On a distant planet the surface value of the gravitational acceleration is to be measured

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

On a distant planet the surface value of the gravitational acceleration

g_{\mathrm p}

is to be measured. A smooth plane of length

6.0\,\text{m}

is tilted so that it makes an angle of

25^{\circ}

with the local horizontal. A rover places a

1.5\,\text{kg}

equipment box at the top of the plane and records that it takes

4.2\,\text{s}

to reach the bottom starting from rest. (i) Derive an expression for

g_{\mathrm p}

in terms of the measured time

t

, plane length

\ell

and angle

\theta

. (ii) Using the given data, calculate the numerical value of

g_{\mathrm p}

on the planet. (iii) Compare this value with Earth’s standard value

g_{\oplus}=9.8\,\text{m}\,\text{s}^{-2}

and state whether the planet’s surface gravity is stronger or weaker. Give the ratio

g_{\mathrm p}/g_{\oplus}

to two significant figures. (iv) For the same box resting momentarily on the inclined plane, find the normal reaction force exerted by the plane on the box on the planet and compare it with the normal reaction that would act on Earth for the same angle.

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