3. A 650-N physics student stands on a metric bathroom scale inside an elevator.

Question

3. A 650-N physics student stands on a metric bathroom scale inside an elevator. The elevator (including the student)

has a total mass of 875 kg. Just after the elevator starts moving, the student checks the scale to find that it reads 550-N.

A short time later, just before the elevator reaches its destination, the student again checks the scale, but now it reads

690-N.

(i) What is the acceleration (magnitude and direction) of the elevator at the time the scale read 550-N?

(ii) What is the acceleration of the elevator at the time the scale read 690-N?

(iii) What is the tension on the elevator cable in both cases?

Explanation / Answer

the scale reading is the normal force acting on the student

we find the normal force using newton's second law applied to the student:

sum of all forces = ma

the forces acting on the student are the normal force (up) and weight (down), so newton's second law reads:

N - mg = ma or N=m(g+a)

when the elevator is at rest, the normal force equals the weight, so we know that the student's weight is 560N, so that the mass is
560/9.8 =57.1 kg

a) in order for the scale to read 800N, the elevator must be accelerating upward, accoring to newton's second law

N- mg = ma

if N = 800N and mg = 560 N, we have that:

800-560=57.1a or a = 4.2 m/s/s

b) for the normal force to be 450N, the elevator must accelerate downward:

450N-560N = ma or a = -1.9 m/s/s

c) if the scale reads zero, then N = 0 and a=-g meaning the elevator is in free fall, and the student should worry

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