Question

A pulley system has an efficiency of 75.2 percent.
The acceleration of gravity is 9.81 m/s
2
.
How much of the rope must be pulled in if
a force of 549 N is needed to lift a 130 kg desk
2.01 m?
Answer in units of m

Answer 1

\[G=mg = 130 kg \times9.81 \frac{ m }{ s^2 } = 130 \times 9.81 N\]
Formula used, since amount of work (energy needed) is same :
\[Work = F \times s =\eta \times W \]
\[130 \times9.81 \times 2.01 = 0.752 \times (549 N \times s) \, (Nm)\]
Solve for distance of rope s:
\[s = \frac{130 \times9.81 \times 2.01}{0.752 \times 549 N} = .. \, (Nm)\]

Answer 2

Additions
\[s=\frac{130×9.81×2.01}{0.752×549}m \approx 6.21 m\]

Answer 3

thank you so much :)

Answer 4

First the needed work to lift 130 kg up 2.01 meters is:
\[W=Fs=mgs = 130 kg \times9.81 \frac{ m }{ s^2 } \times 2.01 m= 130 \times 9.81 \times 2.01 Nm\]

Answer 5

There is some clutter so I thought about reposting the whole thing ... since I couldn't edit the post once posted ..