# Does an impulsive force produce any work?

1. Dec 21, 2008

### valleyman

Studying it within the abstraction of basic mechanics, with the schematization of impulsive forces (so with no effect of external forces during the impact) does an impulsive force produce any work? I've been discussing about this with a friend, as I think they don't, but we still didn't find a final solution or definition. More in particular, within an inelastic impact, do agent forces produce work?

I thought that considering that the time is considered infinitesimal there can't be any movement or shifting of an object under the effect of those forces, whereas Space = velocity * time. Conseguently, there shouldn't be any work, having that work is Work = Force * Space. This would mean also that friction forces cannot be impulsive forces, as they always generate negative work.

Am I wrong?

Thanks for interesting ,
Valleyman

2. Dec 21, 2008

### tiny-tim

Hi valleyman!

There isn't really such a thing as an impulsive force (or impulse) …

it's just a convenient way of summarising the effect of an ordinary force over a time …

the actual time is not infinitesimal … but it's convenient to say it is, and to say the force is infinite, and they have a finite product

the only forces which can never be considered impulsive are those which by their nature are perpendicular to the displacement (eg normal forces and magnetic force) …

if energy is lost or gained, then there is work done and so there is an impulse

(and useful tip: if it makes a noise, then work is done! )

3. Dec 21, 2008

### valleyman

Well, I imagined something like this, but as I said, I wanted to know the answer within the abstraction (or maybe schematization) of basic mechanics. Raw question could be "if my Physics 1 exam asks to calculate the work of an impulsive force, should I say that it doesn't produce work?

I'm not sure if i understood the sense of the answer well, but it sounds to me that you mean that in real life, while I'm asking what would happen in a hypothetical abstract environment, like those which I studied in the first year of university (that means no noise, no air, no compromises )
As I see that, in abstract environments infinitesimal time is inappreciable and so is the conseguent movement during this time (as velocity is not infinite).
Is this a wrong way to intend the schematization of basic mechanics?

Thanks for the help
valleyman

4. Dec 21, 2008

### tiny-tim

Hi valleyman!
No … impulsive force usually does work …

the typical example is a bat hitting a ball …

the ball deforms, and the bat remains in contact with it for a very short (but not infinitesimal) time …

the impulse is then calculated as the integral of force times time (and the work done is the integral of force times distance, but some energy is "lost").
Yes … as I said before, it's convenient to say that the actual time is infinitesimal, and the force is infinite, and they have a finite product.

The movement being notionally zero does not matter, since the force is notionally infinite.

5. Dec 21, 2008

### Staff: Mentor

Following up on what tiny tim said. If you have an infinite force acting over a zero distance then the work is undefined. You will have to determine the work from other considerations like the change in KE.

6. Dec 22, 2008

### valleyman

I think i've understood the point, I've lost the bet
thanks for the help