# Power and efficiency for SQA Higher Physics 1. 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. # 1

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).

6210 N # 2

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).

5.10 kg # 3

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).

5.52 s # 4

The work done by a car moving forward for 2 minutes is 1560000 J. Calculate the power of the car.

Using P = E/t, Power = 1560000 J/(2 × 60) s = 13000 W.

13000 W # 5

A car has a power of 14500 W. It travels a distance of 5 m in 1.5 minutes. Calculate the driving force acting on the car.

P = E/t
14500 W = E/(1.5 × 60)
E = 1305000 J
E = Fs
1305000 J = F × 5 m
F = 261000 N

261000 N End of page