Question

A 550-N physics student stands on a bathroom scale in an elevator that is supported by a cable. The combined mass of student plus elevator is 850 kg. As the elevator starts moving, the scale reads 450 N.

(a) Find the acceleration of the elevator (magnitude and direction).
(b) What is the acceleration if the scale reads 670 N?
(c) If the scale reads zero, should the student worry? Explain.
(d) What is the tension in the cable in parts (a) and (c)?

Answer 1

given,

Weight of physics student, W = 550 N

combined mass of the student and elevator, M = 850

Apparent weight of the student when elevator start moving,N = 450 N

a) When apparent weight is Less than lift is moving downward.

m g - N = ma

N = m(g-a)

`450 = (550)/(9.8)(9.8 -a)`

a = -1.78 m/s²

B) acceleration if scale reads 670 N

In this case lift move upward

N = m(g + a)

`670 = (550)/(9.8)(9.8 +a)`

a = 2.14 m/s²

c) If the scale reads zero

acceleration of the elevator comes out to be

m (g + a) = 0

a = -9.8 m/s²

Hence, the elevator is in free fall.

d) Tension in case a)

T = m (g - a)

T = 850 x (9.81 - 1.78)

T = 6825.5 N

Tension in case c)

T = m (g - a)

T = 850 x (9.81 - 9.81)

T =0 N