Chapter 14.2, Problem 11E

To determine

To find: The energy that an engine expend in ascending vertically for $100\text{m}$ .

Answer to Problem 11E

The required energy is $2.4\text{W}\cdot \text{h}$ .

Explanation of Solution

Given:

The mass of man is $75\text{kg}$ .

The height of the ladder is $12\text{m}$ .

The angle of ladder with horizontal is $78°$ .

Calculation:

Find the magnitude of $F$ .

  $\begin{array}{c}F=Mg\sin \theta \\ =75\times 9.8\times \sin 78°\\ =718.94\text{N}\end{array}$

The displacement $d$ is also upward and has norm $12\text{m}$ .

Find the work done.

  $\begin{array}{c}W=\Vert F\Vert \Vert d\Vert \\ =718.94\times 12\\ =8627.28\text{J}\end{array}$

Find the required energy.

  $\begin{array}{c}E=\frac{8627.28}{3.6\times {10}^6}\\ \approx 2.4\text{W}\cdot \text{h}\end{array}$

Therefore, the required energy is $2.4\text{W}\cdot \text{h}$ .