Conservation of Momentum Issue

[MetxChris]

In Lab last week we ran a simple experiment involving two gliders on an air track to show that momentum is conserved in both an elastic and inelastic collision. We used our hands to begin the motion of the gliders, allowing us to have direct control over the initial velocities of each glider. I understand all of the general concepts concerning this topic, although I'm having an issue with an extra bit of instruction given by the teacher before the lab begin. Right before the lab began, the teacher instructed that we should not give the gliders too hard of an initial push, specifically because more noise will be created during the collision and more momentum will be transfered from the gliders to the air. First of all, obviously more noise is created and more momentum is transfered, but he seems to be implying that the ratio of momentum transfered in respect to the final momentum of the experiment will be noticeably larger as well. My initial feeling is that while the relationship of the transfer of momentum to air might during a collision in respect to initial momentum not be perfectly linear, by no means do I see this as being some kind of exponential function either. Would anyone be willing to shed any light on this initial matter?

 

Secondly, I wanted to calculate the momentum of air actually moved from noise of the collision and compare that value to the initial momentum of each experiment. Using the density of air and speed of sound at 20C, and 1 cm^3 as my area of initial air particle movement (which my friend said was likely extremely generous), my results showed that my initial momentums of the gliders were on average over 200 times larger than the amount of momentum transfered to air. In this sense, would considering the amount of momentum lost to air become almost irrelevant? If it is to be considered still, I would feel that we would also need to calculate for the amount of displacement caused by the uneven distribution of air holes in the air track. I've noticed that when leveling a track for a glider very well, where the glider stays in the same spot over a period of several minutes, it's location still slightly oscillates back and forth. I would think that this would cause a greater disturbance than any momentum transfered to air, before even considering the several other obvious sources of error in the experiments.

 

Also, I wanted to point out real quick that this lab was just a simple lab to test for conservation of energy during a collision. We were never at any point to check for or account for any momentum lost to noise, but rather this issue developed over a quick statement he made right before the lab started, which to me doesn't make much sense.

 

Thanks for the help!

[swansont]

It's not the momentum lost to air as much as the energy — if the sound is isotropic, there is no net momentum to it. But you assumed an elastic collision in the analysis. Since momentum and kinetic energy are related, if energy is lost to sound your calculation of momentum will be in error. I suspect this is still a small effect, as sound doesn't carry a lot of energy, but there will also be energy lost due to heating and deformation of the material at the contact point.