Question

Stand on a bathroom scale on a level floor, and the reading on the scale shows the gravitational force on you, mg. If the floor is slanted at an angle, the scale reading will be less than mg. Discuss why this is so, and why it is a good idea to measure your weight when the scale is on a horizontal surface.

Answer 1

The angle introduces an error on the mesure of the weight

Step-by-step explanation:

Weight and Normal Forces

When an object is resting on a horizontal surface, its weight is directed downwards and the normal force has the same magnitude and opposite direction, i.e. directed upwards. When some angle α exists between the surface and the horizontal plane, the scale keeps 'feeling' the Normal force, but it's not equal to the weight anymore, but to the perpendicular component of the weight to the surface where the scale is placed. It can be found that the component of the weight is m.g.cosα

If, for example
`\alpha=10^o`, the real measure is

`m.g.cos 10^o=0.985(mg)`

That is, 98.5% of the correct weight. So it's important to measure weight on horizontal surfaces