Work, Energy, Power

Work and Power

Mechanical work and energy measure how bodies interact with each other.

• Work: A = F·s·cosα (J). If the force is directed along the displacement, A = F·s.
• Power: N = A/t = F·v (W).
• Efficiency: η = A_useful/A_total · 100%.

Energy

Type of energy	Formula
Kinetic	E_k = mv²/2
Potential (gravitational)	E_p = mgh
Potential (elastic)	E_p = kx²/2

• Law of conservation of mechanical energy: if there is no friction, E_k + E_p = const.
• The work done by the net force equals the change in kinetic energy: A = ΔE_k.

Examples

• If a 25 N force moves a body 6 m in the direction of the force, A = 25·6 = 150 J.
• A body of 4 kg moving at 5 m/s: E_k = 4·25/2 = 50 J.
• If 1000 J of work is done in 25 s, N = 1000/25 = 40 W.

Kinetic energy depends on the square of the speed: if the speed increases 2 times, E_k increases 4 times.