Chained winch

When digging a well, a chained winch is used to balance the material. An empty shackle weighs 8 kg, a full 64 kg. What force must the worker exert on the crank handle when pulling the shackle with a uniform movement from a depth of 5 m, if the shaft diameter is 20 cm and the crank length is 60 cm?

Correct result:

F =  117.72 N

Solution:

$$\begin{gathered} g=9.81{\text{m/s}}^2 \\ {D}_1=20\text{ cm}\to \text{ m}=20\mathrm{/}100\text{ m}=0.2\text{ m } \\ {r}_2=60\text{ cm}\to \text{ m}=60\mathrm{/}100\text{ m}=0.6\text{ m } \\ {m}_1=8\text{ kg } \\ {m}_2=64\text{ kg } \\ {r}_1=D_1\mathrm{/}2=0.2\mathrm{/}2={\displaystyle \frac{1}{10}}=0.1\text{ m } \\ m=m_1+m_2=8+64=72\text{ kg } \\ G=m\cdot g=72\cdot 9.81={\displaystyle \frac{17658}{25}}=706.32\text{ N } \\ G\cdot r_1=F\cdot r_2 \\ F=G\cdot {\displaystyle \frac{r_1}{r_2}}=706.32\cdot {\displaystyle \frac{0.1}{0.6}}={\displaystyle \frac{2943}{25}}={\displaystyle \frac{2943}{25}}\text{ N}=117.72\text{ N} \end{gathered}$$

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