Question

A crane is used to lift $10000kg$ of coal from a mine $100m$ deep. If the time taken by the crane is $1hr$, then find the power of the crane, assuming the efficiency of the crane to be $80$%.
($g=9.8m/s^2$) :

• A. $2567$watt
• B. $2403$ watt
• C. $3403$ watt
• D. $3761$ watt

Answer 1

Answer: (C)

$3403$ watt

We are given that the mass(m) of the crane = 10000 kg and displacement(s) = 100m

Thus, we have Work done $=F\times s$

= $(10000\times 9.8)\times 100$

= $98\times {10}^5$ joule

We also know that power is work done in the given time or $Power=\frac{w}{t}=\frac{98\times {10}^5}{3600}=2.722\times {10}^3$ watt

Now, Efficiency= $\frac{Powerusedtoliftload}{Totalpower}\times 100$

$\Rightarrow P=\frac{2.722\times {10}^3}{80}\times 100=3403watts$

Thus, we have power of the crane ($P$) to be $3403$ watts.