Question

(a) How could a 500 N object be lowered from a roof using a rope which breaks if its tension exceeds 400 N, without breaking the rope? (b) Suppose the same object is hung from a spring balance attacked to the ceiling of an elevator. What is the reading of the balance when the elevator is moving upward with a constant speed of 8.40m/s ? What is the reading of the balance when the elevator is moving upward with the speed of 8.40m/s and deceleration at 3.95 m/s sq?

Answer 1

a) The mass of the object is

If the rope is lowered at an acceleration a the net force on the rope would be

We want this force to be less than 400 N

Solving this gives

Therefore if the rope is lowered at an acceleration greater than or equal to 1.96 m/s² the rope wouldn't break

b) At constant velocity, the weight of the object doesn't change. Hence the reading would be 500 N

c) When the elevator is moving up with deceleration 3.95 m/s² the reading would be