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I recently came across https://www.physics.uoguelph.ca/~jlhunt/morph/5exp.pdf 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.
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.
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