Lesson 7: Power

The rate at which energy is transferred is called power and the amount of energy that is usefully transferred is called efficiency.

When work is done on an object, energy is transferred. The rate at which this energy is transferred is called power. So, the more powerful a device is, the more energy it will transfer each second.

We can define power as the rate of doing work, it is the work done in unit time. 

Work done is measured in joules, the time taken in seconds and so power is measured in joules per seconds or watts (W). 

1 joule per second = 1 W

The SI unit of power is Watt (W). 

The power of very powerful engines is measured in kilowatts (kW) or megawatts (mW).  

1 kW = 1 kilowatt = 1000 watts

1 mW = 1 megawatt = 1 000 000 watts

Sometimes the power of motor vehicles and other machines is given in terms of horsepower (hp), which is equal to 750 watts.

The equation used to calculate the power is:

Power = work/time

Most machines are designed and built to do work on objects. All machines are typically described by a power rating. The power rating indicates the rate at which that machine can do work upon other objects. So, the power of a machine is the work/time ratio for that machine. 

As a simple example, burning one kilogram of coal releases much more energy than detonating a kilogram of TNT, but because the TNT reaction releases energy much more quickly, it delivers far more power than the coal.

A car engine is an example of a machine that is given a power rating. The power rating relates to how quickly the car can accelerate.

Suppose that a 40-hp engine could accelerate the car from 0 km/hr to 60 km/hr in 20 seconds. If this were the case, then a car with four times the horsepower could do the same amount of work in a quarter of the time.  160-hp engine could accelerate the same car from 0 km/hr to 60 km/hr in 5 seconds. 

It makes sense that a more powerful engine can do the same amount of work in less time.

Figure 1: A Porsche 911 has 379 hp and can accelerate from 0 - 60 km/hr in 4.0 seconds.  

A standard single-cab Toyota Hilux has 150 hp.  It can carry a maximum load of 1 tonne. 

A mining truck, such as the T282B, has 3,650 hp engine and a body capable of carrying approximately 400 tons.  Its maximum speed is 68 km/hr. 

Figure 2:  The T282B is the largest capacity mining dump truck in the world. It uses 227 liters of diesel per hour and has 4 m high tyres. 

Which is more powerful?  Which would be more useful to move material at a mine?

The mining truck.  A Hilux could do the work, but it will take much longer because it is not powerful enough to carry large loads unlike the mining truck which can carry 400 tons in one load. 

Personal power

A person is also a machine that has a power rating. Some people are more power-full than others. That is, some people can do the same amount of work in less time or more work in the same amount of time. 

Two students, Emmanuel and Rheema, are lifting weights. Emmanuel lifts the 100 kg barbell over his head ten times in one minute: Rheema lifts the 100 kg barbell over his head ten times in ten seconds. 

Which student does the most work?

Which student delivers the most power? 

They do the same amount of work. They apply the same force to lift the same barbell the same distance above their heads.  Yet, Rhemma is the most "power-full" since he does the same work in less time. 

Activity 1

What you will need:

A flight of stairs

Stopwatch

Measuring tape

1. Measure your weight in newtons.   (This is your mass in kilograms multiplied by 10 to convert it into newtons).

2. Measure the vertical height of the stairs.  Since you are going to lift your body against the vertical force of gravity you will need to know the height. 

3. Time how long it takes you from the bottom to the top of the stairs. 

4. Repeat with other members of the class. 

5. Calculate the work done and the power in your legs. 

Remember the equations:

work done = force x distance moved

and 

Power = work done/ time taken.

Who is the most powerful in your class?