Question

The efficiency of a squeaky pulley system is 73 percent. The pulleys are usedto raise a mass to a certain height. What force is exerted on the machine if arope is pulled 18.0 m in order to raise a 58 kg mass a height of 3.0 m

Answer 1

The efficiency of the machine is defined as

$\eta = \frac{W_{out}}{W_{in}}$

Here

Work out is the work output and Work in is the work input

To find the Work in we have then

$W_{in} = \frac{W_{out}}{\eta}$

$W_{in} = \frac{mgh}{\eta}$

Replacing with our values

$W_{in} = \frac{(58)(9.8)(3)}{73\%}$

$W_{in} = 2335.89J$

The work done by the applied force is

W = Fd

Here,

F = Force

d = Distnace

Rearranging to find F,

$F = \frac{W}{d}$

$F = \frac{2335.89J }{18}$

F = 129.77N

Therefore the force exerted on the machine after rounding off to two significant figures is 130N