Problem 1

A small block of mass

m=2.0\,\mathrm{kg}

is released from rest at the top of a straight, smooth plane inclined at

\alpha=30^\circ

to the horizontal. It travels a distance

s=10.0\,\mathrm{m}

measured along the plane. Take

g=9.80\,\mathrm{m\,s^{-2}}

, neglect air resistance, and choose downhill as positive. (a) Find the block’s acceleration and the normal force exerted by the plane. (b) Find the travel time and its speed at the bottom. (c) Find the work done by gravity and its average power during the descent.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

W_g=mgs\sin\alpha=98.0\,\mathrm{J},\quad \bar P=W_g/t=48.5\,\mathrm{W}

problems.proof.analysis

The vertical drop is $s\sin\alpha$ , so gravity does positive work $W_g=mg s\sin\alpha=98.0\,\mathrm J$ . Average power is this work divided by the descent time: $48.5\,\mathrm W$ .