IB Physics SL A.3.10 Gravitational potential energy

Practise calculating changes in gravitational potential energy from mass, weight and height, including rate and per‑kilogram forms.

Exam points

apply ΔE_p = mgh or weight × height to find an energy change, then choose a sensible rounded value in J or kJ
use power as rate of GPE gain to work backwards to height climbed over a stated time interval
calculate specific gravitational energy as gh from an average height, and include the unit J kg^-1 correctly

[Maximum number: 3]

This question is about a tidal power station.

A tidal power station is built for a coastal town. Sea water is stored in a tidal basin behind a dam at high tide and released in a controlled manner between high tides, so that it passes through turbines to generate electricity.

The following data are available.

Table for Question A.3.10—Gravitational potential energy question 1 — IB Physics SL

Calculate the electrical energy produced between successive high and low tides.

difference in height of centre of mass of water $=\frac{1.8}{2}=0.9(\mathrm{~m})$ ;
$\Delta E_{\mathrm{P}}\left(=m g \Delta h=2.8 \times 10^{8} \times 9.8 \times 0.9\right)=2.5 \times 10^{9}(\mathrm{~J}) ;$
electrical energy $\left(=0.24 \times 2.5 \times 10^{9}\right)=5.9 \times 10^{8}(\mathrm{~J})(=590 \mathrm{MJ})$ ;

Marking guidance:

Allow ECF for [2 max] if candidate omits factor of 2 in first marking points.
Accept $g=10 \mathrm{~m} \mathrm{~s}^{-2}$ giving an answer of $6.0 \times 10^{8}(\mathrm{~J})$ .

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A.3.10—Gravitational potential energy question 1