An elevator is supported by a single cable and there is no counterweight. The el

Question

An elevator is supported by a single cable and there is no counterweight. The elevator receives passengers at the ground floor and takes them to the top floor, where they disembark. New passengers enter and are taken down to the ground floor.

(1) During this round trip, when is the tension in the cable equal to the weight of the elevator plus passengers?

a. when it's moving at a variable rate only
b. when it's moving at a constant rate only
c. when it's stationary and when moving at a variable rate
e.when it's stationary and when moving at a constant rate
f. when it's stationary only

(2) When is it greater?
a. when it's accelerating upward from ground and stopping back at ground
b. never
c. when it's freefalling toward ground only
d. when it's stopping at top floor and accerlerating down from top floor
e. always

(3) When is it less?
a. when it's stopping at top floor and accelerating down from top floor
b. never
c. always
d. when it's at ground level only
e. when it's accelerating upward from ground and stopping back at ground

Explanation / Answer

1. e
2. a
3. a

1. No net force acts on a body when its stationary or moving with constant velocity. Hence balancing the net force, the tension equals force due to gravity.

2. when its accelerating upwards, T-mg = ma, T= mg+ma ....clearly T>mg

    when it is stopping at ground, force = rate of change in momentum (in direction of change in momentum)

    Net Tension = mg + rate of change in momentum, T>mg

3. When its accelerating downwards, mg-T = ma, T = mg-ma ...clearly T<mg

  when it stops, T = mg-rate of change in momentum, T<mg

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