Chained winch

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

Correct answer:

F =  117.72 N

Step-by-step explanation:

$$\begin{gathered} g=9.81{\text{m/s}}^2 \\ {D}_1=20\text{cm}\to \text{m}=20:100\text{m}=0.2\text{m} \\ {r}_2=60\text{cm}\to \text{m}=60:100\text{m}=0.6\text{m} \\ {m}_1=8\text{kg} \\ {m}_2=64\text{kg} \\ {r}_1=D_1/2=\frac{1}{5}/2=\frac{1}{5\cdot 2}=\frac{1}{10}=0.1\text{m} \\ m=m_1+m_2=8+64=72\text{kg} \\ G=m\cdot g=72\cdot 9.81=\frac{17658}{25}=706.32\text{N} \\ G\cdot r_1=F\cdot r_2 \\ F=G\cdot \frac{r_1}{r_2}=\frac{17658}{25}\cdot \frac{\frac{1}{10}}{\frac{3}{5}}=\frac{2943}{25}\text{N}=117.72\text{N} \end{gathered}$$

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