Lesson 17: Newton's 3rd Law (Action-Reaction)

Newton came up with one more law when he started thinking about the interaction of objects.

• He then talked about what happens when there is a force (2nd Law).
• But what happens when you have objects interacting, affecting each other?

# The 3rd Law (The Law of Action-Reaction)

“For every action force there is an equal and opposite reaction force.”

Anytime an object applies a force to another object, there is an equal and opposite force back on the original object.

• If you push on a wall you feel a force against your hand… the wall is pushing back on you with as much force as you apply to it.
• If this wasn't happening, your hand would accelerate through the wall!

Standing on the ground, you push on the ground with a force due to gravity (Fg down) and the ground pushes back on you (FN up).

The term "normal" means anything at a right angle in math or the sciences.
• FN is the normal force.
• It balances out the force due to gravity down.
• The normal force is always perpendicular to the surface the object is on.
• Without it there would be a net force down on you and you would accelerate down.
• This is an example of an action-reaction pair, two forces that are equal but opposite to each other.

There is one ultra important thing to remember when you are looking at action-reaction pairs.

• The two forces that you are looking at are each acting on different objects!
• If you are examining what you think are action-reaction forces, and they are both acting on the same object, they are not.
• In the example above, Fg is the person pushing down on the ground, while FN is the ground pushing up on the person.

Here are some examples of action-reaction forces that depend on the objects being in direct contact, meaning that the two objects involved are actually touching each other to exert forces on each other. These are called "contact forces."

1. Action: the tires on a car push on the road…
Reaction: the road pushes on the tires.
2. Action: while swimming, you push the water backwards...
Reaction: the water pushes you forward.

Action-reaction pairs can also happen without friction, or even with the objects not touching each other, known as "action at a distance" forces …

1. Action: a rocket pushes out exhaust…
Reaction: the exhaust pushes the rocket forward.

One of the original arguments that flight in the vacuum of space was impossible was that there would be nothing to push against. This action-reaction explains how a rocket can fly in space where there is no air to push against.

1. Action: the earth pulls down on a ball…
Reaction: ball pulls up on the earth.

How can this second example be true?!?

Subscripts are often used in pairs to show what the forces are doing. The notation "EFb" should be read as "the force of the Earth acting on the ball".
• There is an action-reaction pair of forces given by EFb = bFE
• We know that the ball will accelerate towards the earth at 9.81 m/s2, but does the earth accelerate towards the ball at the same rate?
• If this is true you would expect the earth to be constantly bouncing up towards falling objects.
• Carefully remember Newton’s 2nd Law (F = ma).
• In this example the forces are equal, but the mass of the earth is considerably more than the ball!
• The earth has more inertia than the ball.
• Let’s assume the ball has a mass of 2.00 kg and do some calculations…

### The Force of the Earth on the Ball

EFb = ma = mg

= (2.00kg) (9.81m/s2)

EFb = 19.6N

This is the force of the Earth acting on the ball, but because of Newton’s 3rd Law, it is also the force of the ball on the Earth.

EFb = bFE = 19.6N

### The Acceleration of the Earth because of the Ball

bFE = ma

a = bFE / m = 19.6N / 5.98e24 kg

a = 3.28e-24 m/s2

This is such a small acceleration of the Earth towards the ball that it can’t even be measured. We can see that although the forces are equal, the accelerations do not have to be!

Sir Isaac Newton hated his own theories about gravity being an "action at a distance" force. He believed so strongly that there must be some material that connects objects that have a gravitational pull on each other, that he was one of the first scientists to seriously suggest there was a mysterious substance called the aether (sometimes spelled ether) that connected all objects in the universe.

Example 1: When a rifle fires a bullet, the force the rifle exerts on the bullet is exactly the same (but in the opposite direction) as the force the bullet exerts on the rifle… so the rifle “kicks back”. The bullet has a mass of 15 g and the rifle is 6.0 kg. The bullet leaves the 75 cm long rifle barrel moving at 70 m/s.

a) Determine the acceleration of the bullet.

Calculate this using a kinematics formula like vf2 = vi2 + 2ad and you should get 3.3e3 m/s2.

b) Determine the force on the bullet.

F = ma will let you calculate the answer 49 N.

c) Determine the acceleration of the rifle.

Again, use F = ma, but make sure that you use the correct mass. You should get 8.2 m/s2.

d) Explain why the bullet accelerates more than the rifle if the forces are the same.

Although have the same amount of force acting on them, they each have a different mass (and therefore a different inertia).

Example 2: If I push on a lawn mower, it pushes back on me with an equal, but opposite force. Explain why we don’t both just stay still.

• The answer is that these forces are acting on different bodies (and there are other forces to consider).
• It doesn’t matter to the lawn mower that there is a force on me… all that matters to the lawn mower is that there is a force on it, so it starts to move!
• Another action-reaction pair you need to consider is that I am pushing backwards on the ground, and it pushes forwards on me. 