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 |
See also:
Energy sources
Kinetic energy
Energy
Work
A VERSION IN WORD IS AVAILABLE ON THE SCHOOLPHYSICS USB
