How did we come about dicovering energy and why is Joule its unit?

[Melac12]

When my textbook talks about energy it starts with kinetic and potential. The derivation goes like this. F=ma=m(dv/dt)=-mg then they split the derivative using chain rule
(dv/dt)=(dv/dy)(dy/dt) therefore since (dy/dt)=v we get F=mv(dv/dy)=-mg then they write mv dv= -mg dy then they integrate ∫mv dv= -∫mg dy and we get
(1/2)(mv^2)-(1/2)(mv^2)=-(mgy)+(mgy)
Then the textbook just defines kinetic and potential energy and says that J=1kg(m/s)^2

I have a hard time understanding why they did this things. If I were a scientist what would make me do all those steps then integrate and then define energy with that unit. What made them think that that derived unit represents energy? How do they know they are right? Energy is not something we see like motion and its not something we feel like force, but we know its there. And clearly energy is related to force so how did scientists put it all together?
If anyone can explain to me why this is a good way to define energy and perhaps also tell me how scientists got to it historically, it would be greatly appreciated.

 

[Dick]

When my textbook talks about energy it starts with kinetic and potential. The derivation goes like this. F=ma=m(dv/dt)=-mg then they split the derivative using chain rule
(dv/dt)=(dv/dy)(dy/dt) therefore since (dy/dt)=v we get F=mv(dv/dy)=-mg then they write mv dv= -mg dy then they integrate ∫mv dv= -∫mg dy and we get
(1/2)(mv^2)-(1/2)(mv^2)=-(mgy)+(mgy)
Then the textbook just defines kinetic and potential energy and says that J=1kg(m/s)^2

I have a hard time understanding why they did this things. If I were a scientist what would make me do all those steps then integrate and then define energy with that unit. What made them think that that derived unit represents energy? How do they know they are right? Energy is not something we see like motion and its not something we feel like force, but we know its there. And clearly energy is related to force so how did scientists put it all together?
If anyone can explain to me why this is a good way to define energy and perhaps also tell me how scientists got to it historically, it would be greatly appreciated.

Homework Statement

Homework Equations

The Attempt at a Solution

Forget about the calculus. If you can feel force then wouldn't make sense that work (energy) should be something like force*distance?

 

[SteamKing]

You have James Prescott Joule to thank for your current headache:

http://en.wikipedia.org/wiki/James_Prescott_Joule

Here is some information on joule (the unit):

http://en.wikipedia.org/wiki/Joule

 

[Andrew Mason]

When my textbook talks about energy it starts with kinetic and potential. The derivation goes like this. F=ma=m(dv/dt)=-mg then they split the derivative using chain rule
(dv/dt)=(dv/dy)(dy/dt) therefore since (dy/dt)=v we get F=mv(dv/dy)=-mg then they write mv dv= -mg dy then they integrate ∫mv dv= -∫mg dy and we get
(1/2)(mv^2)-(1/2)(mv^2)=-(mgy)+(mgy)
Then the textbook just defines kinetic and potential energy and says that J=1kg(m/s)^2

I have a hard time understanding why they did this things. If I were a scientist what would make me do all those steps then integrate and then define energy with that unit. What made them think that that derived unit represents energy? How do they know they are right? Energy is not something we see like motion and its not something we feel like force, but we know its there. And clearly energy is related to force so how did scientists put it all together?
If anyone can explain to me why this is a good way to define energy and perhaps also tell me how scientists got to it historically, it would be greatly appreciated.

These are good questions. It is not immediately obvious why energy is defined this way. It took scientists a long time - almost 200 years after Newtons laws - to realize this. Unfortunately, few introductory physics texts go into the history of how this concept evolved.

It was Joule (1818-1889) who first demonstrated the relationship between heat and work.

With this understanding that heat could be created by work, it was first realized that energy - the ability to do work - is always conserved, in some form, in any interaction. This was fundamental to the development of the field of thermodynamics. The standard unit of energy was named the Joule in recognition of the importance of Joule's contribution.

The History of Energy is quite interesting and I would recommend the wiki article.

AM

 

[arildno]

As Andrew says:
A very good question, and non-trivial.
Basically, what we learn today is the fastest way by means of logic&math to reach "energy"; that fastest way was NOT how, historically, the energy concept developed.

 

[voko]

It has been known since Galileo that the height from which a body falls is proportional to the square of its final velocity.

 

[jtbell]

It seems to me that the earliest of the energy-related concepts was "work" as force times distance, which goes back to the early 1600s in connection with levers. Think of the "law of the lever" in which force times distance is the same on both "sides" of the lever.

www.physicsforums.com/showthread.php?t=584812 (in particular post #9)

 

[voko]

In levers, the "distance" was usually understood as that perpendicular to the force. So I think it is more appropriate to link levers with torque.

It is true, though, that when a lever is in operation, the path (or the would be path) of the force is proportional to the lever's arm, so the (would be) work is indeed proportional to the lever's arm. Even though I think this was understood much later, Lagrange in his Mecanique Analytique attributed the principle (which he termed the "virtual velocity principle") to some late 16th century. He then used this principle to develop his mechanics, where energy plays a central role (even though he does not use the term).