Question

A person's mass is 60 kg. He or she is standing on a bathroom scale in an elevator. Starting from rest, the elevator accelerates downward at 3 m/s for 2 s and then continues at constant speed. Is the scale reading during acceleration greater than, equal to, or less than the scale reading when the elevator us at rest?

Answer 1

The scale reading while the elevator accelerates downward is less than the scale reading when the elevator is at rest, due to the reduction in normal force as a response to the downward acceleration.

Step-by-step explanation:

When the elevator accelerates downward, the scale reading during the acceleration would be less than the scale reading when the elevator is at rest. This is because the downward acceleration reduces the normal force exerted by the scale on the person, which in turn reduces the reading of weight on the scale. To calculate the actual reading, you would use the formula: Fnet = ma = mg - Fscale, where m is the mass of the person, g is the acceleration due to gravity (approximately 9.8 m/s2), and a is the acceleration of the elevator (3 m/s2 in this case).

So, when the elevator accelerates at 3 m/s2, the scale reading in newtons would be Fscale = mg - ma = m(g - a). For a person with a mass of 60 kg, the scale reading during acceleration would be:

Fscale = 60 kg * (9.8 m/s2 - 3 m/s2) = 60 kg * 6.8 m/s2 = 408 N.

At rest, the scale reading would simply be the person's weight, which is the gravitational force: F = mg = 60 kg * 9.8 m/s2 = 588 N. Therefore, during the downward acceleration, the scale reading is less than when the elevator is at rest.