What Newton's third law states

Newton's third law describes how forces work between objects that interact with each other. It states that when two objects interact, they exert forces on each other that are equal in magnitude (size) and opposite in direction. This means if object A pushes or pulls on object B, object B pushes or pulls back on object A with the same amount of force but in the reverse direction.

This law applies to all kinds of interactions, such as when you push something or when things collide. The forces always come in pairs, and they act on different objects.

Equal and opposite forces between interacting objects

Forces between interacting objects are always equal in size but point in opposite directions. Magnitude refers to the strength of the force, measured in newtons (N). For example, if you apply a force of 10 N to an object, that object applies exactly 10 N back on you, but in the opposite way.

Key features of force pairs:

• Equal magnitude - Both forces have the same strength, no matter the objects' sizes
• Opposite directions - One force goes one way, and the other goes exactly the reverse
• Act on different objects - Each force affects a separate object in the pair

These force pairs happen instantly during any interaction, like when two people push against each other or when a ball hits a wall.

Why the resulting motion depends on object masses

Even though the forces in Newton's third law are equal and opposite, the objects involved do not always move the same way. The resulting motion (change in speed or direction) depends on the masses of the objects. Mass is the amount of matter in an object, measured in kilograms (kg).

Smaller masses typically experience more motion because they accelerate (change velocity) more easily under the same force. Larger masses resist changes in motion more, so they move less or not at all.

Connection to Newton's second law

Newton's second law helps explain why motion differs even with equal forces from the third law. It states that 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 in velocity, measured in meters per second squared (m/s²).

Formula for Newton's second law

$a=\frac{F}{m}$

Where:

• a = Acceleration (m/s²)
• F = Net force (N)
• m = Mass (kg)

This formula shows that for the same force, a smaller mass leads to greater acceleration. In force pairs, each object feels the same force magnitude, but the one with smaller mass accelerates more.

Example: Pushing against a wall

A common example of Newton's third law is pushing against a wall. When you push on the wall, you exert a force on it. According to the third law, the wall exerts an equal force back on you, in the opposite direction.

However, you move backward while the wall stays still. This happens because of the masses involved and Newton's second law. Your mass is much smaller than the wall's (which is connected to the massive Earth). The same force causes you to accelerate more (a = F/m), so you move, but the wall does not.

Why this interaction works this way:

• Equal forces - Your push and the wall's push back are the same magnitude
• Mass difference - The wall's huge mass means its acceleration is tiny or zero
• Resulting motion - You experience noticeable acceleration and move away