Concrete column

The concrete column of the highway bridge has the shape of a block with dimensions of 1m x 0.8m x 25m. It should be lifted by crane to a height of 20m. What is the power of his engine if the lifting takes 2 minutes?

Correct answer:

P =  75.21 kW

Step-by-step explanation:

$$\begin{gathered} a=1\text{ m } \\ b=0.8\text{ m } \\ c=25\text{ m } \\ h=20\text{ m } \\ \rho =2300{\text{kg/m}}^3 \\ V=a\cdot b\cdot c=1\cdot 0.8\cdot 25=20{\text{m}}^3 \\ m=\rho \cdot V=2300\cdot 20=46000\text{ kg } \\ t=2\text{ min}\to \text{ s}=2\cdot 60\text{ s}=120\text{ s } \\ g=9.81{\text{m/s}}^2 \\ W=m\cdot g\cdot h=46000\cdot 9.81\cdot 20=9025200\text{ J } \\ W=Pt \\ {P}_1=W\mathrm{/}t=9025200\mathrm{/}120=75210\text{ W } \\ P=P_1\to \text{ kW}=P_1\mathrm{/}1000\text{ kW}=75210\mathrm{/}1000\text{ kW}=75.21\text{ kW}={\displaystyle \frac{7521}{100}}\text{ kW} \end{gathered}$$

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