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 1,575 kg and an upward acceleration of 2.5 m/s². Find T.
-Is your answer consistent with the answer to part (a)?

(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 1.30 m/s². Find T.
-Is your answer consistent with your answer to part (c)?

Answer 1

Multiple questions posted, so answering only first 4 subparts:

a)

The vertical forces acting on the elevator include:

1. Tension T upwards

2.Force due to weight w ,downwards.

Also, elevator is accelerating upwards. Let the magnitude of this acceleration be a.

Using newton's second law,force=mass*acceleration, we get T-w=ma where upward direction has been taken as positive.

So,T=w+ma. So, T is greater than w.

b)

The vertical forces acting on the elevator include:

1. Tension T upwards

2.Force due to weight w ,downwards.

Also, elevator is not accelerating since velocity is constant.. So,acceleration=0

Using newton's second law,force=mass*acceleration, we get T-w=m*0 where upward direction has been taken as positive.

So,T=w. So, T is equal to w.

c)

The vertical forces acting on the elevator include:

1. Tension T upwards

2.Force due to weight w ,downwards.

Also, elevator is accelerating downwards. Let the magnitude of this acceleration be a.

Using newton's second law,force=mass*acceleration, we get T-w=m(-a) where upward direction has been taken as positive.

So,T=w-ma. So, w is greater than T.

d) If elevator has an upwards acceleration,then T=w+ma (derived in part a)

w=mg, where w is weight, m is mass, g is gravitational acceleration. So,here, w =1575*9.8=15435 N

So,T=w+ma=15435+1575*2.5=19372.5 N

Here, T is greater than w which is consistent with part a.