Question

What would your bathroom scale read if you weighed yourself on an inclined plane? Assume the mechanism functions properly, even at an angle.

Short answer

The obtained reading on the bathroom scale is $W\cos \theta$.

Step-by-step solution

Step 1. Measurement of Weight

Weight is expressed as the term that indicates the quantity of force applied on a particular component due to an acceleration field. In the SI system, weight is measured in the units of Newton.

The relation of the weight of a person is given by:

$W=mg$

Here, m is the mass and g is the gravitational acceleration.

Step 2. Determine the reading of weight on the bathroom scale

Consider that your weight is W and the angle made by the inclined plane is $\theta$. In this case, while measuring the weight of the body on an inclined plane, the bathroom scale will read the magnitude of the normal force acting between you and the plane, which is $W\cos \theta$.

Thus, $W\cos \theta$is the reading of your weight.