Power A very powerful firework will produce a lot of light and sound very quickly. It converts a store of chemical energy into Light and sound after having fired itself very quickly up to a great height. We can use tools to help us do a job like saws and pick axes but that relies on our power. If we want to do the same job more quickly we can use….. power power tools.

Power tools use a bigger energy supply from petrol or electricity to convert one type of energy into the useful kind for our job. A more powerful car should convert the Chemical energy in petrol in to kinetic energy at a faster rate and therefore accelerate more quickly. So what is power? Power is the rate of doing work or energy transfer P =  W/  t Watts Measured in Watts 1 Watt is the rate of doing work of 1 Joule per second

Power can also be shown to be worked out form the following equation. Power = work done/ time Power = (Force * distance)/time Power = Force * (distance/time) Therefore… Power = Force * Velocity The questions that follow link all you have done on Energy, Power, Work done and Efficiency

Questions: (g = 10Nkg- 1 ) 1A car of mass 800kg travelling at 40ms -1 comes to rest in 10s. What is the average power absorbed by the brakes? 2How far does it travel before it stops? 3If the driver had not stopped but struck a 200kg milk float at rest and stuck to it, how fast they have moved along at? 4If instead it had hit girder which caused it to stop and flick a 100kg man into the air, how high would he have risen!

1A car of mass 800kg travelling at 40ms -1 comes to rest in 10s. What is the average power absorbed by the brakes? Initial E k = ½ mv 2 = ½*800*40 2 = 640,000 J Power = W/t = 640,000/10 Power = 64,000W

2 How far does it travel before it stops? a = (v-u)/t a = (0 – 40) /10 = -4 ms -2 x = ut + ½at 2 x = 40* / 2 *(-4)*10 2 x = 200 m

3 If the driver had not stopped but struck a 200kg milk float at rest and stuck to it, how fast they have moved along at? Assuming no external forces are acting Initial Momentum = Final Momentum m 1 v 1 = m 2 v 2 800*40 = ( ) * v v = 32ms -1

4 If instead it hit girder which caused it to stop and flick a 100kg man into the air, how high would he have risen? Momentum cannot be conserved in this collision since the man is being thrown into the air and Gravity is acting upon him. Therefore we look at the conservation of energy. Initial E k = ½ mv 2 = ½ * 800 * 40 2 = 64, 000J Final E p = mgh = 800 * 10 * h If energy was conserved then E p = E k 8,000 * h = 64,000  h = 8 m

A wheel of radius 50cm comes to rest after 314 m with a breaking force of 20N acting on it. How much energy did the wheel have to start with? The conclusion that the wheel must be conserving energy leads us to the fact that Kinetic Energy lost = work done by brakes. W = Fd W = 20 * 314 Work Done = 6280J Therefore Kinetic Energy of wheel at start = 6280 J

Efficiency This is a measure of how good a “machine” is at transferring energy from the type supplied to the type wanted. The less is wasted the more efficient it is! A car is apparently only 25% efficient as it wastes ¾ of the energy in the petrol as heat and sound! Therefore not all the energy supplied is used for the intended purpose. The most efficient machine is supposedly a person cycling uphill in the correct gear!

energy or power To calculate efficiency either in terms of energy or power you use the following equation. % Efficiency = Useful output * 100% total input total input

An Electric car has an engine that produces 2000 W but is only 40% efficient in turning that power into motion. This output will maintain a speed of 35 Kmh-1. Calculate the total drag acting on the car at this speed. Answer Input power = 2000 W Useful power output = Force * Velocity = F * (36* 1000/3600) Useful power output = F * 10 Efficiency = (Useful output/Total Input) * 100% 40 = (10F/2000)*100 F = 80 N

Sankey diagram for a power station © Pearson Education Ltd 2008 This document may have been altered from the original

 Calculation sheet 5.4  Application - WEP