# What are limitations of work energy theorem ?

1. Aug 2, 2011

### vkash

what are the limitation work energy theorem ?
this theorem is very helpful in solving questions. But I think there are some limitations of this bold theorem. that is
(1) does not define the direction of velocity &
(2) does not define spontaneity of process, like say there is an body on the floor, assume it's Potential energy to be zero(PEi) if we say that without any external force it attains height h and specific kinetic energy which sums(KEf+PEf) to be zero(PEi). Finally we can say that initial PEi= final KEf+final PEf. there is nothing in these statements according to conservation of energy / work energy theorem but even a child can say from his/her common sense that it is impossible.

My question is
is my second reason correct?
&
what are other limitation of this theorem?
&
differentiate between work energy theorem and conservation of energy.
work energy theorem seems to be derived from law of conservation of energy.

2. Aug 2, 2011

### Steger

If it's on the floor and has no potential energy (and presumably no kinetic energy) then how is it getting to some height h? Is there some initial Kinetic Energy?

As to the work-energy theorem. The conservation of energy is the most infallible and fundamental tenets of physics. However, in the world of blocks and springs the truth of the work-energy theorem relies on this notion of a "rigid object" an infinitely incompressible thing. Obviously there is no such thing in reality, so if you're bouncing a ball or some such you're going to bleed energy into deforming the ball, heating it up, heating up the air, sound, etc. However, if you took that same system, closed it off (allowed no energy to enter or leave) and looked at everything at the level of atoms interacting with each other. The energy would be 100.000000% conserved.

3. Aug 2, 2011

### vkash

I want to say that, work energy theorem will not disobey if something like that occurs(as in 2nd point) since final and initial energies are same. do you got the point?
Actually it does not disobey conservation of energy (keeping Einstein laws aside) but it disobeys general thing we see around us.

4. Aug 2, 2011

### Steger

I'm afraid I really can't understand the situation you're trying to describe, there's a bit of a language barrier. You say there's a ball, on the floor, with no potential energy (and you say nothing about its kinetic energy), then suddenly it's at a height h. How is this happening? If it has no potential energy and no kinetic energy then it just sits there.

5. Aug 3, 2011

6. Aug 3, 2011

### vkash

initially the ball is at the floor and have no kinetics energy see attachment that may help.It seems that here law of conservation energy giving wrong answer(single law can't define all the things). Is my explanation that it is limitation of Work Energy Theorem correct?

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7. Aug 3, 2011

### HallsofIvy

What you are saying is wrong. If the ball goes up its potential energy goes up (becomes positive), not down. Since kinetic energy is always non-negative, there is no kinetic energy that will make the total energy zero.

8. Aug 3, 2011

### Steger

Just because two states have the same energy has nothing to do with whether the system will MOVE between the two states. A system moves along a path that minimizes its energy (essentially) at every instant. The two states you showed would NOT be connected by such a path so the system can't move between them. In order to give a ball that height work must be done on it, against gravity (as Halls_of_Ivy points out the change in potential energy from the ground can't be negative for this point). However, what you describe DOES describe a ball AT height 0 being dropped to the ground at (-h). In which case the motion does occur.

Last edited: Aug 3, 2011
9. Aug 3, 2011

### vkash

work to move ball from ground(h=0) to height h=x is -mg(x-0) (negative sign because force is in downward and motion is in upward). give it some kinetic energy so that total energy sums 0.Is it not now have 0 energy like initial position.

steger you say A system moves along a path that minimizes its energy (essentially) at every instant. I think you should add one more word that is potential energy. A system tries to have minimum potential energy(not kinetic).If i am wrong then tell me.
I like your point that two states have the same energy has nothing to do with whether the system will MOVE between the two states. Just before last reply i made i was thinking about it

10. Aug 3, 2011

### Steger

You are quite correct, the potential energy is dependent on position where the kinetic energy is not (at least not directly). Therefore, minimizing potential energy will give you the particles route through space. What I was hinting at was something called the Principle of Least (or, more correctly, Extremal) Action, which is really the central core of all of physics from which pretty much everything can be derived.