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/s^{2}. 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/s^{2}.
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**

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