Calculate gravitational potential energy and kinetic energy, and apply the law of conservation of mechanical energy to solve real-world problems.
Work is done when a force causes an object to move through a displacement. Work is a scalar quantity measured in joules (J).
where θ is the angle between the force vector and the displacement vector.
The net work done on an object equals its change in kinetic energy:
Kinetic energy is the energy an object has due to its motion. It is always positive (or zero).
Note that KE depends on v² — doubling speed quadruples kinetic energy. KE has units of joules (J) and is a scalar.
GPE is stored energy due to an object's height above a chosen reference level (usually the ground).
where h is height above the reference point, m is mass (kg), and g = 9.8 m·s⁻². GPE is a scalar measured in joules. The choice of reference point is arbitrary — only changes in GPE matter.
The total mechanical energy of an object is the sum of its kinetic and gravitational potential energies:
When only conservative forces act (no friction, no air resistance), mechanical energy is conserved — it stays constant throughout the motion.
When friction is present, some mechanical energy is converted to thermal energy (heat). The work done by friction equals the loss in mechanical energy:
Or equivalently: |Wfriction| = MEinitial − MEfinal
Power is the rate of doing work — how quickly energy is transferred.
Unit: watt (W) = J·s⁻¹. P = Fv applies when force and velocity are in the same direction and both are constant.
Hooke's Law: The force exerted by a spring is proportional to its extension: F = kx, where k is the spring constant (N·m⁻¹) and x is the extension from natural length. This is valid only within the elastic limit.
Elastic Potential Energy: Energy stored in a compressed or stretched spring:
Ep = ½kx²
At maximum compression/extension, all KE has been converted to spring PE (if no energy loss).
Efficiency: No real machine converts 100% of input energy to useful output. Efficiency is defined as:
η = (useful energy output / total energy input) × 100%
Or equivalently: η = (useful power output / total power input) × 100%
Example: A motor uses 500 J of electrical energy to lift a 4 kg mass 10 m. GPE gained = 4 × 9.8 × 10 = 392 J. Efficiency = (392/500) × 100% = 78.4%.
| Point | Height above ground (m) | Speed (m·s⁻¹) |
|---|---|---|
| A (top, starts from rest) | 15 | 0 |
| B | 8 | 11 |
| C (bottom) | 0 | 16 |