Recoil differential equations

[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.

 

[engnr_arsalan]

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..

 

[Jupiter6]

How do I get from momentum… to 300 Newton’s force?

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.

 

[moemag]

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.

Thanks!

 

[alphy]

I completely understand the struggle of trying to understand and apply differential equations without a strong background in calculus. However, don't worry, I am here to help you figure out how to solve your problem!

First, let's define what recoil differential equations are. These are equations that relate the change in momentum of an object (in this case, your system) to the forces acting on it. In other words, they describe how the momentum of your system changes over time due to the forces applied to it.

In your case, you have a system with a known momentum and you are trying to understand how that relates to the force measured by the load cell. To do this, we can use the basic equation for momentum: p = m*v, where p is the momentum, m is the mass, and v is the velocity.

We also know that the force measured by the load cell is related to the change in momentum over time, or the acceleration of the system. This can be expressed as F = ma, where F is the force, m is the mass, and a is the acceleration.

Now, we can relate these two equations by using the concept of impulse, which is the change in momentum over time. This can be expressed as J = F*t, where J is the impulse, F is the force, and t is the time.

So, in your case, we can say that the impulse produced by the explosive force is equal to the force measured by the load cell multiplied by the time it takes for the system to come to a stop. This time can be calculated by using the equation v = u + at, where v is the final velocity (which we know is 0 since the system comes to a stop), u is the initial velocity (which we know from your given information), a is the acceleration (which we can calculate using the force and mass of the system), and t is the time.

Finally, we can combine all of these equations to get an expression for the force measured by the load cell in terms of the known variables:

F = J/t = (m*v - m*u)/t = m*(v-u)/t

Now, we can plug in the values we know and solve for F. This will give us the force measured by the load cell, which is equal to the impulse produced by the explosive force.

I hope this explanation helps you understand the relationship between momentum and force in your system. Remember, as