In this example we will analyze the forces acting on your body as you move in an elevator. Specifically, we will consider the case where the elevator is accelerating. Suppose that you stand on a bathroom scale that rests on the floor of an elevator. (Don’t ask why!) Standing on the scale compresses its internal springs and activates a dial that indicates your weight in newtons. When the elevator is at rest, the scale reads 600 N. Suppose that the elevator is accelerating downward at 2.50 m/s2 . What does the scale read during the acceleration?

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onyebuchinnaji onyebuchinnaji · Answer 1 · 2020-10-05T02:35:55+02:00

Answer:

The reading of the scale during the acceleration is 446.94 N

Explanation:

Given;

the reading of the scale when the elevator is at rest = your weight, w = 600 N

downward acceleration the elevator, a = 2.5 m/s²

The reading of the scale can be found by applying Newton's second law of motion;

the reading of the scale = net force acting on your body

R = mg + m(-a)

The negative sign indicates downward acceleration

R = m(g - a)

where;

R is the reading of the scale which is your apparent weight

m is the mass of your body

g is acceleration due to gravity, = 9.8 m/s²

m = w/g

m = 600 / 9.8

m = 61.225 kg

The reading of the scale is now calculated as;

R = m(g-a)

R = 61.225(9.8 - 2.5)

R = 446.94 N

Therefore, the reading of the scale during the acceleration is 446.94 N