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 $P=\frac{F}{A}$

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

then

$\frac{F}{A}_{1}=\frac{f}{A}_{2}$

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

$f=\frac{744}{2.2}=338.182 N$