Energy

Potential Energy

energy stored by height

Lifting an object stores gravitational potential energy, mass times gravity times height, ready to turn back into motion.

Example

Lifting an object stores energy as gravitational potential energy, mass times gravity times height, ready to turn back into motion. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Potential energy is stored by height

Lifting something stores energy you can get back later. Gravitational potential energy is mass times gravity times height above the ground.

PE=m g hPE = m\,g\,h
A raised cart stores potential energyA cart resting at the top of a sloped track, high above the ground.m

A worked value

A 2 kilogram cart held 5 metres up has potential energy 2 times 10 times 5, or 100 joules — ready to turn into motion.

PE=m g h=2 kg ⋅ 10 m/s2 ⋅ 5 m=100 JPE = m\,g\,h = 2\ \text{kg} \,\cdot\, 10\ \text{m}/\text{s}^{2} \,\cdot\, 5\ \text{m} = \hl{100}\ \text{J}

Same height, more mass, more stored energy

Hold the height fixed. A heavier object stores more gravitational potential energy.

mhPE1 kg5 m50 J2 kg5 m100 J3 kg5 m150 J\begin{array}{c|c|c}m & h & PE \\ \hline 1\ \text{kg} & 5\ \text{m} & 50\ \text{J} \\ 2\ \text{kg} & 5\ \text{m} & 100\ \text{J} \\ 3\ \text{kg} & 5\ \text{m} & 150\ \text{J}\end{array}

Same mass, more height, more stored energy

Hold the mass fixed. Lifting to a greater height stores more potential energy in direct proportion to height.

mhPE2 kg1 m20 J2 kg3 m60 J2 kg5 m100 J\begin{array}{c|c|c}m & h & PE \\ \hline 2\ \text{kg} & 1\ \text{m} & 20\ \text{J} \\ 2\ \text{kg} & 3\ \text{m} & 60\ \text{J} \\ 2\ \text{kg} & 5\ \text{m} & 100\ \text{J}\end{array}
mechanics A 2 kg cart 5 m up with g = 10 gives a clean 100 J of stored energy.