Question

In raising a 6200-N piano with a pulley system, the movers note that, for every 2.2 m of rope pulled down, the piano rises 0.12 m .

Ideally, find the force required to lift the piano.

Answer 1

In the hydraulic press (like raising the piano with a pulley system) which depends on Pascal principle, the pressure (P) on the left side should equal to the pressure in the right side in the ideal processes.

then

`P_(1)=P_(2)`

when
`P=(F)/(A)`

note: using the capital and small symbols to different between the right and left sides

then

`(F)/(A)_(1)=(f)/(A)_(2)`

also, under the save of the energy, the work done on the left side equals to the work done on the right side

`W_(1)=W_(2)`

when
`w=F*y` where y is the distance which the body got up or down

`F*Y_(1)=f*y_(2)`

`6200*0.12=f*2.2`

thus

`f=(744)/(2.2)=338.182 N`