Question

A worker is using a pulley to lift a 33-kilogram crate. If he applies a force of 129 newtons, the crate is lifted 16.5 meters above the ground and the displacement of the rope is 33 meters. What is the efficiency of the pulley? (Given: g = 9.8 meter/second2)

Answer 1

Answer:

79.8 %

Explanation:

The energy in input to the system is equal to the work done by the worker, so:

$E_{in} = Fd$

where

F = 129 N is the force applied

d = 16.5 m is the displacement of the rope

Substituting,

$W_{in} = (129)(33)=4257 J$

The output work of the system is the gravitational potential energy gained by the crate, so

$W_{out} = mg \Delta h$

where

m = 33 kg is the mass of the crate

g = 9.8 m/s^2 is the acceleration of gravity

$\Delta h =16.5 m$ is the gain in height of the crate

Substituting,

$W_{out}= (33)(9.8)(16.5)=5336 J$

So, the efficiency of the pulley is

$\eta = \frac{W_{in}}{W_{out}}=\frac{4257}{5336}=0.798$

So, 79.8 %.