Definition
Newton's third law
When two objects interact, they exert forces on each other that are equal in size and opposite in direction.
Definition
Interaction pair
The two forces produced by one interaction, one acting on each of the two interacting objects.
- Newton's third law states that when two objects interact, they exert forces on each other that are equal in size and opposite in direction.
- The two forces form an interaction pair, often called a third law pair.
- Every third law pair has the same set of features.
- The forces are equal in size.
- The forces act in opposite directions along the same line.
- The forces act on different objects.
- The forces are the same type of force, such as two gravitational forces or two normal contact forces.
- The forces start and stop at the same time.
- The law applies to every interaction, whether the objects are touching or not, and whether they are moving or still.
- A short way to state a pair is "if A exerts a force on B, then B exerts an equal and opposite force on A".
Third law pairs and balanced forces
Definition
Balanced forces
Forces acting on an object that cancel each other out so that the resultant force is zero.
- Third law pairs never cancel each other out, because the two forces act on different objects.
- Forces can only cancel when they act on the same object, and then they are balanced forces.
- A mug resting on a desk shows the difference clearly.
- The weight of the mug (the Earth pulling the mug down) and the normal contact force (the desk pushing the mug up) both act on the mug, so they are a pair of balanced forces, not a third law pair.
- The third law partner of the mug's weight is the mug pulling the Earth upwards.
- The third law partner of the desk pushing the mug up is the mug pushing the desk down.
- Two forces that are equal and opposite are therefore not automatically a third law pair, so you must check which object each force acts on.
Situations in equilibrium
- In equilibrium situations, the object you are studying has balanced forces on it, but third law pairs are still present between it and every object it touches or attracts.
- When you lean on a wall without moving, your hand pushes the wall and the wall pushes your hand back with an equal force, which you feel in your palm.
- When a picture hangs on a hook, the picture pulls down on the hook and the hook pulls up on the picture with an equal force.
- When two teams in a tug of war are not moving, each team pulls the rope and the rope pulls back on each team with an equal force.
Situations that are not in equilibrium
- Third law pairs also act when objects are speeding up, slowing down or changing direction.
- Both objects feel the same size of force, but the effects of the forces can be very different because the objects can have very different masses.
- When you walk, your foot pushes backwards on the ground and the ground pushes forwards on your foot with an equal force, which accelerates you forwards.
- When a swimmer pushes water backwards with her arms, the water pushes her forwards with an equal force.
- When a rocket fires its engines, it pushes hot exhaust gases downwards and the gases push the rocket upwards with an equal force.
- When a gun is fired, it pushes the bullet forwards and the bullet pushes the gun backwards with an equal force, so the gun recoils.
- The bullet has a tiny mass, so it gets a huge acceleration.
- The gun has a much larger mass, so it gets a much smaller acceleration.
- When a car hits a fly, the force on the fly is exactly equal to the force on the car, but the fly is squashed because its mass is so small.
Example
Identifying the pairs for a rowing boat
- A rower pulls the oars so that the blades push water backwards.
- The oars exert a backward force on the water.
- The water exerts an equal forward force on the oars, and so on the boat.
- These two forces are the same type, a contact force between the blades and the water, and they act on different objects, the water and the oars.
- The forward force from the water accelerates the boat because it is larger than the drag on the hull.
Example
Comparing the effects on an astronaut and a satellite
- An astronaut floating in space pushes a satellite with a force of 40 N40\ \text{N}40 N.
- By the third law, the satellite pushes the astronaut with a force of 40 N40\ \text{N}40 N in the opposite direction.
- The astronaut has a mass of 100 kg100\ \text{kg}100 kg and the satellite has a mass of 400 kg400\ \text{kg}400 kg.
- The forces are equal, but the astronaut moves away four times as fast because he has a quarter of the mass.
Common Mistake
- Do not say that the forces in a third law pair cancel out, because they act on different objects.
- Do not call an object's weight and the normal contact force on it a third law pair, because both forces act on the same object.
- Do not say that the larger or faster object exerts the larger force, because the two forces in a pair are always equal in size.
Exam technique
Third law answers
- Name both objects and describe both forces, using "on" and "by" to show which object each force acts on.
- State that the forces are equal in size and opposite in direction, as each of these can earn a separate mark.
- If a question asks why the forces do not cancel, say that they act on different objects.
- When the effects on two objects differ, explain the difference using their masses, not a difference in force.
Self review
- State Newton's third law.
- Give four features shared by the two forces in a third law pair.
- What is the third law partner of the weight of a mug?
- Why do third law pairs never cancel out?
- Explain why a gun recoils with a much smaller acceleration than the bullet.