Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

I did a lab today in Physics in which we launched ball from a spring loaded cannon directly into a pendulum that captured the ball, held it, and swung upwards with it (representing a totally inelastic collision). One question in particular has confused me:

If the collision between the projectile and pendulum had lasted 1 millisecond, what would the average force have been which the projectile exerted on the pendulum for the long-range case?

My attempt at a solution is as follows: From all the searching I've been doing online, I've found the equation $F = {{p_f}-{p_i}\over {t}}$. I know $p_f$, $p_i$, and I'm given t. Is my understanding right? Can I go right ahead and crunch these numbers, or do I have an incorrect equation?

share|improve this question
1  
Hi Mike, and welcome to Physics Stack Exchange! You're close to having a really good question here; the problem is that you just posted the problem but didn't show any attempt to solve or simplify it. As the FAQ says, we don't answer your homework-like questions for you. This is a site for conceptual questions, so what you should do is focus on the particular physical misunderstanding that's keeping you from solving this question yourself, and ask about that. See meta.physics.stackexchange.com/q/714 for more info. Once you fix that, I'll be happy to reopen this. –  David Z Apr 16 '12 at 21:45
    
@David I have made it as general as I think I can, and even found something I think might be the solution. –  Mike Gates Apr 16 '12 at 22:14
    
Great, that's definitely a much better question. –  David Z Apr 16 '12 at 22:30
    
You are right.. –  leongz Apr 17 '12 at 1:57
    
@DavidZaslavsky: Is there any way to answer this without giving the full answer? It's just two formulae--there's no way to "hint" it IMO. Of course, I could explain impulse, but it still amounts to a full solution. –  Manishearth Apr 17 '12 at 3:42

1 Answer 1

up vote 1 down vote accepted

Yep, average force $\langle F \rangle=\frac{p_f-p_i}{t}$

There are two things going on here:

Impulse

For any collision, it is convenient to define a quantity called "impulse". Most collisions consist of large, varying forces acting in a short time. These are hard to calculate, so they can be encoded into the "impulse". The impulse is the change of momentum on a body during a collision. Due to the identity $\vec F=\frac{\rm d\vec p}{\rm dt}$, we get:

$$\vec J=\Delta \vec p=\int\rm{d}\vec p=\int\vec F\rm{d}t$$

Impulses are pretty useful in multi-body problems. Especially when string/friction/etc are present; since we can use them in place of forces and conserve momentum.

Time-averaging

For any quantity $X$ dependant on time, the time average of the quantity is:

$$\langle X\rangle=\frac{\int X\rm{d}t}{\int \rm{d}t}$$ with limits of integration as the time you want it to be averaged over.

In this case, the numerator becomes the impulse (change in momentum).

Note that for any quantity $X=\frac{\rm{d}y}{\rm{d}t}$, $\langle X\rangle=\frac{\Delta y}{\Delta t}$

This is useful for average speed (total distance traveled by total time), average acceleration, and, of course, average force.

share|improve this answer
    
Thank you for the exceptional answer! Very helpful and good to know. –  Mike Gates Apr 17 '12 at 11:47

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.