# Work <-> Forces

1. Feb 20, 2014

### ahyaa

Hello all,

I was wondering if it was possible to have energy without an associated force. More specifically, can there be an energy change in a system without a net force? From what I know, this SHOULD be impossible because energy is the integral of the work function which depends on force. On the other hand, would it be correct to say it is possible to have net forces acting on a system with no net energy change?

2. Feb 20, 2014

### Andrew Mason

You can have energy without an associated force. But, at the macroscopic level at least, work cannot be done with that energy without a force being applied through a distance.

At the quantum level it gets a little murky. The concept of force is not as clear. For example, when an atom absorbs or emits a photon, there is a change in momentum of the atom corresponding to the momentum of the photon emitted or absorbed. But if you contemplate that change being caused by a Newtonian force of the photon on the atom one would have to find that there is a force applied by the atom to the photon. But, unfortunately, the Newtonian concept of force does not really apply to a photon.

AM

3. Feb 20, 2014

### ZapperZ

Staff Emeritus
Show example where you think such a thing is possible.

Zz.

4. Feb 20, 2014

### ahyaa

Wow, interesting, thanks!!

I think I should have re-phrased my original post; I was wondering if it's possible for a system to have an energy change WITHOUT a net force acting over a distance.

I actually don't have my own example of where that would be possible, I was just purely curious.

Some scenarios that did make me think of this:

1) A figure skater pushes off a wall (the system: figure skater and wall). A normal force is exerted on her by the wall, yet no work is done on her by the wall, because there is no displacement of her hands at the same time the normal force of the wall pushes on her hands. Although there is no net work done by the wall, I learned that for this scenario, there is still an energy change associated with the wall's normal force. The energy change here is that of chemical energy the skater metabolizes into kinetic energy.

So, in this scenario, if I'm analyzing this correctly, there's work done by the skater because there's no displacement of the skater's hands, which is the object on which the wall's normal force acts. This is pretty intuitive.

2) Another scenario is in thermodynamics - a change in thermal energy. However, I know that thermal energy is caused by collisions of particles, which exert forces on each other during momentary 'inelastic' periods of their collisions. So there are atomic "normal forces" on each other when two particles of different speeds collide. Thus changes in thermal energy are due to these collisions, so there are still forces acting here even though it's not obvious.

So, other than what Andrew Mason presented I wouldn't have any actual cases in which there would be no energy change associated with a force*displacement.