# Internal Forces and External Forces

1. Dec 18, 2014

Consider a scenario where a car accelerates along a path, with no air resistance. If we model the car as a particle, we have the following equation:

$ΣW_{ext} = ΔK + ΔU$

By question is with regard to the LHS of the equation. It i my understanding that since the engine is a part of the system, "work done by the engine" is not supposed to be a part of the equation. What then causes an increase in the total energy of the system, the system being the car?

When I thought about it, there are really two external nonconservative opposing forces acting on the car: friction and air resistance. Is frictoon the "driving force", for the lack of a better term? And when we talk about "work done by the engine", is it really "work done by friction"?

2. Dec 18, 2014

### A.T.

If you model the car as a particle, then there is no engine or work done by the engine in your model. Switching between different models (levels of detail) always leads to this kind of confusion about work done.

3. Dec 18, 2014

How do we go about analyzing work and energy if we model the car as a particle?

4. Dec 18, 2014

### PhanthomJay

Well this is a good question, as it relates to modeling the car as a car and not a particle.. When accelerating, the air resistance and rolling resistance forces oppose the direction of motion, but it is the static friction force between the driving wheels and the ground that is the driving or traction force that acts in the direction of the acceleration, that is, opposite to the drag and rolling resistance forces. Funny thing is, however, that the friction force, being static, does not do any work. It's called 'pseudo' work, since it is really the engine that delivers the power to turn the wheels and do the work. Using the external work as work done by friction works fine here, even though it really doesn't do work in a real sense of the term. No friction means no acceleration, so it must exist in order for the car to translationally accelerate, regardless of the power delivered by the engine.

5. Dec 18, 2014

### Staff: Mentor

PhanthomJay is exactly right. You can calculate the "work" (pseudowork) done by friction like so:
$$F_{net}\Delta x_{cm}=\Delta (\frac{1}{2}m v_{cm}^2)$$

But don't be fooled into thinking that the friction is a source of energy. The above equation is a consequence of Newton's 2nd law, not conservation of energy.

Last edited by a moderator: Dec 18, 2014
6. Dec 18, 2014

So while friction does not really "do work", we talk about work done by friction as it is an external force in this example, right? Pseudowork, that is.

7. Dec 18, 2014

### Staff: Mentor

Yes. While static friction does no real work (in the thermodynamic sense) it is common to talk about the "work done by friction".

8. Dec 18, 2014

Thanks!
I'm curious to know more about A.T.'s statement though. When we switch to a different level of detail, how does our analysis of forces, work and energy change?

9. Dec 18, 2014

### Staff: Mentor

What is the actual source of the car's kinetic energy? (At least to the next level of detail.)

10. Dec 18, 2014

Chemical reactions in the internal combustion engine.

11. Dec 18, 2014

### Staff: Mentor

Exactly.

12. Dec 18, 2014

### A.T.

13. Dec 19, 2014

### Jano L.

Total energy of car does not increase in such process. Only its kinetic energy increases at the expense of energy evolved in the chemical reactions. Friction does no work in ordinary circumstances where the wheels roll without slipping.

From the standpoint of mechanics, the positive work done on the car is done by internal forces. Internal forces can change system's kinetic energy. Net momentum cannot be changed by internal forces, but kinetic energy can.

14. Dec 19, 2014

### A.T.

There are no wheels in your FBD, if you model the whole car as a particle, or one translating block. If you want to have static friction in your model, then you have to model the wheels as separate bodies, otherwise this friction model is inconsistent with the FBD diagram.

15. Dec 19, 2014

### Jano L.

Modelling a car as a particle is not a good idea if internal forces and their work is to be understood.

16. Dec 19, 2014

### A.T.

Maybe, but if you decide to do so, then you have to stick to it throughout your analysis. If you then find that such coarse model doesn't provide much insight, then you introduce more level of detail.

17. Dec 20, 2014

Right.