Examples of Power Calculations in Real-World Scenarios

📚 Quick Study Guide

• ⚡ Definition: Power is the rate at which work is done or energy is transferred.
• 📐 Formula: The average power ($P$) is calculated as work done ($W$) divided by time ($t$): $P = \frac{W}{t}$. It can also be expressed as force ($F$) times velocity ($v$): $P = Fv$.
• 💡 Units: Power is measured in watts (W), where 1 watt = 1 joule/second (J/s).
• 🏋️‍♀️ Work: Work done is the force applied times the distance over which it is applied: $W = Fd$.
• ⏱️ Time: Be consistent with units. Convert minutes or hours to seconds when using the standard units (meters, kilograms, seconds).

Practice Quiz

1. A crane lifts a 1000 kg car vertically at a constant speed of 2 m/s. What is the power exerted by the crane? (Assume g = 9.8 m/s²)
1. A. 9.8 kW
2. B. 19.6 kW
3. C. 20 kW
4. D. 4.9 kW
2. A runner with a mass of 70 kg runs up a hill 10 m high in 14 s. What is the runner's average power output? (Assume g = 9.8 m/s²)
1. A. 490 W
2. B. 700 W
3. C. 980 W
4. D. 1400 W
3. An electric motor does 1200 J of work in 4 seconds. What is the power developed by the motor?
1. A. 300 W
2. B. 4800 W
3. C. 1204 W
4. D. 0.0033 W
4. A car engine provides a force of 5000 N to move a car at a constant speed of 20 m/s. What is the power developed by the engine?
1. A. 100 kW
2. B. 250 W
3. C. 4 kW
4. D. 250 kW
5. A pump lifts 50 kg of water to a height of 15 m in 10 seconds. What is the power output of the pump? (Assume g = 9.8 m/s²)
1. A. 735 W
2. B. 500 W
3. C. 150 W
4. D. 75 W
6. A 60 W light bulb is left on for 2 minutes. How much energy is used?
1. A. 120 J
2. B. 3600 J
3. C. 7200 J
4. D. 180 J
7. A person pushes a box with a force of 100 N over a distance of 5 meters in 2 seconds. What is the power exerted by the person?
1. A. 100 W
2. B. 250 W
3. C. 400 W
4. D. 500 W