# Conservation of energy

1. Feb 28, 2014

### Miraj Kayastha

" The potential energy U is equal to the work you must do against that force to move an object from the U=0 reference point to the position r. The force you must exert to move it must be equal but oppositely directed."

The above definition is from hyperphysics.

U = -GMm/R

According to the above definition, potential energy of the earth-mass system decreases and the potential energy of the worker increases, when a mass if falling towards earth.

Then why does kinetic energy increase on falling if the energy is conserved?

2. Feb 28, 2014

### Lok

Does your in-falling mass do any work? Is there a "worker" whose potential energy somehow increases?
If so is the kinetic energy really increasing?

A falling mass can be that of an old pendulum clock. Which had a couple of unbalanced masses that drove the whole system. The bigger mass drops towards the ground decreasing it's potential energy. The Clock mechanism uses that energy to do work (it's rotation, friction etc.). All in all the mass will move at a very slow constant speed, having a very small portion of it's initial potential energy transformed into real kinetic energy.
This would be the case for a falling mass that does work, it's potential does not go completely into kinetic.

3. Feb 28, 2014

### Staff: Mentor

When a mass falls to the earth the only force acting is gravity. The gravitational potential energy decreases and the kinetic energy increases.

To conserve energy!

4. Feb 28, 2014

### FactChecker

When you say "the potential energy of the worker", that does not have meaning. The worker just does work. He is not the one gaining or losing potential energy, unless he is also the object being worked on.

5. Feb 28, 2014

### Miraj Kayastha

So the worker gains energy but the total mechanical energy is not conserved?

Last edited: Feb 28, 2014
6. Feb 28, 2014

### Staff: Mentor

No, that's just how you can define the potential at a given point. Once it's defined--you have the formula describing it--you no longer need that imaginary worker exerting a force.

7. Feb 28, 2014

### Staff: Mentor

In the case of the falling mass there is no external "worker".

8. Feb 28, 2014

### Lok

There are two cases and I don't know which you refer to.
1. Epotential=Ekinetic (free-falling mass no work done on a "worker" whatsoever)
2. Epotential=Ekinetic+Uwork (some energy is is transformed into the work of the "worker")

While in case 2 there is still some kinetic energy it is smaller by exactly the amount of work that has been done. The mass will move slower. Of course both potential energies are the same.
So energy is conserved.