Identical smooth planes inclined at to the horizontal are set up on Earth and on the Moon

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics

Problem

Identical smooth planes inclined at

25^{\circ}

to the horizontal are set up on Earth and on the Moon. The acceleration due to gravity on the Moon is

1.6\,\text{m\,s}^{-2}

while on Earth it is

9.8\,\text{m\,s}^{-2}

. A block of mass

3.0\,\text{kg}

is released from rest at the top of each plane whose length is

2.0\,\text{m}

. (i) Show that the magnitude of acceleration of the block along any smooth plane of inclination

\theta

g\sin\theta

. (ii) Calculate the acceleration of the block on the Moon. (iii) Determine the time taken by the block to reach the bottom of the

2.0\,\text{m}

long plane on the Moon. (iv) Compare the normal reactions on the block at the top of the planes on Earth and on the Moon.