# Power and Efficiency

In previous lesson, we have discussed energy, including the kinetic energy, the potential energy, the principle of conservation of energy and the work energy model. In this lesson, we are going to discuss power, equation of power, efficiency and equation of efficiency.

In SPM, there are 3 points that you need to know about power:

1. What is power?
2. What is the unit of power?
3. What is the equation of power? And the related calculation questions.

What is power? Power is defined as the rate at which work is done. If you still remember, when we use the word “rate” in our SPM physics, what we mean is “rate of time”, and “rate of time” means how fast a change happen. Therefore, rate at which work is done means how fast the work is done.

Power is a measure of how fast a work is done. For example, there are 2 machines: machine A and machine B. Machine A can do 1000J of work in 5s. In other words, it can do 200J of work in 1s. This is how fast it can do the work – 200J in 1s. Therefore, we say the power of machine A is 200J/s, meaning it can do 200J of work in 1s.

Machine B can do 600J of work in 4s. In other words, it can do 150J of work in 1s. Therefore, the power of machine B is 150J/s. This is how fast machine B can do work – 150J in 1s.

Which machine has greater power? Machine A. Why we say the power of machine A is higher than machine B? Because machine A can do work faster than machine B.

Power is a measure of how fast a machine does work or how fast a work is done. It is a measure of how much work is done in 1 unit of time. Therefore, in equation, we write P = W/t, where P is the power, W is the amount of work done and t is the time taken to do the work.

For example, a machine can do 24,000J of work in 1 minute. 1 minute is equivalent to 60s. Therefore, the power, P is equal to 24,000J/60s, which is equal to 400J/s. The power of the machine is 400J/s. 1 J/s is also called 1 Watt, denoted by the symbol, W. Watt is the SI unit of power. Therefore, the power is equal to 400W.

In previous lesson, we have discussed the work-energy relationship, where the amount of work done is equal to the amount of energy change. Since amount of work done and the amount of energy change are equal, we can also say that power is a measure of how fast an energy change. In equation, we write this as P = E/t, where E is the amount of energy change. The figure shows an electric motor lifting a box of mass 5.0 kg. The motor takes 4 s to lift the box to a height of 0.8 m. What is the power of the motor? [Assume g = 10 ms-2].

As usual, let’s list down what we have. The mass, m = 5.0kg; the time taken for the motion, t = 4s. The height moved by the object, h = 0.8m. We are asked to find the power of the motor.

Power, P = W/t. Well, if you still remember, work done by a force against the force of gravity is given by the equation W = mgh. Let’s rewrite the equation here. m = 5kg; g = 10 m/s2; h = 0.8m. Therefore, work done = 40J. Plug in this number into the equation of power. t= 4s. Therefore, the power of the motor is equal to 10J/s or 10W.

There are 2 points that you need to know about efficiency:

1. What is meant by efficiency?
2. Equation of efficiency or how efficiency is calculated?

The efficiency of a device is defined as the percentage of the energy input that is transformed into useful energy. For example, the function of a bulb is to transform electrical energy into light energy. Electrical energy is the energy input, light energy is the useful output energy. However, in the process of converting electrical energy into light energy, a lot of heat energy will be produced. The heat energy is not what we want. It is an undesired output. It is a waste of energy.

If 100J of energy is given to a bulb, and the bulb converts the electrical energy into 10J of light energy and 90J of heat energy, then the useful output is only 10% of the input energy. Therefore, the efficiency of the bulb is 10%. Efficiency is the percentage of the energy input that is transformed into useful energy. The appliance is said to be ideal if the efficiency is 100%.

Efficiency can be represented by the equation Efficiency = Eout/Ein x 100%, where Eout is the amount of useful output energy and Ein is the amount of input energy.

The efficiency of a device can also be calculated in terms of useful power output and power input. It is the percentage of the input power that is transformed into useful output power. Therefore, it can also calculated by the equation Efficiency = Pout/Pin x 100%, where Pout is the amount of useful output power and Pin is the amount of input power.

As usual, let’s list down all the information that we have. The mass of the pile head, m = 200kg. It is moved to a height h = 10m. The time for the action, t = 20s. Energy input to the pile driver, E sub in is equal to 40kJ or 40,000J. We are asked to find the output power.

Power is equal to Work done/ time. It this case, work is done against gravity. Therefore, we can calculate work done by using the equation W = mgh. Let’s plug in the numbers. m = 200kg; g = 10 m/s2 and h = 10m. Therefore, the work done is 20,000J.

This is not yet the answer because what we want to find is the output power. Let’s rewrite the equation down here. Work done is equal to 20,000 and the time taken is equal to 20s. Therefore, the output power is 1,000W.

In question b., we are asked to find the efficiency. Efficiency is equal to output energy over input energy x 100%. Output energy is 20,000J, input energy is 40,000J. Therefore, the efficiency of the pile driver is 50%.