# Is work done by friction the same as thermal energy?

1. Feb 22, 2012

### Supernejihh

1. The problem statement, all variables and given/known data

I ask this because my initial assumption was that work done by a non-conservative force (friction in this case) is also equal to thermal energy. However, in my book, it gave an equation with W = Emec + E thermal. They also had an example where they added up the work and the Emec, which in the example was the work done by friction, to get E thermal. This confuses me because I thought work done by friction was equal to E thermal. If they are not, can someone please explain why? Thank you.

2. Relevant equations

W = Emec + E thermal

3. The attempt at a solution

2. Feb 22, 2012

### PhanthomJay

This equation is not correct. The work done by non-conservative forces is the negative of the change of other energy besides mechanical energy, where other energy includes thermal, sound, or chemical energy, etc.

Total energy of a system is always conserved. This implies that
$\Delta U + \Delta K + \Delta E_{other} = 0$, where $\Delta U + \Delta K$ represents the change in mechanical energy of the system.

Since by the work-energy theorem

$W_c + W_{nc} = \Delta K$, and since
$W_c = -\Delta U$, then substituting these 2 equations into the first yields
$W_{nc} = -\Delta E_{other}$

If friction is the only non conservative force acting, and if we ignore sound, chemical, light, and all other forms of non-mechanical energy except heat, then

$W_{friction} = -\Delta E_{thermal}$

In general, friction mostly causes a change in thermal energy, but there is sound energy as well, and some other forms of energy change.

3. Feb 22, 2012

### Supernejihh

I can kinda understand what you are saying, but the equation is somehow in the book. In the book's example, they found the work done by the force to be 20J. They wanted to find the increase in E thermal.

They used W = E mec + E thermal => E thermal = W - E mec.

The work was 20J and the E mec was simple the change in KE due to the fact that there was no potential energy. The change in KE turned out to be -2.2 J, which translates to 20-(-2.2) = 22 J.

My first try at this was that the change in thermal energy would just be the change in E mec, which is the change in KE, due to no potential energy. This led me to have an answer of -2.2 J; I thought 2.2J was the change in thermal energy, but I was wrong..

4. Feb 23, 2012

### PhanthomJay

Where does W = 20 J come from? There must be other forces acting besides friction that do work, Please state the problem in its entirety.