Hello everyone! I have viewed and read many papers on this subject but cant find any help to understand some point about how a short impulse duration situation affects rod´s motion. To illustrate my point here is an example, A small ball hits - a very fast impulse- one end of a long rod. Now we know that the mechanical longitudinal - force carrying- propagation wave through both objects take different times to propagate through each object due tue different lengths. This period, for the wave to propagate from the rod´s first end to the other end, and then to reflect back to the rod´s original end is much longer then the period of the small ball´s wave travel. Lets assume that the ball´s impact/ impulse duration is shorter than the rod´s wave propagation period but is longer than the ball´s wave propagation period, i.e the ball hits the rod, has time to have its wave transmit/reflects and moves away, and right after is removed very quickly from the rod). Now lets see if I understand this correctly: First , in order for any object to move or- the rod in this case-, the wave from the original ball -impulse at the first end of the rod must propagate all the way to the other end of the rod and then back again to the first rod-end again. Only now when the wave has completed a full reflection that the motion force on the rod can reveal itself. Before that instant, no matter how hard the ball hits the rod, the rod itself can not move. (Of course, only local small compression and rarefaction of the rod + minor cg shifts occur during the wave propagation through the rod). Here is my main question: Now, keeping in mind that the impulse duration was shorter than the rod´s period , i.e. the ball "hit and run away" from the rod before the propagation wave inside the rod had time to reflect back. The ball is now no longer in contact with the rod. The wave in the rod is finally "after a long time" reflected back to the original rod´s first end on which the original impulse occurred, but there is no ball there touching!. Will the rod move even if the ball is no longer there touching that first rod-end ? Or will the rod only stay there since there is no ball for the rod´s reflected wave to push on? I know , I can already hear your thoughts now but that is why I am asking. Comments My point is actually not so complicated although it may very well sound so. If you are not understanding anything please dont hesitate to ask me to make anything clearer. I am surely making mistakes here so that is where your help comes in. Oh by the way, the ball rod example is just a rather inefficient bad example,. the best method to have a very short impulse( hitting an object detaching near instantaneously) would be electromagnetic, i.e a capacitor bank discharge into a coil. looking forward for your replies. Thanks. Regards
If I understand your question correctly the answer is yes. Whether the ball is touching the end or not had no bearing on the movement of the compression wave through the rod. With out the ball there to transfer the energy to, the wave will possible reflect up and down the rod a few times before the energy is dissipated.
Thanks for the reply, but I am not sure if I understand your reply fullyPlease Register or Log in to view the hidden image!. Are you answering "yes" about the compression wave or the rod as a whole? I was wondering whether the rod as a whole would accelerate and move forward or not. I know though however that the compression wave of the rod will ofcourse continue to transmit and reflect back and forth regardless of the rods own whole movement. It seems perhaps you are answering "yes" regarding the compression wave and not the rod´s own whole movement/acceleration, ha? but I may be mistaking Thanks again for your help!
You seem to be asking about how fast the rod moves -- as a reaction to compression -- at the molecular level. This mixes scales, which can be confusing. The molecules are always in motion, so you're going to have trouble deciding what "moving rod" means at this level. I don't think you stated what material the rod is made of, but obviously some materials are more rigid than others. In any case, no rod is perfectly elastic, so at least some of the force transmits "immediately" and the rod starts to move "immediately" -- at the macro scale, which is in my mind the only measurement scale which makes sense. You might be able to try to put some limits in "immediate" motion but I'm not sure how that answers the question as you posed it. It almost seems like this question is designed to be confusing. If you say so. I wouldn't say that. I would say that the rod goes into motion beginning "at the moment of the collision" and continues to ring as it accelerates forward. I disagree for the reasons stated above. For stiff materials, the energy distributes nearly ideally. But this is far too speculative to treat fairly. You would need to test the problem and measure the results. Example: Lattice dynamics has been applied to the study of the propagation of a strong, one-dimensional shock wave in a semi-infinite cubic lattice. The lattice model included the simple cubic, face-centered cubic, and body-centered cubic configurations. The interactions between various neighbors and different types of interactions, ranging from Hooke's law forces to forces corresponding to Morse-type potential functions, were considered. The equations of motion for the lattice points were solved approximately by a numerical method. The results showed that with realistic interatomic forces the computed shock velocity increased with particle velocity approximately in a linear manner, in good qualitative agreement with experimental data. However, because of the dispersive nature of the lattice, it was found that the shock wave profile was unsteady in time, and the computed stresses behind the shock front were different from those obtained under the assumption of a steady shock profile. http://onlinelibrary.wiley.com/doi/10.1029/JZ071i010p02601/abstract That depends on the material. I disagree. You would have to show why you assume this to be true. The ball has to reverse direction. It has to compete with, say, air friction. It has it's own shock wave to contend with. And you'd have to know the material of the ball -- it's modulus of elasticity, etc. Here's another example of how you might treat the problem: http://maeresearch.ucsd.edu/~vlubarda/research/pdfpapers/ijss-86.pdf You would have to solve the network equations for the system you have in mind in order to say where everything "is". I wouldn't assume that this fits a particular electrical analogue. Most analogues will break down under this kind of analysis. I suspect you'd be lucky to model your transient response very accurately. I even doubt that this level of analysis would be very repeatable from trial to trial, even if you had a nearly perfect means of measuring the effect.
Appreciating your reply A.I, Being aware of the complications and possible misunderstandings I will try to put it this way. First, the ball and the rod can be made of any material as long as they are made of the same. Yes, the periodic cg shifts and accelerations occur exactly instantly or near that with the collision depending on where the wave is in that instant. That is not what I am talking about. I am talking about the final displacement and movement of the rod as a whole after wave reflected back. When you throw a tennis ball into the air it moves some 30ft, that is the motion I am meaning. Not the compression and rarefaction of the rod. (however I could be wrong at some point so please bear with me) Can the rod as a whole fail to accelerate forward , i.e. fail to translate itself as a whole many times it´s own length, i.e. fail to move forward far away from it´s original location regardless of the magnitude of the impulse?. What I mean,: if the ball´s collision or actual contact duration with the rod is shorter than the period it takes for the wave in the rod to transmit to the other end and reflect back again.., would the rod as a whole then move away just as you hit the tennis ball translating forward many times its own length or would the rod just compress and expand and basically not move forward, do you catch my driftPlease Register or Log in to view the hidden image!? I could be wrong and complications would grow? At any rate misunderstanding is also easy here. Thanks for your help
