# Recoil differential equations

1. Jan 16, 2013

### moemag

I am trying to figure out what I am doing. Forgive me, I’m not very sharp when it comes to differential equations… or even a useful working knowledge of calculus. I understand the concepts but if I can’t figure out how to type it into my TI-89 or get Wolfram alpha to do it… I’m kind of stuck and would appreciate some assistance.

So to start:

I have a system that has a combined momentum of 11.38 kg -meters/second. At least that is what I am estimating it to be. I know the mass of the moving part, and I know how fast it is going at it's peak.

I built a test rig to hold the system, which contains a small explosive force, setting the system into motion. The system is butted against a load cell. After firing the peak force the load cell registered was 300 newtons.

How do I get from momentum… to 300 newton’s force?
I’m guessing it has to do with the spring rate of the load cell… which is very high. I believe the load cell only moves .127mm in its entire stroke and is good for. (http://www.transducertechniques.com/lpo-load-cell.aspx ... its LPO-5K)
I keep thinking it’s somewhere in the relationship 1/2 m*v^2=1/2 k*x^2… but I’m pretty sure that somehow I have to figure out how long it takes the spring of the load cell to de-accelerate the mass, thus producing a force… I just don’t know how to do that/express that mathematically.

-my first post... this seems like where I would put this question, forgive me if it belongs somewhere else.

2. Jan 17, 2013

### engnr_arsalan

Re: Recoil...

u know force.. F=Kx..find "X" displacement of srping..coz k of spring is given by manufacturer..
put "X" in the eq u gave find "v" velocity..now multiply it with mass and get momentum
now at position one at time t=0 the velocity is v=max thus mometum is max..
at state two..t=T2 velocity is v2=0 thus momentum is zero..coz all the kinetic energy has been converted into spring's potential energy..
force is rate of change of momentum i.e
F=dM/dT=M1-M2/T1-T2
u have m1= max what ever the value u calculate and m2=0,u have time t1=0 and T2 can be calculated coz force is known..
but this an approx solution..

3. Jan 19, 2013

### Jupiter6

As engnr_arsalan answered: impulse, but you need to time your experiment, not simply rely on peak force. Can you chart your force vs. time?

A second sensor such as an accelerometer (acceleration) or video(position) would really be needed to confirm results. KE is not something you can rely on. You can rely on it's derivative (MV) but you need a way to time things.

4. Feb 4, 2013

Thanks!