Question

(a) An elevator of mass m moving upward has two forces acting on it: the upward force of tension in the cable and the downward force due to gravity. When the elevator is accelerating upward, which is greater, T or w?

(b) When the elevator is moving at a constant velocity upward, which is greater, T or w?

(c) When the elevator is moving upward, but the acceleration is downward, which is greater, T or w?

(d) Let the elevator have a mass of 1,475 kg and an upward acceleration of 2.9 m/s². Find T.

(e) The elevator of part (d) now moves with constant upward velocity of 10 m/s. Find T.
  

Is your answer consistent with your answer to part (b)?

(f) Having initially moved upward with a constant velocity, the elevator begins to accelerate downward at 1.70 m/s². Find T.

Answer 1

a)T is greater than w

this is because its accelerating upwards:

T = mg + ma

b)at constant velocity, a = 0 ; no net force, In this case

T = w

c)acceleration is downwards, the gravity already acts down, so the net force is downwards.

w is greater in this case

d)m = 1475 kg ; a = 2.9 m/s^2

T = mg + ma

T = 1475 x 9.8 + 1475 x 2.9 = 18732.5 N

T = 18732.5 N

e)T = mg + ma

T = 1475 x 9.8 + 1475 x 0 = 14455 N

Hence, T = 14455 N ; Yes consistent with answer to part (b)

f)T = mg - ma

T = 1475 (9.8 - 1.7) = 11947.5 N

T = 11947.5 N