AP® Physics 1: Algebra-Based review sheet from Aim for Five (aimforfive.com/physics/units/2/2-3)
Unit 2 · Topic 2.3
2.3 Newton’s Third Law
Forces always come in pairs: if A pushes on B, then B pushes back on A with a force of equal size in the opposite direction. The two forces act on different objects, so they never cancel each other. This topic also covers tension and the ideal strings and pulleys used in most problems.
Key terms
- Newton's third law
- force pair (action–reaction)
- internal force
- tension
- ideal string
- ideal pulley
The law
Newton's third law: F_A on B = −F_B on A. The two forces in a pair are equal in size, opposite in direction, the same type of force (both gravitational, both normal, and so on) and happen at the same time. They act on different objects.
This holds every time, whether the objects are speeding up, at rest, or crashing. When a bug hits a truck's windshield, the bug pushes on the truck exactly as hard as the truck pushes on the bug. The effects differ because the masses differ: the same force gives the tiny bug an enormous acceleration and the truck almost none.
Gravity works the same way. Earth pulls down on a 60 kg student with about 600 N, and the student pulls up on Earth with 600 N. Earth's acceleration from that pull is about 10⁻²² m/s², far too small to notice, because Earth's mass is about 6 × 10²⁴ kg.
Third-law pairs versus balanced forces
A book resting on a table has two forces on it: gravity (down, from Earth) and the normal force (up, from the table). They're equal and opposite, but they're not a third-law pair. They act on the same object and are different types of force. They balance because the book isn't accelerating (2.4).
To find a force's partner, swap the two objects: the partner of "Earth pulls down on the book" is "the book pulls up on Earth." The partner of "the table pushes up on the book" is "the book pushes down on the table."
Internal forces
When two objects are both inside your system, their third-law forces are internal. Each pair adds to zero, so internal forces can't change the motion of the system's center of mass. A person standing in a boat can't make the boat-plus-person system's center of mass move by pushing on the boat. Only external forces can.
Tension, strings and pulleys
Tension is the pull a string, rope or cable exerts. It's the combined result of each little piece of the string pulling on its neighbors. A string can only pull, never push, and its force points along the string.
An ideal string has negligible mass and doesn't stretch, so the tension is the same everywhere along it and both ends move together. An ideal pulley has negligible mass and a frictionless axle; it changes the direction of the string without changing the tension. Assume strings and pulleys are ideal unless told otherwise.
If a rope or chain has noticeable mass, the tension isn't the same throughout. In a chain hanging from a ceiling, the top link holds up the whole chain below it, so the tension is greatest at the top and decreases toward the bottom. You only need to describe this qualitatively.
Worked examples
Try each one yourself first, then open the solution.
- Example 1Calculator allowed
Identifying force pairs
A book rests on a table. For each force on the book, name its third-law partner.
Show the solutionHide the solution
- Step 1: Force 1: gravity on the book by Earth, downward. Partner: gravity on Earth by the book, upward.
- Step 2: Force 2: normal force on the book by the table, upward. Partner: normal force on the table by the book, downward.
- Step 3: Gravity on the book and the normal force on the book are equal and opposite, but they act on the same object and are different types of force, so they are not a pair.
Answer: Earth on book ↔ book on Earth (gravitational); table on book ↔ book on table (normal)
- Example 2Calculator allowed
Two skaters push apart
A 60 kg skater and a 40 kg skater stand on frictionless ice. The 60 kg skater pushes the other with a 120 N force. Find the force on the 60 kg skater and each skater's acceleration.
Show the solutionHide the solution
- Step 1: By the third law, the 40 kg skater pushes back on the 60 kg skater with 120 N in the opposite direction.
- Step 2: Each skater has one horizontal force of 120 N. Use a = F/m (2.5).
- Step 3: 60 kg skater: a = 120 ÷ 60 = 2.0 m/s². 40 kg skater: a = 120 ÷ 40 = 3.0 m/s², in the opposite direction.
- Step 4: Equal forces, unequal accelerations: the lighter skater speeds up more.
Answer: 120 N on the 60 kg skater (opposite direction); 2.0 m/s² and 3.0 m/s²
- Example 3Calculator allowed
Pushing two blocks (classic trap)
Block A (3.0 kg) and block B (1.0 kg) sit side by side on a frictionless floor. You push A with 12 N, and A pushes on B. Find the force A exerts on B and the force B exerts on A.
Show the solutionHide the solution
- Step 1: The blocks move together. Treat A + B as one system: a = 12 N ÷ 4.0 kg = 3.0 m/s².
- Step 2: Now take B alone as the system. The only horizontal force on B is the push from A: F_A on B = m_B a = (1.0)(3.0) = 3.0 N.
- Step 3: Third law: B pushes back on A with 3.0 N, opposite to your push. Check A: 12 − 3.0 = 9.0 N net, and 9.0 ÷ 3.0 kg = 3.0 m/s². ✓
- Step 4: The trap is assuming your full 12 N passes on to B. A only needs 3.0 N to give B the same acceleration.
Answer: A pushes B with 3.0 N forward; B pushes A with 3.0 N backward
Common mistakes
- Calling the normal force and gravity on a resting object a third-law pair. Pairs act on different objects and are the same type of force.
- Thinking the bigger or faster object exerts the bigger force in a collision. The forces are always equal; the accelerations differ.
- Cancelling third-law partners on one free-body diagram. They never appear on the same diagram, because they act on different objects.
- Assuming tension equals the weight of a hanging mass even while the system accelerates. Tension equals mg only when the hanging mass isn't accelerating.
On the exam
- Expect conceptual questions comparing forces in collisions or between objects of different mass. The answer is almost always "equal in size" for the forces.
- For connected objects, free-response questions often ask for separate free-body diagrams. The paired forces between them should be drawn equal in length and opposite on the two diagrams.
Connected topics
Videos
Check yourself
4 questions on 2.3 Newton’s Third Law. Pick an answer to see if you got it, and why.
A large truck collides head-on with a small car. During the collision, how does the force the truck exerts on the car compare with the force the car exerts on the truck?
A book rests on a table. Earth exerts a downward gravitational force on the book. What is the third-law partner of this force?
A horse pulls a cart, and the cart pulls back on the horse with a force of equal size. Which explains how the cart can start moving forward?
A skater standing still on ice pushes on a wall with her hands and glides backward. Which force makes her accelerate away from the wall?
0 of 4 answered