In this worksheet, we will practice finding power as a rate of energy conversion and efficiency as a ratio of useful work output to input for a system.

**Q3: **

For how long can you play tennis on the 800 kJ of energy in a candy bar, knowing that playing tennis consumes energy at a rate of 440 W? Give your answer in minutes.

**Q4: **

Shoveling snow can be extremely taxing because the arms have such a low efficiency in this activity. Suppose a person shoveling a footpath metabolizes food at the rate of 800 W and that only of this is used by the arms.

What is her useful power output?

How long will it take her to lift kg of snow 1.20 m? (This could be the amount of heavy snow on 20 m of footpath.) Give your answer in minutes to three significant figures.

**Q5: **

For how many days can a battery that can supply J run a pocket calculator that consumes energy at a rate of W?

**Q6: **

A man of mass 80.0 kg runs up a flight of stairs 20.0 m high in 10.0 s.

How much power is required for the man to rise this far in this time?

If the man’s body has an efficiency of for running up stairs, how much power was required for the run?

**Q7: **

A girl pulls her wagon that has a mass of 15 kg along a flat sidewalk with negligible friction by applying a force of magnitude 10 N at an angle of above the horizontal. The wagon is initially at rest.

How much work does the girl do on the wagon during the first 2.0 s that she pulls it along?

How much instantaneous power does she exert at s?

**Q8: **

A dragster of mass 465.0 kg accelerates from rest to a final speed of 102.5 m/s over a distance of 415.0 m. The dragster accelerates against an average resistive force of N. What is its average power output if the acceleration takes 6.850 s?

**Q9: **

A motor lifts a lift that carries a load of mass kg to a height of 23.8 m in a time of 16.2 s. The total mass of the lift mechanism is kg, including a counterbalancing weight. The lift and the counterweight both accelerate from rest to a final speed of 3.45 m/s. What is the useful power output of the motor?

- A 75.8 kW
- B 31.3 kW
- C 101 kW
- D 33.1 kW
- E 106 kW

**Q10: **

Calculate the power output needed for a 725-kg car to climb a slope inclined above the horizontal at a constant 21.0 m/s. Wind resistance and friction totaling 744 N oppose the motion of the car.

**Q11: **

A man of mass 68 kg requires approximately J of energy from food per day to maintain his bodyweight.

What is the average power output of the man’s body?

If the man runs up a 16-m flight of stairs in 8.8 s, how many times greater is his body’s average power output while running than its average daily power output?

**Q12: **

A -kg-mass aeroplane has engines that produce MW of power. The aeroplane goes from being at rest at sea-level to moving at 250 m/s at a height of 12.0 km.

How much time is required for the aeroplane to reach its final speed and height, assuming negligible air resistance?

- A 216 s
- B 209 s
- C 233 s
- D 224 s
- E 299 s

If the aeroplane takes s to reach its final speed and height, how much useful power did the engines supply? Assume negligible air resistance.

- A 24.8 MW
- B 22.0 MW
- C 21.3 MW
- D 20.7 MW
- E 23.2 MW

The useful power from the aeroplane’s engines allow the plane to reach its final speed and height in s if air resistance is negligible. If the aeroplane takes s to reach its final speed and height, what is the average force of air resistance on the aeroplane?

- A 60.6 kN
- B 50.6 kN
- C 49.7 kN
- D 51.4 kN
- E 60.0 kN

**Q13: **

When jogging at 13.0 km/h on a level surface, a man with a mass of 70 kg converts energy at a rate of 850 W. Assuming an efficiency of for the man, determine the rate at which this man converts energy when jogging at 13.0 km/h upward along a slope inclined at above the horizontal. Assume that the friction force is the same for running on the level surface and on the slope.

**Q14: **

A cyclist in a race must climb a hill sloping at above the horizontal. The cyclist moves with a speed of 5.3 m/s. The mass of the cyclist and their bike is a total of 85 kg. What power output is required from the cyclist?

**Q15: **

An electron in a television tube is accelerated uniformly from rest to a speed of m/s. The electron’s acceleration occurs over a distance of 2.50 cm. What is the power delivered to the electron at the instant that its displacement is 1.00 cm from the point at which it began to accelerate?

**Q16: **

An appliance requires 3.45 kWh of energy per day.

What is the average power input for the appliance?

How many joules of energy must be supplied to the appliance in a year?

**Q17: **

What is the cost of operating a 5.00-W electric clock for a year if the cost of electricity is $0.0750 per kWh?

- A$6.49
- B$5.50
- C$7.25
- D$3.29
- E$9.10

**Q18: **

A horizontal force of 25 N is required to maintain a horizontal speed of 10 m/s for a 36-kg-mass crate. What is the power exerted by the force?

**Q19: **

A coal power plant consumes kg of coal per hour and produces 500 MW of power. If the heat of combustion of coal is 30 MJ/kg, what is the efficiency of the power plant?

- A
- B
- C
- D
- E

**Q20: **

Coal is lifted out of a mine through a vertical upward distance of 34 m by an engine that supplies 475 W to a conveyer belt. How much coal per minute can be brought to the surface? Ignore the effects of friction.

**Q21: **

An 850 kg mass car has a useful power output of 40.0 hp, where 1 hp = 746 W.

How much time will it take the car to accelerate from rest to a speed of 15.0 m/s? Ignore any resistive forces.

How much time will it take the car to accelerate from rest to a speed of 15.0 m/s while climbing a slope that has a height of 3.00 m? Ignore any resistive forces.

**Q22: **

A swimmer exerts an average horizontal backward force of 80.0 N with his arm during each 1.80 m long stroke.

What is his work output in each stroke?

Calculate the power output of his arms if he does 120 strokes per minute.

**Q23: **

Kanellos Kanellopoulos flew 119 km from Crete to Santorini, Greece, on April 23, 1988, in the Daedalus 88, an aircraft powered by a bicycle-type drive mechanism. His useful power output for the 234 min trip was about 350 W. If his efficiency was , calculate the food energy in kilojoules he metabolized during the flight.

- A kJ
- B kJ
- C kJ
- D kJ
- E kJ

**Q24: **

A 55.0 kg woman in a gym does 50 deep knee bends in 3.00 min. In each knee bend, her center of mass is lowered and raised by 0.400 m. (She does work in both directions.) Assume her efficiency is .

Calculate the energy used to do all 50 repetitions in units of kilojoules.

What is her average power consumption rate in watts?

**Q25: **

Energy that is not utilized for work or heat transfer is converted to the chemical energy of body fat containing about 39 kJ/g. How many grams of fat will you gain if you eat kJ one day and do nothing but sit relaxed for 16.0 h (using about 120 W) and sleep for the other 8.00 h (using about 83 W)?