Section 4.6: Power & Efficiency

Power is the rate at which work is done or energy is transferred. Efficiency measures how effectively energy is converted into useful work.

        Power:
        \[ P = \frac{W}{t} \]
        where \(W\) is work done, \(t\) is time.
      

        Efficiency:
        \[ \eta = \frac{\text{Useful Work Output}}{\text{Total Energy Input}} \times 100\% \]
      

Example 1

A machine does 500 J of work in 10 seconds. Find the power output.

\( P = \frac{500}{10} = 50 \text{ W} \)

A motor consumes 600 J of electrical energy to lift a load doing 480 J of work. Find its efficiency.

\( \eta = \frac{480}{600} \times 100\% = 80\% \)

A force of 200 N moves an object 5 m in 2 s. Calculate power.
A machine converts 400 J of energy into 320 J of useful work. Find efficiency.
A motor lifts 50 kg vertically 10 m in 5 s. Determine power output (g=9.8 m/s²).
A device has 75% efficiency. Input energy 800 J. Find useful work.
An elevator consumes 10,000 J of energy to lift a load doing 8,000 J of work. Find efficiency.