⚡ Work, Energy and Power

1. Work

Work is said to be done by a force when the body is displaced in the direction of the applied force.

W = F · S = F S cosθ Where F is force, S is displacement, and θ is the angle between them. Unit is Joules (J).

Positive Work: 0° ≤ θ < 90° (Force assists motion)

Zero Work: θ = 90° (Force is perpendicular to motion, e.g., coolie carrying load on head)

Negative Work: 90° < θ ≤ 180° (Force opposes motion, e.g., friction)

Energy is the capacity to do work. Kinetic Energy (KE) is energy possessed due to motion: KE = ½ mv² = p²/2m.

The net work done by all forces (conservative and non-conservative) on a body equals its change in kinetic energy.

W_net = KE_final - KE_initial

Energy possessed due to position or configuration.

Gravitational PE: U = mgh
Elastic PE of a Spring: U = ½ kx² (where k is spring constant, x is extension)

Power is the rate of doing work. P = W/t = F · v. Unit is Watt (W). 1 HP = 746 W.

Elastic Collision: Both momentum and kinetic energy are conserved. (e.g., ideal billiard balls)

Inelastic Collision: Only momentum is conserved. Kinetic energy is lost (usually as heat/sound).