Question

A mass of 12 kg is resting on a bathroom scale sitting in an elevator. If the elevator is accelerating downward at 4 m/s², which best describes the forces acting on the mass?

1) Large force acting down onto the mass, small force pushing the mass up
2) A force pushing down on the mass is equal in magnitude to a force pushing up on it
3) Little to no force acting down onto the mass, but a large force pushing it upwards.
4) Force acting down onto the mass, with no force acting up. There are two forces of equal magnitudes acting on the sides of the mass.

Answer 1

The forces acting on a 12 kg mass in a downward accelerating elevator involve a smaller downward force due to its weight and a larger upward force from the scale's normal force. The correct forces are captured in option (2) where the force pushing down is smaller, and the force pushing upwards is larger, resulting from the elevator's downward acceleration.

Step-by-step explanation:

If a mass of 12 kg is resting on a bathroom scale in an elevator that is accelerating downward at 4 m/s², the best description of the forces acting on the mass is that there is a force pushing down on the mass that is smaller than the force pushing the mass up. This is because the normal force (the force the scale exerts upwards) must counteract not only the weight of the mass but also allow for the downward acceleration of the mass. To determine the scale reading, we use Newton's second law (Fnet = ma).

The downward force (weight) on the mass is the gravitational force, which can be calculated as mg, where m is the mass (12 kg) and g is the acceleration due to gravity (9.8 m/s²), thus resulting in a downward force of 117.6 N. However, because the elevator is accelerating downwards at 4 m/s², the net force (Fnet) acting on the mass is the difference between the weight and the normal force (N), leading to the equation: Fnet = mg - N. Using the given downward acceleration (a = -4 m/s²), the equation becomes Fnet = m(-4 m/s²) = -48 N. To find the normal force (N), we rearrange the equation to N = mg - Fnet, which gives us the scale reading: N = 117.6 N - (-48 N) = 165.6 N. Therefore, option (1) is incorrect as it states a large force acting down onto the mass and a small force pushing the mass up.

It is clear then, that options (2), (3), and (4) are also incorrect as they do not correctly describe the scenario when the elevator is accelerating downward. The correct scenario would involve a large force (the scale reading, which is the normal force) acting up onto the mass and a smaller downward force (the weight minus the net force due to accelerating), meaning option (2) most accurately represents the forces involved