Question

A pulley system lifts a 1345 n weight a distance of 0.975m. Paul pulls the rope a distance of 3.90m, exerting a force of 375N. A.What is the ideal machine advantage of the system?B.What is the mechanical Advantage?C. How efficient is the system?

Answer 1

A. IMA: 4

The Ideal Mechanical Advantage (IMA) is given by:

`IMA = (d_i)/(d_o)`

where

`d_i` is the input distance

`d_o` is the output distance

For the pulley system in this problem,
`d_i = 3.90 m` and
`d_o = 0.975 m`, so the IMA is

`IMA=(3.90 m)/(0.975 m)=4`

B. MA: 3.59

The actual mechanical advantage (AMA), or simply the Mechanical Advantage (MA), is given by

`MA=(F_o)/(F_i)`

where
`F_o` is the output force and
`F_i` is the input force. For the pulley system in this problem,
`F_i = 375 N` and
`F_o = 1345 N`, so the MA is

`MA=(1345 N)/(375 N)=3.59`

C. Efficiency: 89.8 %

The efficiency of a machine is equal to the ratio between the MA and the AMA:

`\eta = (MA)/(AMA) \cdot 100`

Therefore, in this case,

`\eta=(3.59)/(4)\cdot 100=0.898=89.8 \%`