Forces and Momentum
Forces and Momentum examines Newton’s laws, resultant forces, friction, weight, momentum and impulse. You must be able to explain motion in terms of forces and to solve collision and explosion problems using conservation of momentum.
Core rules and concepts
- Newton’s first law: with no resultant force, an object stays at rest or moves at constant velocity. Mass is a measure of inertia.
- Newton’s second law: resultant force F = ma. Weight is W = mg and acts vertically downward.
- Newton’s third law: if A exerts a force on B, B exerts an equal and opposite force on A. The pair acts on different bodies, so the forces do not cancel.
- Momentum p = mv is a vector. Impulse Ft = Δp = mv − mu. A longer contact time reduces the force for the same change of momentum.
- In a closed system with no external resultant force, total momentum before a collision equals total momentum after it.
- Elastic collisions conserve kinetic energy; inelastic collisions do not, although momentum is still conserved.
Worked example
A 2.0 kg trolley moving at 3.0 m/s collides with a stationary 1.0 kg trolley. They stick together. Find their common velocity and decide whether the collision is elastic. Total momentum before = 2.0 × 3.0 + 1.0 × 0 = 6.0 kg m/s. After collision total mass = 3.0 kg, so 3.0v = 6.0, giving v = 2.0 m/s. Kinetic energy before = ½ × 2.0 × 3.0² = 9.0 J. After = ½ × 3.0 × 2.0² = 6.0 J. Kinetic energy is lost, so the collision is inelastic. Reasoning: momentum is conserved because no external resultant force acts during the short collision.
Traps that cost marks
- Adding momenta without direction signs in one-dimensional problems.
- Saying action–reaction forces cancel: they act on different objects.
- Using mass in kg as weight in N; W = mg.
- Assuming kinetic energy is conserved in every collision.
- Forgetting that momentum, not force, is conserved in an explosion.