CAIE A-Level Physics 5.2.1 Deriving Gravitational Potential Energy

Practise deriving change in gravitational potential energy from work in a uniform field, using delta EP = mg delta h, assumptions and sign convention.

Exam points

derive ΔEP = mgΔh from work done against a uniform gravitational force
show how the change in gravitational potential energy depends on mass, g and vertical height change
state the assumptions and sign convention used when relating work, height and gravitational potential energy

[Maximum number: 2]

A mass m moves a vertical distance $\Delta h$ in a uniform gravitational field and gains gravitational potential energy $\Delta E_{\mathrm{p}}$ . The acceleration of free fall is g.

Use the concept of work done to show that

\Delta E_{\mathrm{P}}=m g \Delta h .

work (done) = force × displacement

M1

( force =m g and distance $=\Delta h)$

(so) work (done) $=m g \Delta h$ and work $=\Delta E_{(\mathrm{P})}$ (so $\Delta \mathrm{E}_{(\mathrm{P})}=m g \Delta h$ )

A1

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5.2.1—W = Fs, the formula ∆EP = mg∆h for gravitational potential energy changes in question 1