# What was the first intuition that lead us to quantify energy with work instead of momentum?

I know where the formula of work comes from and how we get it using integration. The work formula is interesting but it was counter-intuitive for me to choose it to quantify energy. Instead I was inclined to state that energy should be F.t Is it in order to better fit the concept of potential energy? Moreover with work and kinetic energy as a scale, another counter-intuitive concept gave me trouble is that power (of an engine for instance) increases as time passes. If I use the same amount of fuel over time to produce a constant force on an object, whatever the velocity it gains, why would my instataneous power should be higher if I don't spend more energy in the process? I would have been inclined to use the constant jerk instead. I know that momentum are conserved (I can't explain why) and that a part of kinetic energy is converted and lost into thermic form. But I still don't get what lead us on the right track. I can't just swallow it whithout knowing what it is.

I don't want to define a new type of energy. I know we can't just choose as we wish. Momentum as energy scale to describe transmission of energy in all physics phenomena, would have been linearly proportional to velocity whereas kinetic energy as defined today is not linear to it. Therefore we have two really different function growth in respect to displacement and time, two different degree which means that no constant can connect them.

How come momentum is really conserved for two object. Does it not fail to account for the heat produced in a collision (known as coming from the extra amount out of the V² of the kinetic formula), the heat which can be seen as many little particles colliding, each having a momentum too, momentum created though conserved?!

• "If I use the same amount of fuel over time to produce a constant force on an object, whatever the velocity it gains, why would my instataneous power should be higher if I don't spend more energy in the process?" You're starting assumption is wrong here. The expression $P = v * F$ needs to be understood as "the power needed to maintain speed $v$ in the face of resistance $|F|$". If you are maintaining speed than kinetic energy does not increase. If you are gaining speed then P rises from that factor and rises more because the drag increases as well. – dmckee Oct 17 '16 at 17:05

Is it in order to better fit the concept of potential energy?"

Naturally, if you wish to define a new "type" of energy, then it must still have units of Joules before we can call it energy. Otherwise, we would call it something else than energy. For example momentum.

[...] another counter-intuitive concept [that] gave me trouble is that power (of an engine for instance) increases as time passes.

Not true in all cases. Power is an amount of energy per second. The power of an engine (the power that the engine delivers to move the car) will rise as the engine starts and soon reaches a steady level. Fuel is then spent to provide the energy, and that will be at a constant rate of energy per second.

If I use the same amount of fuel over time to produce a constant force on an object, whatever the velocity it gains, why would my instataneous power should be higher if I don't spend more energy in the process?

I don't understand this question. Your instantaneous power might, as explained above, reach a constant level.

I know that momentum are conserved (I can't explain why)

Momentum conservation can be derived from Newton's 3rd law. And this law is a law of nature which no one can prove. We have just seen it to be true infinitely many times, so we trust it to always be.

But I still don't get what lead us on the right track. I can't just swallow it whithout knowing what it is.

The right track to what? This question is missing a word or two before it's a question :)

• Thank you for your answer.Actually I was considering a system with no drag or frcition like a cosmonaut pushing an object in space. Energy per second is what I meant and as energy is work it increases in a manner that is not linear with respect to time, hence I wonder how power might reach a constant level – Lucas Oct 18 '16 at 13:58
• @Lucas "Actually I was considering a system with no drag or friction like a cosmonaut pushing an object in space" Ok. The answer doesn't mention friction; it works for space as well. "as energy is work " Energy might be work, yes (it can also be transfered as heat for example). – Steeven Oct 18 '16 at 14:08
• @Lucas "hence I wonder how power might reach a constant level" I don't see why you don't think this is possible. If I turn on a switch, current runs in the circuit and through the filament of a light-bulb. The filament heats up and sends out some amount of thermal energy per second in the form of light and heat. Very quickly, the added energy from the current every second equals the energy sent out every second. Then the power (the energy sent out) is constant. Same goes on for a car. It will at some point reach an equilibrium and the power is constant – Steeven Oct 18 '16 at 14:11