A person whose mass is m = 100.0 kg steps on a mechanical bathroom scale placed on an inclined plane that makes the angle α = 32.7° with the horizontal. What is the reading on the scale?

Reading=mg*sin A = 980*sin32.7 = 529 N.

= Wt. parallel to the incline.

To find the reading on the scale, we need to consider the forces acting on the person on the inclined plane.

The force of gravity acts vertically downward with a magnitude equal to the weight of the person, which is given by the formula: weight = mass × gravity, where "mass" is the mass of the person and "gravity" is the acceleration due to gravity (approximately 9.8 m/s^2).

In this case, the weight of the person is given by: weight = 100.0 kg × 9.8 m/s^2 = 980 N.

Now, we need to break down the weight into components parallel and perpendicular to the inclined plane.

The component of the weight parallel to the inclined plane is given by the formula: force_parallel = weight × sin(α), where "α" is the angle of the inclined plane.

In this case, the force parallel to the inclined plane is: force_parallel = 980 N × sin(32.7°) ≈ 520.23 N.

This force represents the force the person exerts on the scale and is equal in magnitude to the reading on the scale. Therefore, the reading on the scale is approximately 520.23 N.