AP Physics 1: Newton's 3rd LawAP Physics 1: Newton's 3rd Law

APPHYSICS1 · UNIT2 · F O R C E S A N D N E W T O N ' S L AW S

Newton's Third Law

Action and reaction pairs, and why they never cancel

Big idea. Whenever object A exerts a force on object B, B exerts a force on A that is equal in magnitude, opposite in direction, same type of force, and acts on a different object. Forces come in pairs.

How to name a pair

Use the form “A on B” and flip it: “B on A.” Always name both objects (AP standard 3.A.3.3). Situation Action Reaction

Person pushes on the

ground

Person pushes ground

backward

Ground pushes person forward (this is why you can

walk)

Book sits on a table Earth pulls book down

(gravity)

Book pulls Earth up (gravity)

Book sits on a table Table pushes book up

(normal)

Book pushes table down (normal)

Rocket launches Rocket pushes exhaust gas

down

Gas pushes rocket up

Swimmer Swimmer pushes water

backward

Water pushes swimmer forward

Truck hits car Truck pushes car Car pushes truck (equal size)

Test trap. The two forces in a 3rd-law pair act on different objects, so they never appear on the same FBD and they never cancel each other. A book at rest has Fg and FN on it. Those two balance each other, but they are not a 3rd-law pair.

Equal forces, unequal accelerations

The forces are equal, but the accelerations are not, because a = F/m. The smaller mass accelerates more. Example. A 50 kg skater pushes a 75 kg skater with 30 N. By Newton’s 3rd law each feels 30 N, in opposite directions.

a1 = 30/50 = 0.6 m/s² and a2 = 30/75 = 0.4 m/s² (opposite directions).

Systems and contact forces

A 2 kg block and a 3 kg block touch on a frictionless surface. A 10 N force pushes the 2 kg block into the 3 kg block.

Treat both as one system: a = 10 / (2 + 3) = 2 m/s²

Only the 3 kg block is pushed by the contact force: F = m a = 3x2 = 6 N

By the 3rd law, the 3 kg block pushes back on the 2 kg block with 6 N. Check the 2 kg block: 10 − 6 = 4 N = (2)(2). ✓

Common challenge: “If forces are equal and opposite, how can anything

accelerate?”

Because the pair acts on two different objects. Add up forces on one object only. Net force on that object decides its acceleration.

Quick reference

Same magnitude, opposite direction, same type of force, different objects

Happens at the same instant (neither one “causes” the other)

Pairs never cancel, because they are on different objects

Heavier and lighter objects feel the same force in a collision, but the lighter one accelerates more Practice

1. What is the 3rd-law reaction to the Earth pulling down on a book?

2. What is the reaction to the table pushing up on a book?

3. A truck hits a small car. Compare the forces. Compare the accelerations.

4. A person pushes on a wall with 100 N. What does the wall do?

5. A 50 kg skater pushes a 75 kg skater with 30 N. Find each acceleration.

6. Explain how a rocket accelerates in space with nothing to push on.

7. Why are the normal force and weight of a book at rest NOT a 3rd-law pair?

8. A 2 kg and 3 kg block touch. A 10 N force pushes the 2 kg block. Find the force between the blocks. 9. Why can a swimmer move forward by pushing water backward?

10. True or false: In a tug-of-war, the winning team pulls harder on the other team. Answers

1. The book pulls up on the Earth.

2. The book pushes down on the table.

3. The forces are equal in size. The car has the larger acceleration because it has the smaller mass. 4. The wall pushes back on the person with 100 N.

5. 0.6 m/s² and 0.4 m/s², in opposite directions.

6. It pushes exhaust gas backward, and the gas pushes the rocket forward.

7. They act on the same object (the book) and are different types of force. A 3rd-law pair acts on two objects.

8. 6 N.

9. The water pushes back on the swimmer with an equal and opposite force.

10. False. Both teams exert equal forces on each other. The winner pushes harder on the ground (static friction).