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Power

AP Physics 1· difficulty 4/5

A pump lifts water at 0.020 m3/s0.020\,\text{m}^3/\text{s} to a height of 15 m15\,\text{m} and delivers it with speed 5.0 m/s5.0\,\text{m/s}. Density of water ρ=1000 kg/m3\rho=1000\,\text{kg/m}^3, g=10 m/s2g=10\,\text{m/s}^2. What useful output power is required?

  • A

    P=0.25 kWP=0.25\,\text{kW}

  • B

    P=3.25 kWP=3.25\,\text{kW}

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  • C

    P=15.0 kWP=15.0\,\text{kW}

  • D

    P=3.00 kWP=3.00\,\text{kW}

Explanation

Mass flow m˙=ρQ=20 kg/s\dot m=\rho Q=20\,\text{kg/s}. Power P=m˙gh+12m˙v2=20(10)(15)+12(20)(25)=3000+250=3250 WP=\dot m gh+\tfrac{1}{2}\dot m v^2=20(10)(15)+\tfrac{1}{2}(20)(25)=3000+250=3250\,\text{W}.

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