# Power

The rate at which work is done, or the rate at which energy is converted from one form to another is the POWER, simply defined as:

Power = work done/ time taken

The units of power are watts (W) where one watt is one joule per second.

Since work done = energy converted = force x distance, we may express power as:

Power = force x distance/ time

and you should see that this is equal to force x velocity. So power may be expressed as:

Power = work done/ time taken = force x velocity

Example problem
A lorry of mass 2000 kg moving at 10 m s-1 on a horizontal surface is brought to rest in a distance of 12.5 m by the brakes being applied. Calculate the average retarding force (F).
What power must the engine produce if the lorry is to travel up a hill of 1 in 10 at a constant speed of 10 ms-1 the frictional resistance being 200 N?

Kinetic energy of lorry = ½ x 2000 x 100 = 105 J = Fx 12.5
Therefore:  F = 8000 N

On the hill, height risen per second = 1 m and distance travelled along the slope = 10 m.
Potential energy gained by lorry per second (taking g = 9.8 Nkg-1) =2000x 9.8 x 1 =19600 J.
Work done against friction per second = 200x 10 =2000J.

Total energy required per second = 21600W= 21.6 kW.

 Power of your heart = 1W Power of a rowing eight at the start = 8 HP = 8x746 W = 5968 W = 6 kW Power of a family car = 20 - 100 kW Power of a World War II fighter = 680 HP = 507 kW Power of a power boat = 112 kW at v= 20 ms-1 Power of a coach = 200 - 300 kW Power of a Lynx helicopter = 670 - 835 kW Power of a cross channel ferry = 28 000 HP = 20 MW Power delivered by a power station = 1000 MW

Student investigation
The following data refers to some production model cars.
Use it to calculate:
(a) the mean acceleration from 0-60 mph
(b) the maximum kinetic energy
(c) the force produced by the engine at top speed
 0 - 60 mph Max. power Mass Car 1 11.85 s 51 kW 1300 kg Car 2 7.25 s 110 kW 1700 kg Car 3 13.55 s 77 kW 1750 kg