Problem — Change in potential energy of a box

Gravitational potential energy. A $5\;\mathrm{kg}$ box is lifted from a stool $50\;\mathrm{cm}$ high onto a shelf $1{,}8\;\mathrm{m}$ high. Calculate the change in potential energy.

Solution

Data: $m = 5\;\mathrm{kg}$, initial height $h_i = 0{,}50\;\mathrm{m}$, final height $h_f = 1{,}8\;\mathrm{m}$.

The change in gravitational potential energy depends only on the height difference, not on the path:

$\Delta h = h_f - h_i = 1{,}8 - 0{,}50 = 1{,}3\;\mathrm{m}$

$\Delta E_p = mg\,\Delta h = 5\cdot 9{,}81\cdot 1{,}3 = 63{,}8\;\mathrm{J}$

$\ev{\Delta E_p \approx 63{,}8\;\mathrm{J}}$

Physical reading. The value is positive because the box rises: it gains potential energy at the expense of whoever lifts it. Only the height difference $\Delta h = 1{,}3\;\mathrm{m}$ matters: the zero of potential energy (floor, stool or shelf) is arbitrary and always cancels in the difference.

Collegamenti

Argomenti: Work and energy Concetti: Gravitational potential energy Competenze: Symbolic set-up