4.3 Momentum

Total momentum p=mv is a vector. If external impulse is negligible, Σm u=Σm v before and after a collision or separation.

Choose a positive direction, keep signs on velocities, and define the system before writing the conservation equation.

A 2 kg cart at 4 m s⁻¹ and a 1 kg cart at −1 m s⁻¹ have total momentum 7 kg m s⁻¹ before impact.

Momentum conservation does not imply kinetic-energy conservation; inelastic impacts can dissipate energy.

Impulse J=∫Fdt equals change in momentum Δp. For a constant force, J=FΔt; for a varying force, use the signed area under the force–time graph.

Choose the positive direction and distinguish peak force from average force. The impulse includes direction and can be negative.

A triangular force pulse of base 0.20 s and height 50 N gives impulse 5 N s.

A large peak force over a very short time may give less impulse than a smaller sustained force; peak force is not momentum change.