# Worksheet: Power

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.

**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 3,000 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.

**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?

**Q9: **

A motor lifts an elevator that carries a load of mass 2,120 kg to a height of 23.8 m in a time of 16.2 s. The total mass of the elevator mechanism is 7,150 kg, including a counterbalancing weight. The elevator 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?

**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 airplane has engines that produce MW of power. The airplane 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 airplane to reach its final speed and height, assuming negligible air resistance?

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

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

**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.

**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.

**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 10,000 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)?