Question

A student stands on a bathroom scale in an elevator at rest on the 64th floor of a building. The scale reads 840 N. As the elevator moves up, the scale reading increases to 948 N, then decreases back to 840 N. The acceleration of gravity is 9.8 m/s². Find the acceleration of the elevator. Answer in units of m/s².

As the elevator approaches the 74th floor, the scale reading drops as low as 767 N. What is the acceleration of the elevator? Answer in units of m/s².

Answer 1

The acceleration of the elevator is found by applying Newton's second law to the changes in scale reading, which reflect the net force acting on the person due to the elevator's motion. An increased scale reading indicates upward acceleration, while a decreased reading suggests downward acceleration.

Step-by-step explanation:

When an elevator accelerates upwards, the scale reading will increase because it has to support not only the weight of the person standing on it due to gravity but also provide an additional force to accelerate the person upwards. Conversely, if the elevator accelerates downwards, the scale reading decreases since the required support force is reduced.

To find the acceleration of the elevator, we use Newton's second law of motion, which relates the net force (Fnet), mass (m), and acceleration (a):

Fnet = ma

For the case where the scale reads 948 N, we know the apparent weight is greater than the actual weight, indicating an upward acceleration. The equation is thus:

Fnet = Fs - mg = ma

Solving for a when the scale reads 767 N during downward acceleration:

Fs = ma + mg
767 N = m(a + g)

Plugging in the given values and solving for a gives the acceleration of the elevator.