Gravitational Potential Energy | CAIE 9702 Paper 2 Notes

Chapters

Paper 2

Physics9702

Gravitational Potential Energy

Lift an object and you do work against its weight. That transferred energy is stored as gravitational potential energy.

Near Earth's surface, only the vertical height changematters—not the route taken.

Derive the relation before using it

A hand-drawn block moves from the foot to the top of a sloping ramp. — For gravitational potential energy, use the vertical height change between the start and finish—not the distance travelled along the ramp.

For a slow lift or a lift at constant speed, the upward force equals the weight: $F=mg$ .
The displacement in that force direction is the vertical height change $\Delta h$ .
Work done becomes stored gravitational potential energy, so $\Delta E_p=F\Delta h=mg\Delta h$ .

\Delta E_p = mg\Delta h

Symbols

$\Delta E_p$ = change in gravitational potential energy (J)
$m$ = mass (kg)
$g$ = acceleration of free fall (m s^{-2})
$\Delta h$ = final vertical height − initial vertical height (m)

Moving upward gives a positive height change and a gain in GPE.
Moving downward gives a negative height change and a loss of GPE.
The formula assumes a uniform gravitational field, so $g$ is effectively constant over the height change.

Use vertical height, then check the sign

Worked example

A load lifted by a crane

A crane raises a 240 N load through a vertical height of 150 m. Find the increase in GPE.

The weight is already given, so no mass conversion is needed.
$\Delta E_p=(mg)\Delta h=240\times150=3.60\times10^4\text{ J}$ .

Answer

36.0\text{ kJ}

Your turn9702/21/O/N/24 Q3(b)

A block of mass $m$ is raised vertically at constant speed through height $\Delta h$ . Derive an expression for its change in gravitational potential energy. State the meaning of any other symbol used. (9702/21/O/N/24 Q3(b))

Show worked answer

Worked answer: The lifting force equals the weight, $F=mg$ , where $g$ is the acceleration of free fall. The GPE gain equals the work done: $\Delta E_p=F\Delta h=mg\Delta h$ .