Chapter 4.5, Problem 51E

To determine

To find: To find the ratio of change of weight on moon and earth.

Answer to Problem 51E

The ratio of change of weight on moon and earth is $37.87$ .

Explanation of Solution

Given: $g=5.2{\text{ ft/sec}}^2$ on earth and $g=32{\text{ ft/sec}}^2$ on moon.

Calculation:

Let $y=f(x)$ be a differential function. The differential $dx$ is an independent variable. The differential $dy$ is

  $dy=f\text{'}(x)dx$

Given $W=a+\frac{b}{g}$ .

Find $\frac{dW}{dg}$ .

  $\begin{array}{l}\frac{dW}{dg}=\frac{d}{dg}\left(a+\frac{b}{g}\right)\\ \frac{dW}{dg}=\frac{d}{dg}(a)+b\frac{d}{dg}(g^{-1})\\ \frac{dW}{dg}=0-\frac{b}{g^2}\\ \frac{dW}{dg}=-\frac{b}{g^2}\end{array}$

The ration of change of weight on moon and earth,

  $\begin{array}{l}\frac{dW}{dg}=\frac{1024}{27.04}\\ \frac{dW}{dg}=37.87\end{array}$

Conclusion:

The ratio of change of weight on moon and earth is $37.87$ .