Power and efficiency for OCR A-level Physics
This page covers the following topics:
2. Instantaneous power
Power is defined as the rate of energy transfer and is measured in Watts, W. It can be calculated using: Power = energy transferred/time.
Instaneous power is calculated using the following formula: Power = Force × velocity.
A car of mass 1000 kg and power 74570 W is travelling at a constant speed of 12 m/s for 45 seconds. Calculate the driving force of the car.
Since the car travels at 12 m/s, in 45 seconds Distance = 45 s × 12 m/s = 540 m. Using P = E/t, 74570 W = E/45 s, so Work Done by the car = 3355650 J. Using WD = Fs, 3355650 J = F × 540 m, therefore Driving Force = 6210 N (to 3 significant figures).
An electric motor of power 150 W raises an object for a vertical height of 1.5 m at a constant velocity of 3 m/s. Using g = 9.8 m/s², find the mass of the object.
Time taken = 1.5 m /3 m/s = 0.5 s. Using P = E/t, 150 W = E/0.5 s, so Work Done by electric motor = 75 J. Using WD = Fs, 75 J = F × 1.5 m, so F = 50 N. Using W = mg, 50 N = mass × 9.8 m/s², so mass = 5.10 kg (to 3 significant figures).
Calculate the power exerted by a car travelling at a constant velocity of 23 m/s exerting a thrust of 1000 N.
A drop tower at an amusement park has a power of 253000 W. Given that the total mass of the ride and passengers is 9500 kg, calculate the time taken by the drop tower to raise the passengers to a vertical height of 15 m. Use g = 9.8 m/s².
Using W = mg, Weight of ride and passengers = 9500 kg × 9.8 m/s² = 93100 N. Using WD = Fs, Work Done by ride = 93100 N × 15 m = 1396500 J. Using P = E/t, 253000 W = 1396500 J/time, so time = 5.52 s (to 3 significant figures).
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