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AP Physics 1· difficulty 4/5

A car of mass m=1200 kgm=1200\,\text{kg} ascends a 5.0∘5.0^\circ incline at constant speed v=20 m/sv=20\,\text{m/s}. Air drag and rolling resistance combined equal 400 N400\,\text{N}. What engine output power is required? (use g=10 m/s2g=10\,\text{m/s}^2, sin⁡5∘≈0.087\sin 5^\circ\approx 0.087)

  • A

    P≈28.9 kWP\approx 28.9\,\text{kW}

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  • B

    P≈8.0 kWP\approx 8.0\,\text{kW}

  • C

    P≈12.0 kWP\approx 12.0\,\text{kW}

  • D

    P≈24.0 kWP\approx 24.0\,\text{kW}

Explanation

Driving force balances mgsin⁡θ+fmg\sin\theta+f: F=(1200)(10)(0.087)+400=1044+400=1444 NF=(1200)(10)(0.087)+400=1044+400=1444\,\text{N}. Power P=Fv=1444×20≈28.9 kWP=Fv=1444\times20\approx 28.9\,\text{kW}.

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