Problem 256
A construction crane lifts a load of m = 1.2 t to a height h…
A construction crane lifts a load of $m = 1.2\ \mathrm{t}$ to a height $h = 18\ \mathrm{m}$ in $t = 40\ \mathrm{s}$. Friction consumes 3% of the motor's power. What power must the motor deliver?
Explanation of Method
Motor power of a construction crane.
Step 1: Useful power
\[ P_{\text{useful}} = \frac{mgh}{t} = \frac{1200 \cdot 9.81 \cdot 18}{40} \approx 5297\ \mathrm{W}. \]
Step 2: Motor power
\[ P = \frac{P_{\text{useful}}}{0.97}. \]
\[P \approx 5.46\ \mathrm{kW} \ \ (\text{useful part } 5.30\ \mathrm{kW})\]
$5.46\ \mathrm{kW}$
$\text{motor}$
$\text{lifting } 5.30$
$\text{used for}$
$\text{friction } 3\%$
$P_{\text{useful}} = \frac{mgh}{t} = \frac{1200 \cdot 9.81 \cdot 18}{40}$
Result
\[\boxed{\,P \approx 5.46\ \mathrm{kW} \ \ (\text{useful part } 5.30\ \mathrm{kW})\,}\]
Remark
Check. The original result (5.46 kW) is correct; its intermediate value 5292.6 W should be 5297.4 W, which does not change the rounded answer.