Efficiency Physics Example 2

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Example 2

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An electric motor with 85%85\% efficiency lifts a 200 kg200 \text{ kg} load by 10 m10 \text{ m}. How much electrical energy is consumed? Use g=10 m/s2g = 10 \text{ m/s}^2.

Solution

  1. 1
    Useful work output: Wout=mgh=200×10×10=20,000 JW_{\text{out}} = mgh = 200 \times 10 \times 10 = 20{,}000 \text{ J}.
  2. 2
    Using efficiency: η=WoutWin\eta = \frac{W_{\text{out}}}{W_{\text{in}}}, so Win=WoutηW_{\text{in}} = \frac{W_{\text{out}}}{\eta}.
  3. 3
    Win=20,0000.8523,529 JW_{\text{in}} = \frac{20{,}000}{0.85} \approx 23{,}529 \text{ J}

Answer

Win23,529 JW_{\text{in}} \approx 23{,}529 \text{ J}
Because the motor is not perfectly efficient, it must consume more electrical energy than the useful work output. The difference is wasted as heat in the motor.

About Efficiency

The ratio of useful output energy (or power) to total input energy, expressed as a percentage — always less than 100% due to energy losses.

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