Question

A tower worker at the top of a wind turbine tower is letting down a small broken part of mass 4.3 kg tied to a practically massless rope.

The top of the tower is 14.4m above the ground, and the wind is blowing at 6.3 m/s at the top of the tower and decreases linearly with height to 1.7 m/s at the ground.

She is letting the rope slide thru her leather gloves at a rate of 0.30 m/s, and the friction between the rope and her gloves is making the gloves warm. What power is being

dissipated as heat where rope is sliding on the gloves?

Answer 1

we can solve this problem in this way.

Since the rope is moving with a constant speed that is 0.30 m/s.
From this we can calculate the total time required for the mass to reach the Bottom of the Tower

     ---equat(1)

Now Since the rope is moving at constant spped that means there is no net force acting on it

From this we can calculate the force applied by the gloves to balance the Force due to gravity and it will be in the form of friction of the gloves.

So Frictionla force applied by the gloves is

and the total work done by the Glove to bring the mass to the ground is

---- equ(2)

and using these we can calculate the Power dessipated as heat