# A simple collision experiment and a question

1. Mar 16, 2017

### brainpushups

I recently came across this paper in The Physics Teacher that describes a handful of experiments which can be performed with common materials. The collision experiment in particular caught my eye because it seems like most collision experiments require equipment that I either don’t have the budget to purchase or the space to store. Part of this post is to simply share the article because I’m sure others will find it helpful, but I also have a question about something I’d like to add to the experiment.

In the article the author describes a simple experiment using coins (nickels) in which a ‘shooter’ nickel is flicked from a paper chute into a ‘target’ nickel. I tried the experiment with poker chips since I happen to have a bunch in my classroom. Like the nickels, the collision between two chips is nearly elastic as evidenced by the behavior of head-on collision between them. The author then suggests making the collision oblique to test conservation of momentum in the transverse direction. To do so the center-to-center distance between the position upon contact and position after skidding to a stop is measured for both the shooter and target. The square root of the ratio of these distances gives the ratio of the speeds of the chips. By measuring the angle of deflection from the initial direction of the shooter chip one can confirm that the transverse momentum is conserved. I got good results (within about 3%) for both equal mass and also for the case of a shooter that is twice the mass of the target. I did this by taping two chips together to form the shooter by placing a small tube of tape between the chips.

Since it is straightforward to find the ratio speeds after impact by taking the root of the ratio of the distances traveled I thought I’d add a component to the experiment in which students test predictions about the relative speeds of different mass ratios of chips after a head-on collision. They could do this by taping the chips in stacks like I did with the oblique collision I described above. Letting $M$ and $V$ represent the shooter’s mass and speed respectively after the collision and $m$ and $v$ represent the target’s mass and speed after the collision the ratio of the speeds after the collision is $$\frac{V}{v} = \frac{M-m}{2M}$$ which follows directly from the conservation of momentum and kinetic energy for a one dimensional collision.

So I did a few tests and the results were not good. At first I thought I made an error, but I haven’t been able to find any. Interestingly, for mass ratios of 2:1, 3:1, 4:1, and 5:1 the measurements are all about double the prediction (within 5%). Other ratios (3:2 and 5:3) the results were also misaligned with the predictions but differed by a factor of 3.5 and 4 respectively.

Am I missing something? I'm a bit surprised given the good agreement for the oblique collision with differing masses.

Last edited: Mar 16, 2017
2. Mar 16, 2017

### John Park

I wonder if KE is being lost in stretching the tape. It seems noteworthy that you're getting the biggest discrepancies in the cases where you presumably have multiple chips for both shooter and target. You could see if the post-collision speeds change for equal masses but with a varying number of chips making up both shooter and target. Can you say anything about the longitudinal momenta in the oblique case with different masses?

3. Mar 17, 2017

### brainpushups

Thanks. I thought that too. I tried some other collisions which I didn't mention. A quarter and a poker chip (masses 5.7gr and 2.2gr) and also nickel (5.0gr) and quarter which eliminated the tape. These results were also inconsistent (I didn't try oblique collisions though). I didn't try to measure what the difference in the friction coefficients is so that may help account for this discrepancy.

For the 3:2 and 5:3 mass ratios I did tape additional chips on the target. The chips sort of 'lock' together due to some ridges they have. When taped and seem pretty rigid. It's very hard to wiggle them at all with your fingers. The collision is also fairly 'soft' to make sure it stays on the paper which are some reasons I started writing off the possible effect of the tape. Maybe it's more pronounced than I thought. EDIT: I'll try using wood glue or a hard epoxy to attach a couple to see if that makes a difference. There is a little more give than I noticed at first.

Good idea about the longitudinal momenta for the oblique collision. That crossed my mind, but it was getting late. I'll have a look later today.

I also noticed that with equal mass ratios for which the chips were taped together the results were somewhat finicky. It is definitely possible to get a good nearly elastic collision, but sometimes the shooter just keeps sliding.

Last edited: Mar 17, 2017
4. Mar 17, 2017

### brainpushups

An update:

Wood glued chips work much better so it does appear the tape was part of the problem. The results were consistent this time (but still not satisfactorily predictable by assuming the collision is elastic). My best result differed 15% from prediction and the worst was about 30% different (much better than yesterday's 100% though!).

Still could be a worthwhile extension to the experiment. The oblique collisions could be a good lead in to discuss strategy in billiards. Field trip to the bar!

5. Mar 17, 2017

### John Park

Glad that things seems to be making sense. It occurred to me after I posted that if the stacked discs weren't perfectly aligned, a small area could be taking the brunt of the collision, and perhaps being distorted (and using up KE) in the process . . . maybe something to debate in the bar?