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

86%

Step-by-step explanation:

MA= 3.33X10^2/129=2.5

IMA=38/19=2.9

e=2.5/2.9 X 100%= 86%

this is the correct answer on Plato

Answer 2

79.8 %

Step-by-step 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 = (W_(in))/(W_(out))=(4257)/(5336)=0.798`

So, 79.8 %.