Motor efficiency

Calculate the power input of a motor operating at an efficiency of 58% that will lift an elevator car (weighing 390 kg) with twenty boxes (each 25 kg) to a height of 85 m in 29 seconds.

Correct answer:

P =  42634.4 W

Step-by-step explanation:

$$\begin{gathered} \xi =58\%=\frac{58}{100}=\frac{29}{50}=0.58 \\ {m}_1=360\text{kg} \\ {m}_2=20\cdot 25=500\text{kg} \\ h=85\text{m} \\ t=29\text{s} \\ g=9.81{\text{m/s}}^2 \\ m=m_1+m_2=360+500=860\text{kg} \\ W=m\cdot g\cdot h=860\cdot 9.81\cdot 85=717111\text{J} \\ Q=\frac{W}{t}=\frac{717111}{29}\doteq 24727.9655\text{W} \\ \xi =\frac{Q}{P} \\ P=Q/\xi =24727.9655/0.58=42634.4\text{W} \end{gathered}$$

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