# Newton's Third Law of Motion: Examples of the Relationship Between Two Forces

## Newton's Third Law of Motion

Are you sitting down for this? If not, take a seat. You might notice that you're not falling through the chair or floor. That's because the forces acting on you are balanced. A **force** is a push or a pull in a given direction. The force of gravity pulling you down against your chair is balanced by the force of the chair pushing up against you.

The forces acting on you as you sit in your chair are just one example of **Newton's third law**, which states that for every **action force** there is an equal and opposite **reaction force**. In fact, all forces come in pairs. No force exists in isolation. That's one of the fundamental symmetries of our universe.

## Identifying Action & Reaction Forces

Suppose you're standing on the ground. The force of gravity pulls you down towards the earth, which presses your feet against the ground. Let's call that the action force - the force of your feet against the earth. The reaction force is the force of the earth pushing against your feet.

Now imagine that instead of standing, you decide to jump.

**Action:** You push your feet down against the ground. **Reaction:** The ground pushes back up against your feet.

When you take a step forward, your feet are pushing back against the ground; it is only because the ground pushes back against your feet in the forward direction that you're able to move forward.

Now, on to some trickier examples of Newton's third law:

How does a rocket move in space where there's nothing to push off of?

A rocket is basically a controlled explosion. As the rocket fuel burns, it quickly expands outwards in every direction, including against the rocket itself. Here's where Newton's third law comes in.

**Action:** The expanding gas particles push against the rocket.**Reaction:** The rocket pushes against the expanding gas particles.

## Equal and Opposite

All of the examples we've discussed so far have involved direct contact between two objects, so let's expand our horizons a bit.

You probably know that the moon orbits the Earth because it feels the tug of Earth's gravity. Let's call the action force the force of the Earth's gravity pulling on the moon. Where's the reaction force? Well, since the moon has mass, it also has its own gravitational field. The moon actually pulls on the Earth with the same force that the Earth pulls on the moon.

How can it be that the forces are the same, given that the Earth is nearly 100 times more massive than the moon? The answer lies in the force of gravity itself: the force of gravity between two objects is proportional to the product of the masses of those objects. The more massive the objects, the stronger the force of attraction; but, regardless of their mass, both objects will experience the same-sized force.

Imagine a train runs into a car.

**Action:** The train pushes against the car.**Reaction:** The car pushes against the train.

It's pretty clear that the train and car are pushing each other in opposite directions, but how can these forces be equal? To answer this question, we need **Newton's second law:** force equals mass times acceleration. The train has a huge mass (*M*), while the car's mass (*m*) is much smaller relative to the train. During the collision, the train will experience a small acceleration (*a*), whereas the car will experience a much larger acceleration (*A*). Setting the two forces equal to each other, we get:

*Ma* = *mA*

Or, the large mass of the train times the small acceleration of the train equals the small mass of the car times the car's large acceleration. These forces are equal and opposite.

## Lesson Summary

In summary, **Newton's third law** states that for every action there is an equal and opposite reaction. These actions are **forces**, a push or a pull on an object that results from interaction with another object. The interacting objects experience two forces that are equal in magnitude and opposite in direction. No matter the size of the interacting objects, the forces are always equal and opposite. Newton's law applies to objects on Earth and in space.

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## Newton's Third Law of Motion: Conceptual Problems

This activity will assess whether or not you grasp the central ideas of Newton's Third Law of Motion.

### Guidelines

To do this activity, kindly print this page on a piece of paper. Then, carefully read each of the given statements and provide a brief explanation for the questions that follow.

#### Problem 1

Jenna likes to play baseball with her friends. She hits the baseball real hard and gets a home-run most of the time. In this scenario,

- If we call the force of the bat against the ball the action force, what is the reaction force?
- Are these forces equal in magnitude and opposite in direction?
- If Jenna hits the baseball with a much lesser force, will the reaction force decrease? Why do you say so?

#### Problem 2

Jake urges his horse to pull a carriage, yet it refuses. The horse says that such an effort will disobey Newton's Third Law of Motion. The horse concludes that it can't exert a greater force on the carriage than the carriage exerts on itself, so it wouldn't be able to move the carriage. What explanation can Jake offer to convince his horse to pull?

### Sample Answers

#### Problem 1

- The force of the ball on the bat is the reaction force.
- Yes. According to Newton's Third Law of Motion, for every action force, there is an equal and opposite reaction force.
- If Jenna hits the baseball with less force, it would follow that the reaction force acting opposite to this force will have a smaller magnitude.

#### Problem 2

Jake should tell his horse to push the ground, not pull the carriage. Pushing the ground will also push the horse in the direction of motion, leading to the movement of the carriage attached to the horse.

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