Chapter 12, Problem 87A

To determine

To Calculate: The number of times that the rock can be rolled up.

Explanation of Solution

Given:

Mass of the rock, $m=215\text{kg}$

Height of the hill, $h=33\text{m}$

Average power produced, $P_{avg}=0.2\text{kW}$

Time, $t=1\text{h = 60}\times \text{60}\text{s}$

Formula Used:

Average power can be obtained by:

  $P=\frac{W}{t}$

Here, W is the work done and t is the time.

Work done to move the rock up the hill can be obtained by:

  $W=mgh$

Here, m is the mass, g is the acceleration due to gravity and h is the height.

Calculations:

Let the number of times for which rock is rolled in one hour be n .

  $\begin{array}{l}P=\frac{nmgh}{t}\\ 0.2\times {10}^3=n\frac{215\times 9.8\times 33}{1\times 60\times 60}\\ n\approx 10\end{array}$

Conclusion:

Thus, the number of times that the rock can be rolled up is 10.