# How should I understand work?

What is the intuitive meaning of work or analogy used to understand work?

I'm able to understand math, but I can't grasp the idea of energy and work.

For acceleration, say $$+2\frac{\text m}{\text s^2}$$, we can imagine the speed of the body is incremented the previous speed by $$+2$$ each second.

For momentum, I imagine a mosquito and truck moving at same velocity and colliding with a wall. I measure momentum in terms of "Damage".

For force, say $$10\,\text N$$, I imagine a dumbbell of weight $$1\,\text{kg}$$, the feeling I get when I lift it.

### What about work and energy?

what does it mean if we did $$5\,\text J$$ of work? or $$10\,\text J$$ of energy?

Does it mean I can boil $$100\,\text{ml}$$ of water, if I converted it this $$10\,\text J$$ of energy into pure heat assuming that no heat has escaped?

What does it mean when I did $$5\,\text J$$ of work? Does that measure how tired I am when I lifted $$10\,\text{kg}$$ barbell?

What are the analogies that you use to understand or wrap your head around for understanding work or energy?

$$W = F\cdot S\cos\theta$$ doesn't help at all.

• How is this not a duplicate (11 years in)? Aug 15, 2021 at 19:15

Work is the physical concept that we use to relate force and energy. It's good to have a clear idea about 'work'.

When you push a box on a table, you give a speed to the box. So your force caused the increase of kinetic energy of the box. So your force has done a positive work on the box. If you try to stop the moving box with an opposite force, your force is slowing down the box, which means sucking the kinetic energy of the box. Therefore, your force has done a negative work on the box.

But if you try to push a wall, you can't move that wall. Therefore it is called that no energy is transferred. That means no work is done. This obeys the mathematical formula $$W=FS$$.

As a gist, work in mechanics is the relationship between force and energy.

Boiling water is related to thermodynamics. In that subject work is directly difined as

work performed by a system is energy transferred by the system to its surroundings

Thus it is easy to comprehend 'work' as a measure of energy transferred, in any subject regardless mechanics or thermodynamics or whatever.

• I have another question why are we tired when we push the wall? seems obvious but isn't the work done is zero? where did my "energy" went? Aug 15, 2021 at 12:45
• @Rambalheartremo this may solve your problem :physics.stackexchange.com/q/1984/305718
– ACB
Aug 15, 2021 at 12:53

You can think of work as any form of force times distance.

Some examples:

• Climbing up a flight of stairs (gravity and height)

• Dragging a heavy weight for many miles (friction and length)

• Push down on the long side of a lever with small force and large distance, to exert a large force and small distance on the other end of the lever.

• Pull on a pulley for a length of rope.

You can also think of it as any potential energy. Any increase in height, any way to charge a battery, heating something up to let it cool down, and burning calories. Even spinning a top and storing energy in rotational momentum is a form of work.

It's very important that you should not confuse "effort" with work as you mentioned

For force, say 10N, I imagine a dumbbell of weight 1kg, the feeling I get when I lift it.

The feeling you get as a biological organism is about the effort and some other chemical reactions in your body.

Work is rather a concept to actualize the energy transfer going on for a moving object.

Let me try to reduce them into simple terms:

Work: energy transferred

Energy: work done

They refer to each other in the classical mechanics and they need each other to be meaningful.

Let's think of an analogy given that analogies are not exactly correct but help us internalize the concept.

The analogy I would use is Car and Fuel. The fuel you put in your car, which is oil, is like your energy. You've got 5 J of energy that you can burn. All right, what happens then when you burn that energy of 5 J? You'll do some work on the object. But what's the amount? It's 5 J of work done, which can also be measured by the thrust (F) that the engine creates burning it times the displacement (d).

You've burned 5 J of energy to do 5 J of work on the car.

Having work without transferring energy is not possible as it's defined to explain the energy transfer. When we transfer energy, we actually do work.

I visualized kinetic energy for the first time by thinking about a heavy ball hitting a wall. The more velocity it has, the more damage it does. When you break, say, a wood branch, you literally transmit some of your energy to the branch, in particular to its molecules and molecular bonds, in the same way as a heavy ball would. Work can be a bit trickier to visualize: imagine you're lifting something straight up, not helped by machines or anything. When you move up your object, you apply a force in a similarly to when you break a wooden branch: you still apply a force with both of your arms. When you're not actively lifting the object, it may rest on your back, or shoulder, or hanging from your arm and you don't feel like doing any work (except for the weight but it's another feeling imo). But in the act of lifting, there is not a way you could take it up without working. Here's my explanation, hope you can get something out of it :)

Yes, intuitively it's a measure of how tired you would get, as in your example of lifting a 10 kg barbell.

A useful way is from work done = force x distance

If you lifted the barbell through a large distance (or lifted it many times) you would have done a large amount of work and be very tired.

You would also feel tired after lifting a 500 kg mass through a smaller distance.

However, energy can be converted into other forms. For the heat example, imagine how much stirring you would have to do and how tired you would feel, if you wanted to raise the 100 mL of water by 1 °C (it's actually 420 J). If you wanted to raise its temperature by 10 °C, it would be 4200 J - lots of stirring and you'd feel very tired.

The other types of energy can be obtained from the mechanical way, for example, gravitational potential energy by lifting a mass, or electrical energy by winding the handle of a dynamo - lots of electrical energy from lots of winding making you feel tired.

• When trying to push a wall, we feel tired, although no work is done. How to comprehend that?
– ACB
Aug 15, 2021 at 10:19
• I don't like your interpretation because it's misleading. When it comes to talk about conservative forces, some students ask "How comes no work is done when returning back to the initial point? I get tired!". You should not unlink work from the force involved, the system on which it is done, and the path Aug 15, 2021 at 10:19
• @ACB just lean against the wall, you could have a rest and not get tired. Aug 15, 2021 at 10:21
• @FGSUZ ithe questioner wanted a straight forward intuitive way to understand energy. Also tell your students if they were on a bike going down and then up a curved track, they could get from one point to another without any effort. Aug 15, 2021 at 10:37