Is work done by friction the same as thermal energy?

[Supernejihh]

Homework Statement

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.

Homework Equations

W = Emec + E thermal

The Attempt at a Solution

 

[PhanthomJay]

Homework Statement

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.

Homework Equations

W = Emec + E thermal

The Attempt at a Solution

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.

 

[Supernejihh]

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.

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..

 

[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.

 

[asteriatic]

The work done by friction and thermal energy are not the same thing. While they may seem similar in some cases, they are fundamentally different concepts.

Work done by friction is the force applied to an object multiplied by the distance it moves in the direction of that force. It represents the energy needed to overcome the resistance of friction and maintain motion.

On the other hand, thermal energy is the internal energy of a system due to the movement of particles. It is a form of kinetic energy and is related to the temperature of the system.

In the equation W = Emec + E thermal, the Emec represents the mechanical energy of the system, which includes the potential and kinetic energy. The work done by friction is a part of the Emec, but it is not the same as thermal energy.

In the example given, the work done by friction was added to the Emec to calculate the total energy of the system, which includes both the mechanical energy and the thermal energy. This does not mean that the work done by friction is equal to thermal energy, but rather that it contributes to the total energy of the system.

In summary, work done by friction and thermal energy are two separate concepts and should not be used interchangeably. They have different definitions and represent different forms of energy.