Study notes
Energy, Work & Power
Energy stores and how energy is transferred between them, the formulas for kinetic and gravitational potential energy, conservation of energy, and how work, power and efficiency are calculated.
Learn it step by step
Energy is stored in different forms
Energy can be stored as kinetic (in a moving object), gravitational potential (in a raised object), chemical (in fuels and food), elastic (in a stretched or compressed spring), nuclear (in an atom's nucleus), or internal energy (in a substance's temperature and state). Energy is never created or destroyed, only transferred between stores.
Energy is transferred by several mechanisms
Energy moves from one store to another mechanically (by a force doing work), electrically (by a current), by heating, or by waves (light or sound). A phone battery, for example, transfers energy electrically to the phone's speaker, which transfers it further by sound waves.
Kinetic energy depends on mass and the SQUARE of speed
The kinetic energy of a moving object is , where is mass and is speed. Because speed is squared, doubling an object's speed quadruples its kinetic energy, not just doubles it.
Gravitational potential energy depends on height
The gravitational potential energy gained by raising an object is , where is mass, is gravitational field strength, and is the height risen. This is the energy available to be converted into other forms, such as kinetic energy, as the object falls back down.
Total energy is always conserved
In any process, the total amount of energy before and after is the same, energy only changes form or moves between stores, it is never created or destroyed. A swinging pendulum, for example, continuously exchanges energy between kinetic energy (moving fastest at the bottom) and gravitational potential energy (highest at each end of the swing).
Work done transfers energy using a force over a distance
Work done is , where is the force applied and is the distance moved in the direction of that force, measured in joules (J). Doing work on an object is exactly how energy gets transferred to or from it, work done and energy transferred are the same quantity.
Power is how quickly energy is transferred
Power is , the energy transferred (or work done) per unit time, measured in watts (W), where . Two machines can do the same amount of work, but the one that finishes faster has the greater power.
Efficiency compares useful output energy to total input energy
Efficiency is . No real machine is 100% efficient, some input energy is always wasted, usually as heat, so efficiency is always less than or equal to 100%.
Worked examples
- Use E_k = 1/2 x m x v^2.
- m = 2 kg, v = 5 m/s, so v^2 = 25.
- E_k = 1/2 x 2 x 25 = 25 J.
- The ball's kinetic energy is 25 J.
- Use E_p = m x g x h.
- m = 3 kg, g = 10 N/kg, h = 4 m.
- E_p = 3 x 10 x 4 = 120 J.
- The crate gains 120 J of gravitational potential energy.
- Work done: W = F x d = 50 x 6 = 300 J.
- Power: P = E / t, using the work done as the energy transferred.
- P = 300 / 10 = 30 W.
- The work done is 300 J and the power developed is 30 W.
- Use efficiency = (useful energy output / total energy input) x 100%.
- useful energy output = 350 J, total energy input = 500 J.
- efficiency = (350 / 500) x 100% = 0.7 x 100%.
- The motor's efficiency is 70%.
Mind map
Mind map for Energy, Work & Power.
- Energy stores
- kinetic, gravitational potential, chemical
- elastic, nuclear, internal
- Transfer mechanisms
- mechanically, electrically
- by heating, by waves
- Kinetic energy
- E_k = 1/2 m v^2
- Gravitational potential energy
- E_p = mgh
- Conservation of energy
- energy never created or destroyed, only changes form
- Work done
- W = force x distance moved in direction of force
- Power
- P = energy transferred / time
- Efficiency
- useful output / total input x 100%
- always <= 100%