Back to P1 Home
P1 G) Power
P1 G) Power
Power is the rate of energy transfer or the rate of doing work. A powerful machine is a machine that can transfer a lot of energy in a short period of time. Power is measured in watts, where 1 watt is 1 joule of energy transferred per second. There are two ways that power can be measured; energy transferred and work done.
1) Energy Transferred
The power formula for energy transferred is shown below:
The power formula for energy transferred is shown below:
Power is measured in watts (W), energy transferred is measured in joules (J) and time is measured in seconds (s).
Example 1
A motor transfers 3.6 kJ of energy in 3 minutes. Find the power of the motor.
We find the power of the motor by dividing the energy transferred (in joules) by the time (in seconds).
Example 1
A motor transfers 3.6 kJ of energy in 3 minutes. Find the power of the motor.
We find the power of the motor by dividing the energy transferred (in joules) by the time (in seconds).
We are told in the question that the energy transferred is 3.6 kilojoules; we need to convert this to joules. 1 kilojoule is 1,000 joules, so we convert kilojoules to joules by multiplying by 1,000; the energy transferred is 3,600 joules (3.6 x 1,000 = 3,600).
The question also tells us that the motor transferred this energy in 3 minutes; we need to convert this to seconds. There are 60 seconds in 1 minute, so we can convert time from minutes to seconds by multiplying by 60; the time in seconds is 180 seconds (3 x 60 = 180).
We now have everything that we need in the correct units to work out power; we sub the energy transferred in as 3,600 and the time in as 180.
The question also tells us that the motor transferred this energy in 3 minutes; we need to convert this to seconds. There are 60 seconds in 1 minute, so we can convert time from minutes to seconds by multiplying by 60; the time in seconds is 180 seconds (3 x 60 = 180).
We now have everything that we need in the correct units to work out power; we sub the energy transferred in as 3,600 and the time in as 180.
Therefore, the power of the motor is 20 watts. This means that the motor transfers 20 joules of energy per second.
2) Work Done
The second way that we can work out power is by dividing the work done by time. The formula is:
The second way that we can work out power is by dividing the work done by time. The formula is:
Power is measured in watts (W), work done is measured in joules (J) and time is measured in seconds (s).
The only difference between the two power formulas is that the first formula uses energy transferred and the second formula uses work done. Both of these values are measured in joules, so there isn’t much of a difference between the two formulas.
The only difference between the two power formulas is that the first formula uses energy transferred and the second formula uses work done. Both of these values are measured in joules, so there isn’t much of a difference between the two formulas.
Comparing Power
We are now going to have a look at an example whereby we compare the power of 2 motors.
Question
We have two cranes (A and B) that are powered by two different motors. They are both lifting a piano that has a mass of 200 kg to the second floor of a building, which is 8 metres above where the piano is currently situated. Crane A lifts the piano to the second floor in 8 seconds and crane B lifts the piano to the second floor in 20 seconds. Find the power of both of the motors in the two cranes and say which crane has the most powerful motor.
Use gravitational field strength as 9.8 N/kg and assume that the crane lifting the piano is 100% efficient (no energy is wasted due to heat or sound).
We work out the power of the motors by dividing the energy transferred by time.
We are now going to have a look at an example whereby we compare the power of 2 motors.
Question
We have two cranes (A and B) that are powered by two different motors. They are both lifting a piano that has a mass of 200 kg to the second floor of a building, which is 8 metres above where the piano is currently situated. Crane A lifts the piano to the second floor in 8 seconds and crane B lifts the piano to the second floor in 20 seconds. Find the power of both of the motors in the two cranes and say which crane has the most powerful motor.
Use gravitational field strength as 9.8 N/kg and assume that the crane lifting the piano is 100% efficient (no energy is wasted due to heat or sound).
We work out the power of the motors by dividing the energy transferred by time.
The cranes are lifting the piano to the second floor. This means that the motors for the cranes will be transferring energy to the piano’s gravitational potential energy stores. Therefore, in order to work out the power of the motors, we need to first work out the amount of energy transferred, which is the change in energy in the piano’s gravitational potential energy store. The equation for working out change in gravitational potential energy is shown below.
In this formula, Ep is the change in gravitational potential energy measured in joules (J), m is the mass measured in kilograms (kg), g is the gravitational field strength measured in newtons per kilogram (N/kg) and h is the change in height in metres (m).
The mass of the piano is 200 kg, the gravitational field strength is 9.8 N/kg and the change in height is 8 metres. We sub these values into the formula to find the change in gravitational potential energy.
The change in energy in the piano’s gravitational potential energy store is 15,680 joules. This will be the energy transferred for both the motor in crane A and crane B because both cranes are lifting the piano the same height. We can now work out the power for crane A and crane B.
Crane A
We are told that it takes crane A 8 seconds to lift the piano. We find the power by dividing the energy transferred (15,680 joules) by time (8 seconds).
Crane A
We are told that it takes crane A 8 seconds to lift the piano. We find the power by dividing the energy transferred (15,680 joules) by time (8 seconds).
The power of the motor in crane A is 1,960 watts.
Crane B
We are told that it takes crane B 20 seconds to lift the piano. We find the power by dividing the energy transferred (15,680 joules) by time (20 seconds).
Crane B
We are told that it takes crane B 20 seconds to lift the piano. We find the power by dividing the energy transferred (15,680 joules) by time (20 seconds).
The power of the motor in crane B is 784 watts.
Compare
We now compare the powers of both of the motors. When we do this, we see that the motor in crane A (1,960 watts) is more powerful than the motor in crane B (784 watts). This is what we would have expected because crane A transfers the same amount of energy in a shorter period of time (it takes crane A 8 seconds to lift the piano, and it takes crane B 20 seconds to lift the piano).
Compare
We now compare the powers of both of the motors. When we do this, we see that the motor in crane A (1,960 watts) is more powerful than the motor in crane B (784 watts). This is what we would have expected because crane A transfers the same amount of energy in a shorter period of time (it takes crane A 8 seconds to lift the piano, and it takes crane B 20 seconds to lift the piano).