Displacing an object by applying force is called work. For work to happen, force must be applied on the object and the object must cover a distance in the direction of the applied force. Power is the work done in unit time, that is, the rate of doing work.
Who is doing work?
Look at the pictures. A security guard is on duty at a gate, a girl is reading, a man is playing a madal, and a man is walking in a park. In the language of science, have all of them done work? Identify who has done work, and give your reason.
In fact, standing still while holding a load is not counted as work. This is the sentence that surprises everybody, so read it carefully. For work to happen, two things must both be true. Force must be applied to an object, and the object must cover a distance in the direction of that force. If either one is missing, no work has been done, however tired the person is.
| The person | Force applied to an object? | Did it move in that direction? | Work done? |
|---|---|---|---|
| The guard standing at the gate | Yes, his legs hold up his own body | No. Nothing moves at all | No |
| The girl reading a book | Almost none. The book is resting | No | No, although her brain is certainly busy |
| The man playing the madal | Yes, his hands strike the skin of the drum | Yes, his hands move and the drum skin is pushed in | Yes |
| The man walking in the park | Yes, he pushes against the ground | Yes, his body moves forwards | Yes, this is work done against friction |
Students reasonably object that a guard standing for eight hours has worked extremely hard, and of course he has, in every ordinary sense of the word. Here is why science draws the line where it does. Work in physics measures energy transferred to an object. If the object has not moved, no energy has gone into it, no matter how much effort was spent. The guard's muscles are burning energy the whole time, but that energy is going into his own body as heat, not into the wall or the gate. That is precisely why you can be exhausted and still have done no work in the scientific sense. So the definition is not being unfair to the guard. It is answering a different question: not how tired are you, but how much energy did you give to that object.
The formula and its unit
| Work (W) = Force (F) × displacement (s) |
The S.I. unit of work is the joule, written J. When a force of 1 N is applied on an object and a distance of 1 m is covered, then 1 joule of work has been done. So 1 J = 1 N × 1 m.
Two kinds of work with names
| Kind of work | What the force is working against | Examples |
|---|---|---|
| Work done against friction | If the force applied acts in the direction opposite to the force of friction, the work is called work done against friction. It happens whenever an object is dragged or rolled. | Walking, riding a bicycle, pushing a cart, walking while carrying a load |
| Work done against gravity | If the force applied acts in the direction opposite to gravity, the work is called work done against gravity. It happens whenever an object is lifted or thrown upwards. | Drawing water up from a well, lifting an object, walking uphill |
One useful habit follows from this table. Whenever a problem asks for work, first ask what the force is fighting. If it is fighting friction, the force is the friction force given in the question. If it is fighting gravity, the force is the weight of the object, which means you must first work out m × g. Getting that one step right solves most work problems, and getting it wrong makes them impossible.
Power: the same work, done faster
To go from one place to another, which gets there sooner, a bicycle or a motorcycle? Is the capacity of a bicycle and a motorcycle to do work the same?
Not all people or machines work at the same rate. Some people or machines can do a job in a short time, while others take longer over the same job. The reason is that the work capacity of different people or machines is different.
Datarama takes 3 hours to dig a field, while Sohan digs a field of the same area in 2 hours. What difference is there in the work they have done? Here both of them have done equal work, but Sohan has done that same work in less time than Datarama. If you look at the work done in unit time, the work Sohan does per hour comes out greater than Datarama's. Whoever completes the same work in less time has the greater power.
| Power = \( \dfrac{\text{Work } (W)}{\text{time } (t)} \) |
Work done per second, that is, in unit time, is called power. Power is the rate of doing work, and it is measured in watt. Here work is measured in joule and time in seconds, so power is measured in joule per second, and 1 joule per second is also called 1 watt.
If the power of a machine is known, we can tell how fast it does work. Saying that an object has a power of 1 W means that this object can do 1 J of work in 1 s.
| Unit | Relationship |
|---|---|
| Horse power | The power of a machine is also measured in horse power. 1 horse power = about 746 watt |
| Kilowatt | 1000 W = 10³ W = 1 kW |
| Megawatt | 1000000 W = 10⁶ W = 1 MW |
Look at the shape of the power formula and you should recognise it. Speed was distance divided by time. Velocity was displacement divided by time. Acceleration was the change in velocity divided by time. And now power is work divided by time. Four of the quantities in this unit are the same idea applied to four different things: how much of something happens per second. Once you see that, power stops being a new formula to memorise and becomes an old one wearing a different hat. It also tells you what a rate question always looks like: something has been divided by a time, so the answer will be per second, and if the time in the question is in hours or minutes you will have to convert it first.
Worked example: a crane lifting a jeep
A crane takes 20 s to lift a 1500 kg jeep up to a height of 120 m. Find the work done by that crane and its power.
| Step | Working |
|---|---|
| What is the force fighting? | Gravity, because the jeep is being lifted. So the force is the weight of the jeep. |
| Force | F = m × g = 1500 × 9.8 = 14700 N |
| Work | W = F × s = 14700 × 120 = 1764000 J |
| Power | P = \( \dfrac{W}{t} = \dfrac{1764000}{20} = 88200 \) W, which is 88.2 kW |
So the crane does 1764000 J of work and its power is 88200 W. Notice the shape of the solution, because almost every work and power problem follows it: decide what the force is fighting, find the force, multiply by the displacement to get the work, then divide by the time to get the power.
Worked example: one load, two kinds of work
A man carries a 50 kg sack of rice on his shoulder to the roof of a bus 3 m high, then drags it 4 m along the roof against a friction force of 450 N to reach the front. How much work is done against gravity, and how much against friction?
| Against gravity: the force is the weight, F = m × g = 50 × 9.8 = 490 N. Then W = 490 × 3 = 1470 J |
| Against friction: the force is given as 450 N. Then W = 450 × 4 = 1800 J |
This problem is worth studying because it shows the two kinds of work sitting side by side in one job. The height of 3 m goes with the weight, and the 4 m along the roof goes with the friction force. Pairing the wrong distance with the wrong force is the commonest mistake in this whole topic, and asking what is the force fighting here prevents it.
Worked example 1 in the textbook has Rashmila carrying 20 kg of maize 2 km to a water mill in 1 hour. The printed working computes the force as 2 × 9.8 = 19.6 N, which then gives 39200 J and 10.89 watt. The mass is 20 kg and not 2 kg, so the force should be 20 × 9.8 = 196 N. Worked through correctly, the work is 196 × 2000 = 392000 J and the power is 392000 ÷ 3600 = 108.89 watt. This is noted here so that you are not confused when the printed answers and your own working disagree. Your method was right. If you meet this question in an examination, show the full working line by line, because a correct method with the mass written clearly as 20 kg is what earns the marks.
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