Physics / Unit 5: Work, Energy and Power
5.3 Potential Energy
Notes
Potential energy is stored energy due to position or shape.
- Gravitational potential energy: $PE_g = mgh$, where $h$ is the height above a chosen zero level.
- Elastic potential energy in a stretched or compressed spring: $\displaystyle PE_s = \frac{1}{2}kx^2$, where $k$ is the spring constant (N/m) and $x$ is the stretch.
- Only changes in $PE$ matter, so you may choose any zero level.
- Example: a 5 kg box on a shelf 4 m high: $PE_g = 5 \times 9.8 \times 4 = 196 \text{ J}$.
Practice
How much gravitational potential energy does a 2 kg book gain when lifted 1.5 m?
$PE = mgh = 2 \times 9.8 \times 1.5 = 29.4 \text{ J}$.
A spring with $k = 200 \text{ N/m}$ is compressed 0.1 m. How much elastic energy is stored?
$\displaystyle PE_s = \frac{1}{2}(200)(0.1^2) = 100 \times 0.01 = 1 \text{ J}$.
Two identical balls sit on shelves. Ball A is 3 m high and ball B is 1 m high. Compared with B, A has:
$PE_g$ is proportional to $h$.
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