Power

1. Characterize the physical quantity power.

Solution:

Power is a physical quantity that characterizes the rate of doing work.

Power P is the work done per unit time.

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Efficiency:

The work supplied to a mechanical system per time t is called the input power Pp.

The work performed by the mechanical system per time t is called the output power P.

It holds: P < Pp    ΔP = Pp – P are the losses.

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2.The elevator motor lifts a load of mass 240 kg to a height of 36 m in 90 s with uniform motion.

  • a.) What is the motor’s output power?
  • b.) What is its input power if η = 96% = 0.96?

Solution:

Analysis:

m = 240 kg, h = 36 m, t = 90 s, η = 96%

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The motor has output power P = 960 W and input power Pp = 1000 W.

3.In what time will a crane, whose electric motor has input power Pp = 9000 W, lift a load of mass 12 tons to a height of 9 m with uniform motion, if the motor’s efficiency is η = 0.654?

Solution:

Analysis:

Pp = 9000 W, m = 12 t = 12 000 kg, h = 9 m, η = 0.654

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The crane will lift the load in about 3 minutes and 3 seconds.

4.An electric motor with input power 3.5 kW pumps water to a height of 30 m. How much water will it pump in 14 hours, if η = 60%?

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5. A hiker climbs from Štrbské Pleso (1350 m a.s.l.) to Gerlachovský štít (2663 m a.s.l.). The hiker’s mass is 68 kg, the backpack he carries has a mass of 12 kg. What was his power if the ascent took 5 hours?

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6. A cyclist rides up a hill at a constant speed. The crank length is 25 cm, the time for one pedal rotation is 2 s, and the average force on the pedal is 150 N. Determine the cyclist’s average power!

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7.A four‑engine jet aircraft flies straight and level, covering 12 km every minute. Each engine operates at a power of 800 kW. What is the magnitude of the drag force acting on the airplane?

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8.A car of mass 1.5 tons accelerates for 0.5 minutes at a constant power of 22.5 kW. What speed did it reach? (Neglect friction and drag.)

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9.The water consumption for one turbine of a hydroelectric power plant is 630 m3·s-1. The turbogenerator output is 100 MW at η = 90%. Determine the difference in water levels at the dam and below the dam!

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10.A train of mass 5·105 kg moving at a speed of 72 km·h-1 begins braking until it stops.

  • a.) How much heat was generated during braking, assuming all the work used for braking was converted to heat?
  • b.) What was the braking power if the braking lasted 40 s?

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11.The airplane has a mass of 3 000 kg. In 1 minute it climbs to a height of 1 km and reaches a speed of 180 km·h-1. Determine the engine power!

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