Page 93 - Physics Coursebook 2015 (A level)

Chapter 5: Work, energy and power
WORKED EXAMPLE
6 The motor of the lift shown in Figure 5.18 provides a force of 20 kN; this force is enough to raise the lift by 18 m in 10 s. Calculate the output power of the motor.
Step1 First,wemustcalculatetheworkdone: work done = force × distance moved
=20×18=360kJ
Step 2 Now we can calculate the motor’s output power:
power= workdone = 360×103 = 36kW
time taken 10
Hint: Take care not to confuse the two uses of the letter ‘W’:
W = watt (a unit)
W = work done (a quantity)
So the lift motor’s power is 36 kW. Note that this is its mechanical power output. The motor cannot be 100% efficient since some energy is bound to be wasted as heat due to friction, so the electrical power input must be more than 36 kW.
Moving power
An aircraft is kept moving forwards by the force of its engines pushing air backwards. The greater the force and the faster the aircraft is moving, the greater the power supplied by its engines.
Suppose that an aircraft is moving with velocity v. Its engines provide the force F needed to overcome the drag of the air. In time t, the aircraft moves a distance s equal to v × t. So the work done by the engines is:
It may help to think of this equation in terms of units. The right-hand side is in N×ms−1, and Nm is the same
as J. So the right-hand side has units of J s−1, or W, the unit of power. If you look back to Question 18 above, you will see that, to find the power of the car engine, rather than considering the work done in 1 s, we could simply have multiplied the engine’s force by the car’s speed.
Human power
Our energy supply comes from our food. A typical diet supplies 2000–3000 kcal (kilocalories) per day. This is equivalent (in SI units) to about 10MJ of energy. We need this energy for our daily requirements – keeping warm, moving about, brainwork and so on. We can determine the average power of all the activities of our body:
average power = 10 MJ per day
= 10 × 106 = 116 W 86 400
So we dissipate energy at the rate of about 100 W. We supply roughly as much energy to our surroundings as a 100 W light bulb. Twenty people will keep a room as warm as a 2 kW electric heater.
Note that this is our average power. If you are doing some demanding physical task, your power will be greater. This is illustrated in Worked example 7.
Note also that the human body is not a perfectly efficient system; a lot of energy is wasted when, for example, we lift a heavy load. We might increase an object's g.p.e. by 1000 J when we lift it, but this might require five or ten times this amount of energy to be expended by our bodies.
QUESTION
19 In an experiment to measure a student’s power, she times herself running up a flight of steps. Use the data below to work out her useful power.
number of steps = 28 height of each step = 20 cm acceleration of free fall = 9.81 m s−2
mass of student = 55 kg time taken = 5.4 s
work done = force × distance W = F×v×t work done
and the power P (= time taken) is given by: P=W=F×v×t
tt
and we have: P=F×v
power = force × velocity
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