Power - UNSOLVED PRACTICE SET
Chapter: Work Energy and Power | Topic: Power
POWER - UNSOLVED PRACTICE SET
Topic: Power
Multiple Choice Questions
Q1. Power is defined as:
- Work done per unit time
- Force per unit area
- Energy per unit mass
- Work done per unit distance
Q2. The SI unit of power is:
- Joule
- Watt
- Newton
- Pascal
Q3. A machine does 1000 J of work in 5 seconds. Its power is:
- 200 W
- 5000 W
- 2000 W
- 500 W
Q4. The power delivered by a force F acting on a body moving with velocity v is:
- F/v
- F × v
- F · v
- F + v
Q5. One horsepower is equal to:
- 746 W
- 1000 W
- 550 W
- 476 W
Q6. The slope of a work-time graph gives:
- Energy
- Power
- Force
- Velocity
Short Answer Questions
Q7. Define power. Distinguish between average power and instantaneous power.
Q8. A 60 kg student runs up a staircase of height 4 m in 5 seconds. Calculate the power output. (Take g = 10 m/s²)
Q9. A pump lifts 1000 kg of water to a height of 10 m in 2 minutes. Calculate the power of the pump. (Take g = 9.8 m/s²)
Q10. In your school, a 500 W motor is used to lift a 100 kg load. Calculate the maximum height the load can be lifted in 10 seconds. (Take g = 10 m/s²)
Q11. A car engine develops a power of 50 kW. If the car moves at a constant speed of 25 m/s against a resistive force, calculate the magnitude of the resistive force.
Q12. Why are electric motors rated in kilowatts rather than in kilojoules? Explain the practical significance of power rating.
Long Answer Questions
Q13. Define power and derive its various expressions:
(i) P = W/t
(ii) P = F · v
(iii) P = dW/dt
Discuss the difference between average power and instantaneous power with examples. Why is the power rating of electrical appliances important?
Q14. A 1000 kg car accelerates from rest to 20 m/s in 10 seconds on a level road. The resistive force is 500 N.
(a) Calculate the work done by the engine.
(b) Calculate the average power developed by the engine.
(c) Calculate the instantaneous power at t = 5 s (assume uniform acceleration).
(d) If the engine efficiency is 30%, calculate the rate of fuel consumption (fuel provides 4 × 10⁷ J/kg).
(e) Discuss why the instantaneous power is not constant during acceleration.
Q15. Analyse the power requirements for different modes of transport:
(i) A cyclist climbing a hill at constant speed
(ii) A jet aircraft taking off
(iii) An elevator moving upward at constant velocity
For each case, identify the forces against which power must be supplied and derive the expression for required power.
Application-Based Problems
Q16. A hydroelectric power station has water falling from a height of 50 m at a rate of 1000 kg/s.
(a) Calculate the power available from the falling water.
(b) If the turbine-generator system has an efficiency of 80%, calculate the electrical power output.
(c) How many 100 W bulbs can this power station light up?
(d) Calculate the energy produced in one day.
(e) If the water flow rate decreases by 20% during dry season, what is the new power output?
Q17. A 70 kg athlete runs up a flight of 30 stairs, each 20 cm high, in 6 seconds.
(a) Calculate the work done against gravity.
(b) Calculate the athlete's power output.
(c) If the human body is 25% efficient at converting food energy to mechanical work, calculate the energy the athlete must consume.
(d) If 1 g of carbohydrate provides 17 kJ of energy, how many grams of carbohydrate does the athlete need?
(e) Compare this power output with the power rating of common household appliances.
Qappliances.
18. A car of mass 1200 kg moves up an incline of angle 5° at a constant speed of 15 m/s. The frictional resistance is 800 N.
(a) Calculate the component of weight down the incline.
(b) Calculate the total force the engine must overcome.
(c) Calculate the power developed by the engine.
(d) If the engine efficiency is 25%, calculate the rate of fuel consumption (fuel energy = 4.5 × 10⁷ J/kg).
(e) What power is required to maintain the same speed downhill?