Identify the reaction force.

The ground pushes forward on the foot.

Answer: The action-reaction pair is:

• foot pushes backward on ground
• ground pushes forward on foot

Why it matters: The forward push from the ground helps move the student forward.

Worked Example 4: Book on a table

Situation: A book is resting on a table.

Question: What is one Newton's Third Law pair in this situation?

Step 1: Look for two interacting objects.

The book and the table are interacting.

Step 2: Name the two forces.

• The book pushes down on the table.
• The table pushes up on the book.

Answer: The force of the book on the table and the force of the table on the book are a Third Law pair.

Extra reminder: The table pushing up on the book and Earth pulling down on the book are not a Third Law pair, because both act on the book.

How to identify a Third Law pair

Use these steps whenever you are unsure:

1. Find the two objects interacting.
2. Ask: How does object A push or pull on object B?
3. Then ask: How does object B push or pull on object A?
4. Check: Are the forces equal in size and opposite in direction?
5. Check: Do they act on different objects?

If the answer to both checks is yes, you have found a Newton's Third Law pair.

Key ideas to remember

• All forces come in pairs.
• The two forces are equal in size.
• The two forces are opposite in direction.
• The forces act on different objects.
• Because they act on different objects, they do not cancel each other out.

Brief Summary

Newton's Third Law says that whenever two objects interact, they exert forces on each other that are equal in size and opposite in direction.

These action-reaction forces always act on different objects. That is why objects can still move even though the forces are equal.

You can see this law in everyday life when you walk, jump, swim, kick a ball, or push on a wall.

Free Body Diagrams help us show all the forces acting on one object. A force is a push or a pull. Even though forces are invisible, we can draw them as arrows so we can understand how an object moves.

When scientists draw a free body diagram, they focus on just one object. Then they draw arrows to show every force acting on that object. These arrows help us figure out the net force, which is the overall force after all the pushes and pulls are combined.

This lesson will teach you what a free body diagram is, how to draw one, how to read one, and how to use it to decide whether an object will stay still, move at a steady speed, or change its motion.

What is a free body diagram?

A free body diagram is a simple picture of one object with arrows showing the forces acting on it. The object is usually drawn as a box or a dot. The arrows point in the direction of each force.

The length of each arrow matters. A longer arrow shows a stronger force. A shorter arrow shows a weaker force. This is why we say the forces are shown with scaled vectors. A vector is a quantity that has both size and direction.

Why do we use free body diagrams?

• They help us organize our thinking.

• They show which forces are balanced and which are unbalanced.

• They help us find the net force.

• They help explain why an object speeds up, slows down, stops, or changes direction.

Common forces you may see

In 7th Grade science, you will often work with a few common forces:

• Gravity: the force that pulls objects downward toward Earth.

• Normal force: the support force from a surface pushing up on an object.

• Friction: a force that opposes motion when surfaces rub against each other.

• Applied force: a push or pull from a person or another object.

• Tension: a pulling force from a rope, string, or cable.

• Air resistance: a force from the air that opposes motion.

How to draw a free body diagram

1. Choose one object. Only focus on that object, not the whole situation.

2. Draw the object as a box or dot.

3. Identify every force acting on it. Ask: What is pushing or pulling on this object?

4. Draw arrows starting from the object.

5. Label each arrow with the type of force.

6. Make arrow lengths match force sizes. Bigger force, longer arrow.

Important rule: Only draw forces acting on the object. Do not draw forces the object is causing on something else.

Balanced and unbalanced forces

If the forces on an object cancel out, the forces are balanced. Then the net force is zero.

When the net force is zero, we can write:

$$F_{net} = 0$$

If the net force is zero, the object will either:

• stay at rest, or

• keep moving at the same speed in the same direction.

If the forces do not cancel out, the forces are unbalanced. Then the object’s motion changes. It may speed up, slow down, or change direction.

Finding net force

To find net force, combine the forces in the same line of motion. Forces in opposite directions subtract.

For example, if a box is pushed right with 10 N and friction pushes left with 4 N, then:

$$F_{net} = 10\text{ N} - 4\text{ N} = 6\text{ N to the right}$$

The object will change its motion to the right because the net force points right.

Directions matter

Forces are not just numbers. Direction is very important. A 5 N force to the right is different from a 5 N force to the left.

That is why arrows are used in free body diagrams. The arrows show direction clearly.

Vertical and horizontal forces

Many free body diagrams have both vertical and horizontal forces.

For example, if a book rests on a table:

• gravity pulls the book downward,

• the table pushes upward with the normal force.

If the book is not moving up or down, those vertical forces are balanced.

If someone also pushes the book sideways, then there may be horizontal forces too, such as an applied force and friction.

Worked Example 1: A book resting on a table

A book sits still on a table. What forces act on it?

Step 1: Focus on the book only.

Step 2: Identify the forces.

• Gravity pulls downward.

• The table pushes upward with the normal force.

Step 3: Draw the free body diagram.

• One arrow down labeled gravity.

• One arrow up labeled normal force.

If the book is resting and not moving up or down, the arrows should be the same length. That means the forces are balanced.

So:

$$F_{net} = 0$$

Conclusion: The book stays still because the forces are balanced.

Worked Example 2: A box pushed across the floor

A student pushes a box to the right with 12 N of force. Friction pushes to the left with 5 N.

Step 1: Focus on the box.

Step 2: Identify horizontal forces.

• Applied force: 12 N to the right

• Friction: 5 N to the left

Step 3: Identify vertical forces.

• Gravity downward

• Normal force upward

If the box is not moving up or down, the vertical forces are balanced. So we focus on the horizontal net force:

$$F_{net} = 12\text{ N} - 5\text{ N} = 7\text{ N}$$

The direction is to the right.

Conclusion: The forces are unbalanced, so the box’s motion changes to the right.

Worked Example 3: Tug-of-war

Two teams pull on a rope. Team A pulls left with 20 N. Team B pulls right with 20 N.

Step 1: Focus on the knot in the middle of the rope, or one point you are studying.

Step 2: Draw one arrow left for 20 N and one arrow right for 20 N.

The arrows should be the same length because the forces are equal.

Now find the net force:

$$F_{net} = 20\text{ N} - 20\text{ N} = 0\text{ N}$$

Conclusion: The forces are balanced. There is no overall force to the left or right.

Worked Example 4: Falling object with air resistance

A ball is falling straight down. Gravity pulls down with 9 N. Air resistance pushes up with 3 N.

Step 1: Focus on the ball.

Step 2: Identify the forces.

• Gravity: 9 N downward

• Air resistance: 3 N upward

Step 3: Find the net force.

$$F_{net} = 9\text{ N} - 3\text{ N} = 6\text{ N downward}$$

Conclusion: The forces are unbalanced, so the ball’s motion changes downward.

Tips for reading free body diagrams

• Count how many forces are acting on the object.

• Check the direction of each arrow.

• Compare arrow lengths to see which forces are stronger.

• Look for opposite forces that may cancel out.

• Find the net force in each direction.

Common mistakes to avoid

• Drawing forces on the wrong object: only show forces acting on the object you chose.

• Forgetting gravity: if an object is near Earth, gravity usually acts downward.

• Forgetting the normal force: if an object rests on a surface, the surface usually pushes up.

• Making equal forces different arrow lengths: equal forces should have equal arrow lengths.

• Mixing up motion and force: an object can move and still have balanced forces if it is moving at a steady speed in a straight line.

How free body diagrams connect to motion

Free body diagrams help explain motion, but they do not show the path the object takes. They only show the forces acting at that moment.

An object can be:

• not moving with balanced forces,

• moving at constant speed with balanced forces, or

• changing motion with unbalanced forces.

This is why net force is so important. The net force tells us whether motion will stay the same or change.

Quick check questions

1. A cup sits on a desk. Which two main forces act on it?

2. A sled is pulled right with 8 N and friction acts left with 8 N. What is the net force?

3. If a force diagram has a longer arrow to the left than to the right, which direction is the net force?

4. Why should equal forces be drawn with equal arrow lengths?

Answers

1. Gravity downward and normal force upward.

2. 0 N, so the forces are balanced.

3. To the left.

4. Because arrow length shows the size of the force.

Summary

A free body diagram is a drawing that shows all the forces acting on one object. Each force is shown with an arrow that points in the direction of the force, and the arrow length shows the force’s size.

When forces are balanced, the net force is zero. When forces are unbalanced, the object’s motion changes. By learning to draw and read free body diagrams, you can better understand how pushes and pulls control motion.

Lesson: Static and Kinetic Friction

Have you ever tried to push a heavy box and noticed that it is hardest to get it moving at first? But once it starts sliding, it becomes a little easier to keep it going. That happens because of friction.

Friction is a force that happens when two surfaces touch and try to move past each other. It acts in the opposite direction of motion, or in the opposite direction of the attempted motion.

There are two main kinds of friction in this lesson: static friction and kinetic friction. Understanding the difference between them helps explain why starting motion and keeping motion going are not the same.

What is static friction?

Static friction is the friction that acts on an object that is not moving yet. It keeps the object from starting to move.

Imagine pushing a chair very gently. If the chair does not move, static friction is pushing back against your push. It matches your force up to a certain limit.

This means static friction can change in size. If you push a little, static friction is little. If you push harder, static friction gets bigger too. But it can only grow to a maximum value. Once your push becomes greater than that maximum, the object starts moving.

We can show the largest possible static friction with this formula:

and sometimes

You do not need to memorize every symbol yet, but here is what they mean:

• \(f_s\) = static friction
• \(f_{s,\max}\) = maximum static friction
• \(\mu_s\) = a number that depends on the surfaces
• \(N\) = the support force pushing the surfaces together

What is kinetic friction?

Kinetic friction is the friction that acts when an object is already moving and sliding across a surface.

Once the chair begins to slide, static friction is no longer the main type. Kinetic friction takes over. Kinetic friction usually has a nearly constant size and is often smaller than maximum static friction.

That is why it is often harder to start an object moving than to keep it moving.

The formula for kinetic friction is:

• \(f_k\) = kinetic friction
• \(\mu_k\) = a number that depends on the surfaces
• \(N\) = the support force

Why does friction happen?

Even surfaces that look smooth have tiny bumps and rough spots. When two surfaces touch, these tiny rough places catch on each other. That creates resistance to motion.

Friction is not always bad. In fact, we depend on it every day.

• Friction helps your shoes grip the floor when you walk.
• Friction helps car tires grip the road.
• Friction helps you hold a pencil.

But friction can also cause problems.

• It can make it harder to move objects.
• It can wear out surfaces over time.
• It can produce heat.

Static vs. kinetic friction

Here is the key difference:

• Static friction acts before motion starts.
• Kinetic friction acts after motion has started.

Another important difference is how they behave.

• Static friction changes to match your push, up to a maximum.
• Kinetic friction is usually more constant while the object slides.

How friction affects motion

If the force you apply is equal to the friction force, the object will not speed up.

If your force is smaller than static friction, the object stays still.

If your force becomes greater than the maximum static friction, the object begins to move.

Once the object is moving, if your push is equal to kinetic friction, it keeps moving at a steady speed. If your push is greater than kinetic friction, it speeds up. If your push is less than kinetic friction, it slows down.

Worked Example 1: A small push on a box

A student pushes a box with a force of 10 N. The box does not move. What kind of friction is acting?

Step 1: Notice that the box is not moving.

Step 2: If it is not moving, the friction must be static friction.

Step 3: Static friction matches the push, so the friction force is 10 N in the opposite direction.

Answer: The box experiences static friction, and its friction force is 10 N.

Worked Example 2: Starting motion

A crate needs 35 N of force to start moving. A student pushes with 30 N. Will the crate move?

Step 1: Compare the push to the force needed to overcome static friction.

Step 2: The student pushes with 30 N, but 35 N is needed.

Since

the push is not large enough to overcome the maximum static friction.

Answer: No, the crate will not move. Static friction keeps it at rest.

Worked Example 3: Keeping an object moving

A sled is already sliding across snow. The kinetic friction acting on it is 12 N. If a student pulls with 12 N, what happens?

Step 1: The sled is already moving, so this is kinetic friction.

Step 2: Compare the pull and the friction.

The pull is 12 N and the kinetic friction is also 12 N.

If the forward force and backward friction are equal, the forces balance.

Answer: The sled keeps moving at a steady speed.

Worked Example 4: Using the kinetic friction formula

A box slides across the floor. The coefficient of kinetic friction is \(\mu_k = 0.20\), and the support force is \(N = 50\text{ N}\). Find the kinetic friction.

Step 1: Use the formula

Step 2: Substitute the values.

Step 3: Multiply.

Answer: The kinetic friction is 10 N.

Real-life examples

• Pushing furniture: It takes a big push to get it started because of static friction. After it starts sliding, kinetic friction acts, and it may feel easier.
• Walking: Your foot pushes backward on the ground, and static friction helps push you forward without slipping.
• Sliding a book: A book on a desk resists movement at first because of static friction. Once it slides, kinetic friction slows it down.

How can friction be changed?

Friction can become larger or smaller depending on the surfaces and how hard they press together.

• Rough surfaces usually have more friction.
• Smooth surfaces usually have less friction.
• Heavier objects often have more friction because they press down more.

People also reduce friction by using oils, grease, or wheels. These help surfaces move more easily.

Common mistakes to avoid

• Do not assume friction always has the same value. Static friction can change up to a maximum.
• Do not mix up static and kinetic friction. Ask: Is the object moving or not?
• Do not think friction only slows things down. Sometimes friction helps motion, like when you walk or ride a bike.

Quick check for understanding

1. If an object is not moving while you push on it, what kind of friction acts on it?
2. Which is usually greater: maximum static friction or kinetic friction?
3. If you push harder than maximum static friction, what happens?
4. If a moving object has 8 N of kinetic friction and you pull with 8 N, how will it move?

Brief summary

Friction is a force that opposes motion between touching surfaces. Static friction keeps an object from starting to move, and it can change up to a maximum value. Kinetic friction acts on an object that is already sliding and is usually smaller than maximum static friction. This is why starting motion is often harder than keeping motion going.

Fluid Drag and Terminal Velocity

When an object moves through a fluid, the fluid pushes back on it. This push is called fluid drag. A fluid can be a liquid like water or a gas like air.

For example, when you ride a bike fast, you feel air pushing against you. When you swim, the water pushes against your body. That pushing force is drag.

Another important force is gravity. Gravity pulls objects downward toward Earth. When something falls, gravity pulls it down, but air drag pushes up against the motion.

This lesson explains how drag changes with speed and how an object can reach terminal velocity, which is the steady speed where it stops speeding up.

1. What is fluid drag?

Fluid drag is a force that acts in the opposite direction of an object’s motion through a fluid.

• If a ball falls downward through air, drag acts upward.
• If a car moves forward, air drag acts backward.
• If a swimmer moves forward, water drag acts backward.

Drag depends on how the object moves through the fluid. In 7th grade, the most important idea is this:

The faster an object moves through a fluid, the greater the drag force becomes.

So if an object is moving slowly, drag is small. If it is moving very fast, drag is much larger.

2. Forces on a falling object

Imagine dropping a skydiver from a plane. Two main forces act on the skydiver:

• Gravity pulls downward.
• Air drag pushes upward.

At the very start of the fall, the skydiver is not moving yet, so air drag is very small. Gravity is stronger, so the skydiver speeds up downward.

As the skydiver falls faster, the air drag gets bigger. Now gravity is still pulling down, but drag is pushing up more and more.

Eventually, the upward drag becomes equal to the downward force of gravity. At that moment, the forces are balanced.

Balanced forces mean the net force is zero:

When gravity and drag are equal,

so

When net force is zero, acceleration is zero. That means the object is no longer speeding up or slowing down. It keeps moving at a constant speed.

That constant falling speed is called terminal velocity.

3. What is terminal velocity?

Terminal velocity is the steady speed reached by a falling object when air drag becomes equal to gravity.

At terminal velocity:

• The object is still moving.
• The object is still falling downward.
• The forces are balanced.
• The acceleration is zero.
• The speed stays constant.

This is an important idea: zero acceleration does not mean zero motion. An object at terminal velocity is still moving, but its speed is no longer changing.

4. How speed changes while falling

A falling object usually goes through these stages:

1. Start: Gravity is much bigger than drag, so the object speeds up.
2. Middle: As speed increases, drag increases too, so the speeding up becomes less and less.
3. Terminal velocity: Drag equals gravity, so the object stops speeding up and falls at a constant speed.

You can think of it like a tug-of-war between gravity and drag. At first gravity is winning. Later the forces become equal. Then neither side wins, so the speed stays the same.

5. What affects fluid drag?

Several things can change how much drag an object experiences:

• Speed: Faster motion usually means more drag.
• Shape: Wide or flat shapes often have more drag than smooth, narrow shapes.
• Surface area: More area facing the fluid usually means more drag.
• Type of fluid: Water usually causes more drag than air because it is thicker and harder to move through.

For example, a parachute creates a lot of air drag because it has a very large surface area. That large drag helps slow the skydiver.

6. Terminal velocity can be different for different objects

Not all objects have the same terminal velocity. Some fall faster than others before drag balances gravity.

An object may have a higher terminal velocity if it:

• has less drag,
• has a smaller area facing the air, or
• is shaped to move through air more easily.

An object may have a lower terminal velocity if it:

• has more drag,
• has a larger area facing the air, or
• uses something like a parachute.

This is why a crumpled paper ball falls faster than a flat sheet of paper. The flat sheet has more air drag.

7. A simple force idea with numbers

We can compare forces using simple subtraction:

For a falling object:

If the net force is positive downward, the object speeds up downward.

If the net force is zero, the object moves at constant speed.

We will not use difficult formulas for drag here. The main rule is enough:

As speed increases, drag increases.

Worked Example 1: Beginning of a fall

A dropped object has a downward gravity force of 10 N and an upward drag force of 2 N.

Step 1: Find the net force.

Step 2: Decide what happens.

Because the net force is downward, the object accelerates downward. It speeds up as it falls.

Worked Example 2: Later in the fall

Now the same object is moving faster. Gravity is still 10 N downward, but drag has increased to 7 N upward.

Step 1: Find the net force.

Step 2: Explain the motion.

The object is still speeding up downward because gravity is still stronger than drag. But it speeds up less than before, because the net force is smaller now.

Worked Example 3: Terminal velocity

A falling object has 10 N of gravity downward and 10 N of drag upward.

Step 1: Find the net force.

Step 2: Decide what happens.

With zero net force, the acceleration is zero. The object keeps falling, but now it falls at a constant speed. It has reached terminal velocity.

Worked Example 4: Why a parachute works

A skydiver is falling fast. When the parachute opens, the surface area becomes much larger.

What happens to drag?

The drag force becomes much larger because more air pushes against the parachute.

What happens next?

• Right after opening, drag may become greater than gravity.
• The skydiver slows down.
• As the skydiver slows, the drag becomes smaller again.
• Eventually drag equals gravity once more.

Then the skydiver reaches a new terminal velocity that is much slower and safer.

8. Everyday examples

• Skydiving: A skydiver speeds up at first, then reaches terminal velocity. Opening a parachute lowers the terminal velocity.
• Raindrops: Raindrops do not keep speeding up forever. Air drag increases until they reach terminal velocity.
• Paper vs. coin: A flat paper has lots of drag, so it falls slowly. A coin has less drag, so it falls faster.
• Cycling: Riders bend down to reduce air drag and move faster.

9. Common mistakes to avoid

• Mistake: “If acceleration is zero, the object is not moving.”
  Correct idea: The object can still move at constant speed.
• Mistake: “Drag only exists when an object is very fast.”
  Correct idea: Drag can act whenever an object moves through a fluid, though it is smaller at low speed.
• Mistake: “At terminal velocity, gravity stops.”
  Correct idea: Gravity still pulls downward. It is just balanced by drag.
• Mistake: “Heavier always means faster.”
  Correct idea: Shape and drag matter too.

10. Quick check for understanding

Ask yourself these questions:

• What force always pulls a falling object downward? Gravity.
• What force pushes opposite the motion through air or water? Fluid drag.
• What happens to drag as speed increases? It increases.
• What happens when drag equals gravity? Net force is zero, acceleration is zero, and the object moves at terminal velocity.

Brief Summary

Fluid drag is the force that opposes motion through air or water. For a falling object, gravity pulls down while drag pushes up. As the object falls faster, drag increases. When drag becomes equal to gravity, the forces balance, acceleration becomes zero, and the object falls at a constant speed called terminal velocity.

Momentum and Impulse help us describe how objects move and how their motion changes when forces act on them. These ideas are important in sports, car safety, and everyday life.

In this lesson, you will learn what momentum is, what impulse is, how to calculate both, and how they are connected.

Momentum is the amount of motion an object has. An object with more mass or more speed has more momentum.

The formula for momentum is:

$$p = m \times v$$

In this formula:

• p = momentum
• m = mass
• v = velocity, or speed in a certain direction

Momentum depends on two things:

• How much matter is in the object (its mass)
• How fast the object is moving

If either mass or speed increases, momentum increases. A heavy, fast-moving object has a lot of momentum. A light, slow-moving object has little momentum.

For example, a bowling ball rolling down a lane has more momentum than a tennis ball rolling at the same speed because the bowling ball has more mass.

Also, a bicycle moving quickly has more momentum than the same bicycle moving slowly because its speed is greater.

Direction matters too. Since velocity includes direction, momentum also has direction. If two objects move at the same speed but in opposite directions, their momentum is not the same because their directions are different.

Impulse is what changes an object's momentum. Impulse happens when a force acts on an object for a period of time.

The formula for impulse is:

$$J = F \times t$$

In this formula:

• J = impulse
• F = force
• t = time the force acts

This means a small force acting for a long time can have the same impulse as a large force acting for a short time.

Impulse and momentum are connected by this idea:

$$F \times t = \text{change in momentum}$$

This means impulse equals the change in momentum. If you change an object's speed, stop it, start it moving, or change its direction, you are changing its momentum.

You can also write this as:

$$J = \Delta p$$

The symbol \(\Delta\) means change in. So \(\Delta p\) means change in momentum.

This connection explains many real-life situations.

• When a soccer player kicks a ball, the foot applies a force for a short time, giving the ball impulse and changing its momentum.
• When a baseball player catches a ball and moves the glove backward, the catching time increases. This reduces the force on the hand.
• Seat belts and airbags increase the time over which a person stops in a crash, which lowers the force on the body.

Why does increasing time reduce force? If the change in momentum stays the same, then making the stopping time longer means the force can be smaller.

That is why soft landing mats, helmets, and airbags help protect people. They increase the time of impact and reduce the force.

Comparing momentum and impulse:

• Momentum tells how much motion an object has right now.
• Impulse tells how a force changes that motion over time.

Let us look at some worked examples.

Worked Example 1: Finding momentum

A cart has a mass of \(4\) kg and moves at \(3\) m/s. What is its momentum?

Use the formula:

$$p = m \times v$$

Substitute the values:

$$p = 4 \times 3$$

$$p = 12$$

The cart's momentum is 12 kg·m/s.

Worked Example 2: Comparing two objects

Object A has a mass of \(2\) kg and moves at \(5\) m/s. Object B has a mass of \(5\) kg and moves at \(2\) m/s. Which has more momentum?

Find the momentum of each object.

For Object A:

$$p = 2 \times 5 = 10$$

For Object B:

$$p = 5 \times 2 = 10$$

Both objects have the same momentum: \(10\) kg·m/s.

This shows that different combinations of mass and speed can give the same momentum.

Worked Example 3: Finding impulse

A force of \(6\) N acts on a ball for \(2\) seconds. What is the impulse?

Use the formula:

$$J = F \times t$$

Substitute the values:

$$J = 6 \times 2$$

$$J = 12$$

The impulse is 12 N·s.

Worked Example 4: Impulse changes momentum

A toy car starts at rest, so its starting momentum is \(0\). A force gives it an impulse of \(8\) N·s. What is the car's change in momentum?

Use the relationship:

$$J = \Delta p$$

So:

$$\Delta p = 8$$

The toy car's momentum changes by 8 kg·m/s.

Since it started at \(0\), its final momentum is 8 kg·m/s.

Important ideas to remember

• More mass means more momentum, if speed stays the same.
• More speed means more momentum, if mass stays the same.
• A force acting for a longer time creates more impulse.
• Impulse causes a change in momentum.
• Increasing the time of impact can reduce the force.

Everyday examples of momentum and impulse

• A truck is harder to stop than a skateboard because the truck usually has much more momentum.
• A karate instructor pulls a hand back after striking to change momentum over time.
• A gymnast bends knees when landing to increase stopping time and reduce force.
• A catcher in baseball moves the glove backward to make the stop gentler.

Common mistakes to avoid

• Do not confuse mass with speed. Momentum needs both.
• Do not forget that direction matters for momentum.
• Do not think only big forces matter. A smaller force over more time can also create a large impulse.
• Do not forget that impulse changes momentum; it does not just describe force alone.

Quick check questions

1. If two objects move at the same speed, which has more momentum: the one with greater mass or the one with smaller mass?
2. If the same force acts for twice as long, what happens to the impulse?
3. Why do airbags help reduce injury during a crash?
4. If an object stops moving, what happens to its momentum?

Answers

1. The one with greater mass has more momentum.
2. The impulse doubles.
3. Airbags increase the stopping time, which reduces the force on the person.
4. Its momentum becomes zero.

Summary

Momentum is the amount of motion an object has, and it depends on mass and velocity. Impulse is the effect of a force acting over time, and impulse changes momentum. These ideas help explain motion, stopping, collisions, and safety devices like helmets and airbags.

Simple Machines are basic tools that make work easier. They do not reduce the total amount of work that must be done, but they can change how much force you need to use or the direction of that force.

In 7th Grade science, simple machines are important because they help us understand how forces affect motion. When you lift, push, or pull an object, a simple machine can help you do that job more easily.

The three simple machines we will focus on are levers, pulleys, and inclined planes.

First, what is work? In science, work happens when a force moves an object over a distance.

The basic idea of work can be written as:

$$\text{Work} = \text{Force} \times \text{Distance}$$

or

$$W = F \times d$$

This means that if you use a smaller force, you may need to move the object over a longer distance to do the same amount of work.

Why simple machines help

• They can reduce the amount of force needed.
• They can change the direction of a force.
• They can help us do jobs more safely and more easily.

Now let’s look at each type.

1. Levers

A lever is a rigid bar that turns around a fixed point. The fixed point is called the fulcrum.

When you push down on one part of the lever, another part moves. Levers help us lift or move objects using less force.

The main parts of a lever are:

• Fulcrum: the pivot point
• Effort: the force you apply
• Load: the object being moved

Examples of levers include:

• See-saws
• Crowbars
• Scissors
• Bottle openers

A lever works best when the effort is applied farther from the fulcrum. This gives your force more turning effect.

For example, using a long crowbar is easier than using a short one because the longer bar lets you use less force.

2. Pulleys

A pulley is a grooved wheel with a rope or chain running over it. Pulleys make lifting easier by changing the direction of force or by sharing the load.

With a single fixed pulley, you pull down to lift an object up. This does not always reduce the force a lot, but it can make lifting more convenient.

With more than one pulley, the weight of the load is spread across multiple rope sections. This means less force is needed to lift the object.

Examples of pulleys include:

• Flagpoles
• Window blinds
• Construction cranes
• Some gym equipment

If a pulley system has more supporting rope sections, the effort force usually becomes smaller, but you must pull more rope.

3. Inclined Planes

An inclined plane is a flat surface set at an angle, like a ramp. Instead of lifting an object straight up, you move it up the slope.

An inclined plane reduces the force needed to raise an object, but the object must travel a longer distance.

Examples of inclined planes include:

• Wheelchair ramps
• Slides
• Loading ramps for trucks
• Sloped roads up hills

Imagine pushing a heavy box into a truck. Lifting it straight up takes a lot of force. Pushing it up a ramp takes less force, even though the box travels farther.

Force, distance, and trade-offs

Simple machines are helpful because they create a trade-off. A trade-off means you gain one advantage, but you give up something else.

For simple machines, the trade-off is usually this:

• Less force needed
• But more distance moved

This is why simple machines do not magically remove work. They change how the work is done.

For example, if you use a ramp to push a box into a truck, you use less force than lifting it straight up. But you push the box over a longer path.

Mechanical advantage

Mechanical advantage tells us how much a machine multiplies force. A machine with a greater mechanical advantage makes the job easier by reducing the effort force.

A simple way to think about it is:

$$\text{Mechanical Advantage} = \frac{\text{Output Force}}{\text{Input Force}}$$

or

$$MA = \frac{F_{out}}{F_{in}}$$

If the mechanical advantage is greater than 1, the machine helps you use less input force than the force needed to move the load directly.

For example, if you pull with 50 N and the machine lifts a load with 100 N of force, then:

$$MA = \frac{100}{50} = 2$$

This means the machine doubles your force.

Important note: In real life, friction can make machines less efficient. That means you may need more force than the ideal amount. But the main idea stays the same: simple machines help make tasks easier.

Worked Example 1: Lever on a playground

A student uses a long lever to lift a rock. Without the lever, it takes 120 N of force to lift the rock. With the lever, the student only uses 40 N.

What is the mechanical advantage?

Use the formula:

$$MA = \frac{F_{out}}{F_{in}}$$

Substitute the values:

$$MA = \frac{120}{40} = 3$$

Answer: The mechanical advantage is 3. The lever makes the student’s force 3 times as effective.

Worked Example 2: Pulley changing direction

A bucket is lifted from a well using a single fixed pulley. The person pulls down on the rope, and the bucket goes up.

What is the main benefit of this pulley?

Step 1: Think about what the pulley changes.

The pulley allows a downward pull to lift the bucket upward.

Step 2: State the benefit.

Answer: The main benefit is that the pulley changes the direction of the force. This can make lifting easier and more comfortable.

Worked Example 3: Inclined plane and distance

A box must be raised into a truck. Lifting it straight up requires a large force over a short distance. Using a ramp requires a smaller force over a longer distance.

Why does the ramp make the job easier?

Step 1: Identify the machine.

A ramp is an inclined plane.

Step 2: Explain the trade-off.

The ramp spreads the lifting work over a longer distance.

Answer: The ramp makes the job easier because it reduces the force needed, even though the box must move a greater distance.

Worked Example 4: Finding input force

A pulley system lifts a load with 200 N of output force. The mechanical advantage is 4. How much input force is needed?

Use the formula:

$$MA = \frac{F_{out}}{F_{in}}$$

Substitute the known values:

$$4 = \frac{200}{F_{in}}$$

Solve for input force:

$$F_{in} = \frac{200}{4} = 50$$

Answer: The input force needed is 50 N.

Comparing the three simple machines

• Lever: a bar that pivots on a fulcrum; helps lift or move loads with less force.
• Pulley: a wheel and rope system; changes the direction of force and can reduce effort when multiple pulleys are used.
• Inclined plane: a sloped surface; reduces force by increasing the distance over which the force is applied.

Everyday examples around you

You use simple machines more often than you may realize.

• Opening a paint can with a screwdriver uses a lever.
• Raising a flag uses a pulley.
• Rolling a cart up a ramp uses an inclined plane.

When you see these tools, ask yourself:

• Is the machine changing the size of the force?
• Is it changing the direction of the force?
• Is it making the job easier by increasing the distance?

Common mistakes to avoid

• Thinking a simple machine removes all work. It does not; it changes how the work is done.
• Thinking less force means less work every time. Often, less force means more distance.
• Forgetting that a pulley may change direction, not just force size.
• Forgetting that the fulcrum is the pivot point of a lever.

Brief Summary

Simple machines make work easier by changing the size or direction of a force. A lever uses a bar and fulcrum, a pulley uses a wheel and rope, and an inclined plane uses a sloped surface. These machines often reduce the force needed, but they usually require the force to act over a longer distance.

Mechanical Advantage and Efficiency

Machines help us do work more easily. A machine can make a job easier by changing the size of the force, the direction of the force, or the distance over which the force is applied.

In this lesson, you will learn two important ideas about machines: mechanical advantage and efficiency. These ideas help us understand how well a machine helps us and why real machines are not perfect.

What is a machine?

A machine is a tool that makes work easier. Simple machines include levers, pulleys, ramps, wheels and axles, screws, and wedges.

For example, a ramp helps lift something heavy by spreading the work over a longer distance. A pulley can change the direction of your pull. A lever can help you lift a heavy object with less force.

What is work?

In science, work happens when a force moves an object over a distance. You can think of work as force times distance.

The formula for work is:

$$Work = Force \times Distance$$

Or with symbols:

$$W = F \times d$$

Work is often measured in joules, but for this lesson, the most important idea is how force and distance are connected.

Input force and output force

When you use a machine, you put in a force. This is called the input force. The machine then applies a force to the object. This is called the output force.

• Input force: the force you apply to the machine
• Output force: the force the machine applies to the object

A good force-multiplying machine gives a larger output force than the input force.

Mechanical advantage

Mechanical advantage tells how much a machine increases force. It compares the output force to the input force.

The formula is:

$$Mechanical\ Advantage = \frac{Output\ Force}{Input\ Force}$$

Or:

$$MA = \frac{F_{out}}{F_{in}}$$

If the mechanical advantage is greater than 1, the machine multiplies your force. If the mechanical advantage is 1, the machine does not multiply force. If the mechanical advantage is less than 1, the machine does not increase force, but it may still help by changing the direction of force or speed.

Understanding mechanical advantage

• If \(MA = 2\), the machine doubles your force.
• If \(MA = 4\), the machine makes the output force 4 times as large as the input force.
• If \(MA = 0.5\), the output force is half the input force.

Machines do not create energy. If a machine gives you more force, you usually must apply that force over a longer distance.

Input work and output work

Machines cannot give out more work than is put into them. You do input work on the machine, and the machine gives output work to the object.

• Input work: work done on the machine
• Output work: work done by the machine

The formulas are:

$$Input\ Work = Input\ Force \times Input\ Distance$$

$$Output\ Work = Output\ Force \times Output\ Distance$$

Or:

$$W_{in} = F_{in} \times d_{in}$$

$$W_{out} = F_{out} \times d_{out}$$

Ideal machines and real machines

An ideal machine would have no friction, so all the input work would become output work. In an ideal machine:

$$W_{in} = W_{out}$$

But real machines have friction. Friction turns some energy into heat, so some of the input work is lost. That means:

$$W_{out} < W_{in}$$

Efficiency

Efficiency tells how much of the input work becomes useful output work. It is usually written as a percent.

The formula is:

$$Efficiency = \frac{Output\ Work}{Input\ Work} \times 100\%$$

Or:

$$Efficiency = \frac{W_{out}}{W_{in}} \times 100\%$$

If a machine is 100% efficient, no energy is lost. In real life, machines are always less than 100% efficient because of friction and other small losses.

Why efficiency matters

Two machines may do the same job, but one may waste less energy. The more efficient machine uses more of the input work for useful output work.

For example, if you push a box up a rough ramp, some energy is lost to friction between the box and the ramp. A smoother ramp would usually be more efficient.

Mechanical advantage and efficiency are not the same

These two ideas are related, but they are different.

• Mechanical advantage tells how much the machine changes force.
• Efficiency tells how much input work becomes useful output work.

A machine can have a high mechanical advantage but still lose energy to friction. That means it may help a lot with force, but it is not perfectly efficient.

Worked Example 1: Finding mechanical advantage

A student pushes down on a lever with an input force of 20 N. The lever lifts a rock with an output force of 60 N.

Step 1: Write the formula.

$$MA = \frac{F_{out}}{F_{in}}$$

Step 2: Substitute the values.

$$MA = \frac{60}{20}$$

Step 3: Solve.

$$MA = 3$$

Answer: The mechanical advantage is 3. The lever multiplies the input force by 3.

Worked Example 2: Finding output force from mechanical advantage

A pulley system has a mechanical advantage of 4. A person pulls with an input force of 15 N. What is the output force?

Step 1: Use the formula.

$$MA = \frac{F_{out}}{F_{in}}$$

Step 2: Substitute the known values.

$$4 = \frac{F_{out}}{15}$$

Step 3: Solve for \(F_{out}\).

$$F_{out} = 4 \times 15$$

$$F_{out} = 60\ N$$

Answer: The output force is 60 N.

Worked Example 3: Finding input work and output work

A student uses a ramp to lift a box. The student pushes with an input force of 50 N over a distance of 6 m. The ramp lifts the box with an output force of 120 N through a height of 2 m.

Step 1: Find input work.

$$W_{in} = F_{in} \times d_{in}$$

$$W_{in} = 50 \times 6$$

$$W_{in} = 300$$

Step 2: Find output work.

$$W_{out} = F_{out} \times d_{out}$$

$$W_{out} = 120 \times 2$$

$$W_{out} = 240$$

Answer: The input work is 300 J and the output work is 240 J.

Notice that the output work is less than the input work. Some energy was lost, likely because of friction.

Worked Example 4: Finding efficiency

Use the values from Example 3. The input work is 300 J and the output work is 240 J. What is the efficiency?

Step 1: Write the formula.

$$Efficiency = \frac{W_{out}}{W_{in}} \times 100\%$$

Step 2: Substitute the values.

$$Efficiency = \frac{240}{300} \times 100\%$$

Step 3: Solve.

$$Efficiency = 0.8 \times 100\%$$

$$Efficiency = 80\%$$

Answer: The machine is 80% efficient.

This means 80% of the input work became useful output work, and 20% was lost, mostly to friction.

Common mistakes to avoid

• Do not mix up force and work. Force is a push or pull. Work is force times distance.
• Do not confuse mechanical advantage with efficiency. Mechanical advantage uses forces. Efficiency uses work.
• Remember that efficiency is written as a percent.
• If output work is larger than input work, check your math. In a real machine, output work should not be greater than input work.

Quick review of formulas

• $$W = F \times d$$
• $$MA = \frac{F_{out}}{F_{in}}$$
• $$W_{in} = F_{in} \times d_{in}$$
• $$W_{out} = F_{out} \times d_{out}$$
• $$Efficiency = \frac{W_{out}}{W_{in}} \times 100\%$$

Real-life examples

• Ramp: Lets you use less force to lift an object, but you push it over a longer distance.
• Lever: Can multiply force to lift heavy objects.
• Pulley: Can change the direction of your pull and sometimes increase force.
• Bike gears: Help change how force and speed work together.

Summary

Machines make work easier, but they do not remove the need for work. Mechanical advantage tells how much a machine changes force. Efficiency tells how much of the input work becomes useful output work.

Real machines lose some energy to friction, so they are always less than 100% efficient. When solving problems, pay close attention to whether the question is asking about force, work, mechanical advantage, or efficiency.