Potential Energy
Introduced| English |
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| potential energy/pəˈtenʃl ˈenədʒi/ |
A raised hammer holds energy, waiting
- Lift a hammer above a nail and it just... waits. Yet it now holds energy, ready to strike.
- Energy can be stored by position or shape, not only by motion.
- We call this stored energy potential energy 势能.
- Release it and the store pours back out as motion.
Gravitational potential energy
- Lifting a mass $m$ to a height $h$ stores gravitational PE: $E_p = mgh$.
- It equals the work done against gravity to raise it.
- The higher you lift, or the heavier the mass, the more energy is stored.
- Let it fall and this $mgh$ converts into kinetic energy.
Store energy by lifting
Raise the starting height and see how much potential energy is stored, ready to become kinetic energy.
Lift a $2\ \text{kg}$ book to a $1.5\ \text{m}$ shelf ($g = 9.8\ \tfrac{\text{N}}{\text{kg}}$). How much gravitational PE is stored, in joules?
$E_p = mgh = 2 \times 9.8 \times 1.5 = 29.4\ \text{J}$.
Gravitational potential energy $mgh$ increases when you increase which of these?
$E_p = mgh$ grows with mass, height and $g$. Colour is irrelevant.
When a raised object falls, its gravitational potential energy converts into kinetic energy.
As height drops, $mgh$ falls and the lost PE reappears as kinetic energy $\tfrac12 mv^2$.
Elastic potential energy
- A stretched or compressed spring also stores energy: elastic PE $E_p = \tfrac12 k x^2$.
- Here $k$ is the spring constant and $x$ the extension.
- A drawn bow, a wound spring, a squeezed trampoline — all hold elastic PE.
- Release the deformation and the store becomes motion.
The elastic potential energy of a spring is $\tfrac12 k \_\_$ (fill in the missing part).
$E_p = \tfrac12 k x^2$ — it grows with the square of the extension.
Potential energy is relative
- Gravitational PE depends on the reference level you choose for $h = 0$.
- Only changes in PE ($\Delta E_p$) matter physically, so you may pick any zero.
- PE goes with conservative forces — gravity and springs — whose stored energy is fully recoverable.
- Friction is not conservative: its energy turns to heat and cannot be recovered as PE.
Gravitational potential energy has one absolute value, the same for every observer.
It is measured relative to a chosen zero height; only the change in PE is physically meaningful.
Which force's stored energy can be fully recovered as potential energy?
Gravity is a conservative force — its energy is fully recoverable. Friction turns energy into heat.
Gravitational PE is measured relative to a chosen zero height — there is no absolute value. Always state where $h = 0$ is (the floor, the ground, the table). Only the change in PE affects the physics.
Lift a $2\ \text{kg}$ book to a shelf $1.5\ \text{m}$ high ($g = 9.8\ \tfrac{\text{N}}{\text{kg}}$).
- $E_p = mgh = 2 \times 9.8 \times 1.5 = 29.4\ \text{J}$.
That $29.4\ \text{J}$ is stored, ready to become kinetic energy if the book falls.
Potential energy is stored energy of position or shape. Gravitational PE is $E_p = mgh$; elastic PE is $E_p = \tfrac12 kx^2$. Gravitational PE is measured relative to a chosen zero, and only its change matters. It comes from conservative forces.