Chapter 4, Problem 21Q

To determine

Reading on your bathroom scale if you weighed yourself on an inclined plane.

Answer to Problem 21Q

Solution:

The scale on your bathroom reads your weight is $W\cos \theta$

Explanation of Solution

If you weighed yourself on an inclined plane i.e. you incline at an angle, $\theta$ then this weight will be resolved in horizontal and vertical components as given below:

$\begin{array}{l}{W}_x=W\sin \theta \\ W_y=W\cos \theta \end{array}$

Now the reading on the bathroom scale is determined by the normal force exerted on a person by an incline. Thus, the horizontal will neglect and the magnitude of normal force will be as given below:

$\begin{array}{c}N=W_y\\ =W\cos \theta \end{array}$