Forces, Momentum and Newtonian Mechanics
Newton’s laws and equilibrium
Newton’s first law: a body stays at rest or moves at constant velocity unless a resultant force acts. Second law: resultant force F = ma. Third law: forces occur in equal and opposite pairs acting on different bodies. For equilibrium, the resultant force is zero and the resultant moment about any point is zero. Moment = force × perpendicular distance from the pivot. Weight acts through the centre of gravity.
Momentum and impulse
Momentum p = mv and is a vector. Impulse = FΔt = Δp. In a closed system with no external resultant force, total momentum is conserved. In elastic collisions kinetic energy is also conserved; in inelastic collisions it is not, although momentum still is. Explosions conserve momentum from an initial total of zero.
Worked example
A 2.0 kg trolley moving at 3.0 m/s collides with a stationary 1.0 kg trolley; they stick together. Total momentum before = 2.0 × 3.0 = 6.0 kg m/s. After: (2.0 + 1.0)v = 6.0, so 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. The 3.0 J loss shows the collision is inelastic.
Traps
Using mass instead of weight; taking a moment distance along the force rather than perpendicular to it; assuming kinetic energy is always conserved; ignoring direction signs in momentum; confusing impulse with force; forgetting that Newton’s third-law pairs act on different objects, not the same one.