Question

A person whose mass is m = 59.5 kg steps on a mechanical bathroom scale placed on an inclined plane that makes the angle ? = 25.5� with the horizontal. What is the reading on the scale?

Answer 1

Concepts and reason

The concepts used in solving this problem are resolution of vectors. The reading

on the bathroom scale is calculated by resolving the vectors as the scale is placed on the inclined plane.

Fundamentals

Resolving a vector, A is finding the components in mutually perpendicular directions. The magnitude of the two components can be written as $A\cos \theta$ and $A\sin \theta$ .

The pictorial description for the problem is as follows:

In the above figure, $\theta$ is the angle made by the scale with the horizontal , m is the mass, g is the acceleration due to gravity, $mg\cos \theta$ is the horizontal component, and $mg\sin \theta$ is the vertical component of the scale

As the bathroom scale is placed on the inclined plane angled $25.5^\circ$ with the horizontal, the reading on the scale is given by,

$W = mg\cos \theta$

Substitute 59.5 kg for mg and $25.5^\circ$ for $\theta$ .

$\begin{array}{c}\\W = 59.5\,{\rm{kg}}\left( {\cos 25.5^\circ } \right)\\\\ = 53.70{\rm{ kg}}\\\end{array}$

Therefore, the reading on the bathroom scale is $53.70{\rm{ kg}}$ .

Ans:

The reading on the bathroom scale is 53.70 kg.