Recent content by Jpcgandre

Ok, thank you for the help. ##F_{net}## for me is the resultant in a segment of the rod. I can make it as small as I wish to that the approximations I assume in this segment (namely velocity profiles) don't affect the overall accuracy of the motion.

But from ##F_{net}## I can also get the displacement of the top and bottom of the section I'm analysing by the material deformation of the rod. I can use Runge-Kutta or finite difference methods to estimate this motion. This may be sufficient for me. About the velocity ##\frac...

Thank you for all the replies. One thing not clear yet is that it is my interpretation that I can divide the determination of the motion of rod/hammer or rod/ground sort of problems in two components: 1- Wave component, where the ##u_{w}(x,t)## from the wave is given by the wave function. 2-...

@Dave my point on the constant acceleration equation was for me to get a first insight of how to work with the wave equation with a simple case. If a reference is available can you point it to me? Thank you very much

THanks Arjan82 for the clarifications! I will have to go deeper into the wave equation and ways to solve it for my problem which is the impact between two deformable objects (the rod example was just a simple proxy).

Thanks for the inputs. Yes, I meant local deformations and displacements. Yes, I know the initial conditions of the hammer or the drop of the rod and I was using them in my model. Yes, I am talking of longitudinal waves :) and finally yes my ##dt## is very very small just for that reason. I'm...

Thanks Dale, is there a way to get from the wave equation the classic motion equation of an object under constant acceleration i.e. ##u = u0 + v0*t + 1/2*a*t**2## ?

@Dale Ok, thanks. This my starting point. Just one follow up question. This equation remains valid as long as not all rod is affected by the wave, or even after this occurs it's still the equation to solve to get the displacements? In other words, when do I have to use F=m*a? Thanks

@Dale yes I have an engineering background. I've a python code which I've been working for some days now which I want to use. It's "working" without computer errors but it's not working because of issues in the physical modelling of the problem.

@Dale I want to compute the deformation, displacement and impact force over time.

Just to add another possible use of F=m*a: 3) The affected mass at time instant $t_{2}$ and the velocities at time instants $t_{2}$ and $t_{1}$ Here mass will be the same, multiplied by the velocities' values existing at time instants $t_{2}$ and $t_{1}$ $$F_{net}|t_{2}*dt = M|t_{2}*(v|t_{2}-...

Imagine a long deformable rod which has just been hammered on the top end (the bottom end is clamped to Earth). Consider a time interval $dt = t_{2} - t_{1}$ in which the pressure wave is traveling somewhere within the length of the rod (meaning some portion of the object has already "felt" the...

Thanks, having though a litlle bit about this I think Eq. (2) in my original post is wrong. For the scenario I defined at the end of my original post: Using Eq. (1), one gets from the ##Impulse = Change of momentum## theorem: 1) Before the pressure wave reaches Earth: Net force on object B...

Hi Berkeman, I gave it a shot, but not sure if Latex is showing up correctly... I see the "code" and not the intended result. Added links.

I'm struggling with trying to find how conceptually need demand and capacity to be conciliated during impact. In particular, I find two different formulas in papers and websites dealing with impact. In all cases, they state that there are two forces acting on objects on impact, where they...