Crane counterweight weight

What is the weight of the counterweight of a crane that lifts a 20 t weight? The arm's length is 15 m, and the arm's length with the counterweight is 10 m. Write the answer in tons.

Final Answer:

m₂ =  30 t

Step-by-step explanation:

$$\begin{gathered} m_1=20\text{t} \\ a=15\text{m} \\ b=10\text{m} \\ {M}_1=M_2 \\ {F}_1\cdot a=F_2\cdot b \\ {m}_1\cdot g\cdot a=m_2\cdot g\cdot b \\ {m}_1\cdot a=m_2\cdot b \\ {m}_2=\frac{a}{b}\cdot m_1=\frac{15}{10}\cdot 20=\frac{15\cdot 20}{10}=\frac{300}{10}=30\text{t} \end{gathered}$$

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