Newton’s Third Law and Action-Reaction Pairs
Newton’s third law states that when one object exerts a force on a second object, the second object exerts a force of equal magnitude and opposite direction on the first; these two forces form an action-reaction pair, act on different objects, and are of the same type. In brief: forces always come in pairs: FAB = −FBA. Because the two forces act on different bodies, they never cancel each other. The accelerations they cause differ if the masses differ, as a = F ÷ m. Rockets, walking, swimming and jumping depend on this law.
A swimmer pushes the water backward and the water pushes the swimmer forward. A rocket pushes gas downward, and the gas pushes the rocket upward. This guide states the law, explains how to identify action-reaction pairs, discusses common confusions such as the horse-and-cart puzzle, compares pairs and balanced forces in a table, works through examples and corrects common mistakes.
What does the third law say?
Forces are interactions between two objects. If A exerts a force on B, then B exerts a force on A with the same magnitude, in the opposite direction, along the same line, and at the same time. Neither force is “first”: which is called the action and which the reaction is arbitrary. The two forces are always of the same kind: gravitational with gravitational, contact with contact, electric with electric.
How do you identify action-reaction pairs?
Use the sentence form: “A exerts a force on B” and “B exerts a force on A”. Examples:
- The Earth pulls on a book (weight); the book pulls on the Earth with an equal force upward.
- The book pushes down on the table; the table pushes up on the book (normal force).
- A foot pushes backward on the ground; the ground pushes forward on the foot (friction), which makes walking possible.
- A swimmer pushes the water backward; the water pushes the swimmer forward.
- A rocket expels gas downward; the gas pushes the rocket upward. This works in a vacuum, as it does not need air to push against.
- A bat hits a ball; the ball hits the bat with an equal and opposite force, for the same time.
Note that the weight of a book and the normal force from the table are not an action-reaction pair, although they may be equal and opposite: they act on the same object, and they are of different kinds. The reaction to the weight is the book’s pull on the Earth.
Why does anything accelerate?
If forces are equal and opposite, how can a horse pull a cart? The key is to consider the forces on one object at a time. The cart accelerates because the net force on the cart (the pull of the horse minus friction) is not zero. The horse accelerates because the ground pushes it forward (friction on its hooves) with a force larger than the pull of the cart backward. The action-reaction pair (horse-cart) acts on two different objects, so they do not cancel in the analysis of either one. In a collision between a small car and a large truck, the forces on each are equal in magnitude, but the car, having a smaller mass, experiences the larger acceleration (and damage to its occupants).
Action-reaction pairs and balanced forces compared
| Feature | Action-reaction pair | Balanced forces on one object |
|---|---|---|
| Act on | Two different objects | The same object |
| Magnitude | Always equal | Equal when balanced |
| Type of force | Always the same type | Can be different types |
| Cancel out? | No | Yes (net force zero) |
| Example | Book on table: weight and book’s pull on Earth | Book on table: weight and normal force |
Worked example: skaters and a rocket
- Two skaters. Skater A (60 kg) pushes skater B (40 kg) on frictionless ice. A accelerates backward at 2.0 m/s2. The force on A is F = ma = 60 × 2.0 = 120 N. By the third law, A exerts 120 N on B in the opposite direction, so B’s acceleration is a = 120 ÷ 40 = 3.0 m/s2. The lighter skater accelerates more.
- Collision. A 1,000 kg car and a 3,000 kg truck collide head on. If the average force on the truck is 60,000 N, the force on the car is also 60,000 N. The truck’s acceleration is 60,000 ÷ 3,000 = 20 m/s2, and the car’s acceleration is 60,000 ÷ 1,000 = 60 m/s2, three times greater.
- Rocket. A rocket expels exhaust gas at a rate of 100 kg/s with a speed of 2,000 m/s relative to the rocket. The force on the gas is the rate of change of its momentum: 100 × 2,000 = 200,000 N, and the force on the rocket (thrust) is 200,000 N upward. For a rocket of mass 10,000 kg, the net force is 200,000 − 98,000 (weight) = 102,000 N, giving an initial acceleration of 10.2 m/s2.
- Book on a table. A 2.0 kg book rests on a table. Pair 1: the Earth pulls the book down with 19.6 N, and the book pulls the Earth up with 19.6 N. Pair 2: the book pushes down on the table with 19.6 N, and the table pushes up on the book with 19.6 N. The book is in equilibrium because the two forces acting on it (19.6 N down and 19.6 N up), which are from different pairs, are balanced.
How was the law established?
Newton stated the law in the Principia (1687): “To every action there is always opposed an equal reaction.” He illustrated it with a horse pulling a stone, where the stone pulls back on the horse, and with collisions. Experiments of Wren, Huygens and Wallis on collisions, in the 1660s, were one of the foundations of the law. The law was extended to include conservation of momentum, and it was used in the design of rockets by Konstantin Tsiolkovsky in 1903.
Which mistakes are common?
Mistake 1: Thinking that action and reaction cancel
They act on different objects, so they cannot cancel.
Mistake 2: Saying that the bigger object exerts the larger force
The forces are equal. The accelerations differ because of the masses.
Mistake 3: Treating the normal force as the reaction to the weight
The reaction to the weight is the gravitational pull of the object on the Earth.
Mistake 4: Thinking that the reaction comes after the action
They occur at the same time.