Concrete column

A concrete column for a motorway bridge is a cuboid with dimensions 1 m × 0.8 m × 25 m. A crane must lift it to a height of 20 m. What is the minimum power of the crane's engine if the lift takes 2 minutes?

Final Answer:

P =  75.21 kW

Step-by-step explanation:

$$\begin{gathered} a=1\text{m} \\ b=0.8\text{m} \\ c=25\text{m} \\ h=20\text{m} \\ \rho =2300{\text{kg/m}}^3 \\ V=a\cdot b\cdot c=1\cdot 0.8\cdot 25=20{\text{m}}^3 \\ m=\rho \cdot V=2300\cdot 20=46000\text{kg} \\ t=2\text{min}\to \text{s}=2\cdot 60\text{s}=120\text{s} \\ g=9.81{\text{m/s}}^2 \\ W=m\cdot g\cdot h=46000\cdot 9.81\cdot 20=9025200\text{J} \\ W=Pt \\ {P}_1=W/t=9025200/120=75210\text{W} \\ P=P_1\to \text{kW}=P_1:1000\text{kW}=75210:1000\text{kW}=75.21\text{kW}=75.21\text{kW} \end{gathered}$$

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