6.5 - Newton’s Third Law
The statement of Newton's third law
Newton's third law describes how forces work between interacting objects. This law states that when two objects interact, they exert forces on each other that are equal in magnitude but opposite in direction. These forces are often called action-reaction pairs, and they always occur together.
This means that no single force exists in isolation—every force has a corresponding force of the same strength acting in the reverse direction. For example, if object A pushes on object B, object B pushes back on object A with exactly the same amount of force but in the opposite way.
Characteristics of forces in interacting objects
Forces between interacting objects have specific features that help explain how they affect motion.
Key features of action-reaction forces:
- Equal magnitude - The strength (or size) of the force exerted by each object is exactly the same
- Opposite directions - The forces point in reverse directions to each other, meaning they act against one another
- Act on different objects - Each force acts on a separate object; the action force acts on one, and the reaction force acts on the other
These characteristics ensure that the forces balance each other in terms of strength and direction, but they do not cancel out because they affect different objects.
How motion outcomes depend on object masses
When two objects interact and exert equal and opposite forces, the resulting motion does not affect both objects equally. The outcome depends on the mass of each object, which is the amount of matter it contains. Mass is measured in kilograms (kg) and determines how much an object resists changes in its motion.
Objects with smaller masses experience more noticeable changes in motion compared to objects with larger masses. This occurs because the same force applied to a smaller mass causes a greater change in speed or direction. In contrast, a larger mass resists the change more, leading to less movement.
The connection to Newton's second law
Newton's second law explains why masses affect motion outcomes during interactions described by the third law. This law states that the acceleration (a) of an object is equal to the net force (F) acting on it divided by its mass (m). Acceleration is the rate of change of velocity, measured in meters per second squared (m/s2).
Formula for Newton's second law:
Where:
- a = Acceleration (m/s2)
- F = Net force (N)
- m = Mass (kg)
In action-reaction pairs, both objects experience the same magnitude of force (F), but from Newton's second law, the acceleration is inversely proportional to mass. This means a smaller mass results in larger acceleration (a bigger change in motion), while a larger mass results in smaller acceleration. As a result, when forces are equal, the object with less mass moves more.
Worked example - Calculating accelerations in an interaction
Two ice skaters push against each other on frictionless ice. Skater A has a mass of 50 kg, and skater B has a mass of 80 kg. They exert a force of 200 N on each other. Calculate the acceleration of each skater.
Step 1: Formula
Step 2: Calculation for skater A
Step 3: Calculation for skater B
Step 4: Interpretation
Skater A (smaller mass) accelerates at 4.0 m/s2, while skater B (larger mass) accelerates at 2.5 m/s2 in the opposite direction, showing how equal forces lead to different motion outcomes based on mass.
Examples of Newton's third law in everyday phenomena
Newton's third law appears in many situations, helping explain why objects move the way they do during interactions.
Examples of Newton's third law:
- Pushing against a wall - When you push on a wall, you exert a force on it, and the wall exerts an equal force back on you. The wall has a much larger mass (connected to the building and ground), so its acceleration is tiny and unnoticeable. Your smaller mass leads to greater acceleration, causing you to move backward instead of the wall moving.
- Interactions between medium-mass objects - If two people of similar masses push against each other (like in a game), both experience noticeable acceleration. Each moves backward because the forces are equal, but their comparable masses result in similar accelerations in opposite directions, causing both to move.
These examples show how the third law, combined with the second law, determines real-world motion.