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

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

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.

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.

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

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".

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.