Section 3.5: Power

Power is the rate at which work is done:

\( P = \frac{W}{t} \)

Where \(P\) = power, \(W\) = work done, \(t\) = time taken.

Alternate forms:
  • If a constant force \(F\) moves an object at velocity \(v\): \( P = F \cdot v \) (dot product for angled forces).
  • 1 watt = 1 joule/second (SI unit of power).

Example 1

A worker lifts a 50 kg crate vertically 3 m in 6 s. Find the power developed. (g = 9.8 m/s²)

Work done: \( W = m g h = 50 * 9.8 * 3 = 1470 \text{ J} \)

Power: \( P = W/t = 1470 / 6 \approx 245 \text{ W} \)

Example 2

A car engine exerts a constant force of 2000 N to move a car at 15 m/s. Find the power output.

Power: \( P = F \cdot v = 2000 * 15 = 30000 \text{ W} = 30 \text{ kW} \)

Practice Problems

  1. A 60 kg person climbs a 5 m staircase in 8 s. Calculate the power developed.
  2. A 500 N force pushes a box at constant speed 4 m/s. Find the power.
  3. A 2 kg object is lifted 10 m in 5 s. Compute the power.
  4. An engine exerts 1500 N to pull a car at 20 m/s. Find power output.
  5. A weightlifter lifts 100 kg barbell 2 m in 2 s. Determine the average power.
  6. A 5 kg box slides along a horizontal floor under 10 N applied force for 3 m in 2 s. Find the power.
  7. A crane lifts 2000 kg load 15 m in 30 s. Calculate power.
  8. A cyclist exerts 300 N to pedal at 6 m/s. Find the mechanical power delivered.
  9. A 50 kg mass is pulled up a slope 4 m in 4 s. Find average power.
  10. A 70 kg person jumps vertically 0.8 m in 0.5 s. Compute power output.
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