The third law, conservation of momentum and equilibrium

The third law: when body A pushes or pulls body B, B pushes or pulls A with a force that is equal in size and opposite in direction, at the same instant. We call them action and reaction, but neither comes first.

The two forces act on different bodies, so they never cancel each other. A horse pulls the cart and the cart pulls the horse back, yet they move: the horse is pushed forward by the ground, and that outside force is what counts for the horse.

Everyday examples:

• A gun recoils when it fires a bullet.
• A rocket or a jet engine pushes hot gas backwards; the gas pushes the rocket forwards.
• A boat moves backwards when a person jumps forwards off it.

Conservation of momentum: inside a system, every force has its pair, and the pairs cancel. So if no external force acts, the total momentum stays constant. A 60 kg boy jumps forward off a 120 kg boat at 2 m/s. Before, the total momentum was zero; after, 60 × 2 + 120v = 0, so the boat moves back at 1 m/s.

A body or a point is in equilibrium when the net force on it is zero: the x, y and z components each add to zero.

Example: a 20 N lamp hangs from two strings that are at right angles to each other, one at 30° to the vertical and one at 60°. Up–down: T₁ cos 30° + T₂ cos 60° = 20. Sideways: T₁ sin 30° = T₂ sin 60°. These give T₁ = 20 cos 30° ≈ 17.3 N and T₂ = 20 cos 60° = 10 N: the string nearer the vertical takes more of the weight.

A ball bouncing off a wall: the wall can only push straight out from its surface, so the impulse on the ball, and the force on the wall, is normal to the wall, whatever angle the ball arrives at.