# Momentum (apparently) not conserved in one of my class' experiments

I am a TA for an introductory mechanics course. We performed an experiment yesterday examining two-dimensional collisions. One of the things we hoped to show in the course of this experiment is that in such collisions, momentum is conserved. Oddly, one of my groups got a result where the momentum was significantly not conserved. After going over their calculations, experimental setup, and data collection, I could not understand their anomalous result.

The experiment is quite simple. We have a track set up on a table. The track begins vertically, curves, and then ends up horizontal. The horizontal part runs just off the edge of the table. A projectile marble is placed on the top of the track and released. At the bottom it collides obliquely with a target marble. Both marbles then fall to the ground, and the position they hit the ground is recorded using carbon paper on a large sheet of drawing paper. Since there are no horizontal forces acting on either marble once they collide, we expect that the horizontal components of momentum will be conserved.

To get the initial momentum, the students are told to allow the projectile marble to fall to the floor unimpeded by the target marble. They repeat this process ten times, draw a circle around the points that the marble lands, and use the center of the circle as the average position that the marble landed. The circles had a typical diameter of 1.5 cm. They put the origin directly below the point of collision. Finding the origin is accomplished using a plumb bob. Connecting the origin with the center of their circle gives them their x-axis. Thus, the coordinate system is chosen so that all of their mometum should be on the x-axis. The y-axis is drawn using a protractor. The mass of the projectile (and target) is measured using a scale, and the time of flight is measured by measuring the height of the track and using kinematics. This gives them all the information they should need to find the initial momentum.

The final momentum is found using a similar process. You simply record where both the target and projectile marbles land, and calculate.

Now, if a group had two identical marbles, we would expect the absolute value of the y-components of where they land to be equidistant from the x-axis and on opposite sides of the x-axis, as this is what ensures that there is no momentum in the y direction. I had a group have this exact scenario, except the y-component of their target marble's position was -19 cm, and their projectile marble's was 8.5 cm. I simply do not understand how to explain this. I, and another TA checked where they drew their origin, and we agreed that their origin was drawn reasonably correctly. We checked their data. Their projectile (impeded and unimpeded) and target were landing where they indicated on their drawing paper. The marbles were not different in any way to the naked eye. The scale indicated an identical mass up to 0.1 grams (16.4 g and 16.3g). The marbles appeared to collide with their centers of masses at the same height, as their time of flight was not visually or audibly different, therefore it doesn't appear that their was any initial vertical component of velocity.

I really can't think of what other explanation there might be. For most of my other groups, the percent difference in the absolute values of the y-components of the target and projectile were less than 5%. I was wondering if anyone might have any other ideas to explain this.

• I've taught physics labs for years and if there's one thing I've learned, it's that students will always find a way of performing an experiment such that it violates the laws of physics. There never is a violation, obviously, but the problem could be something so small or so hidden that you might not ever find out what it was. My policy is to look at the methods. If they did it right and analyzed the results properly, ignore the rest. I was once in a lab where the student managed to indefinitely power an LED without any sort of power source or anything else in the circuit
– Jim
Mar 27, 2015 at 14:21
• You just have to keep in mind Murphy's Law and remember that explanations aren't always easy or even possible to find
– Jim
Mar 27, 2015 at 14:22

If you get another chance to observe such a problem (where adjacent "identical" experiments give different but individually repeatable results), try changing one factor at a time.

• swap marbles (projectile/target)
• swap marbles with another experiment
• swap tracks
• swap location in the lab
• swap operators

And look at all the data: is the distance flown by this projectile significantly different than that in other setups? Is there a bend in the track so the projectile has some angular momentum that pushes it sideways and messes with your coordinates? When you look at the point of impact of the projectile by itself, does it line up (visually) with the direction of the track? Does the result hold when you change the offset of the point of impact between the two projectiles (from almost head-on to glancing)?

I admit that as you described it, the result is puzzling - but a wise mentor told me years ago

If you think you did the same experiment but you got a different result, then you didn't really perform the same experiment.

It is up to you to find what is different. Systematic study and careful comparison will get you there.

Keep in mind that momentum is conserved. These results can indicate that the marble on the track had an initial y component of momentum, the stationary marble had an initial y component of momentum, or that more forces were acting on the marbles than you are aware of. Or something else went wrong, like the carbon paper was moved.

I would guess that this group's results are not repeatable. This would mean that something went wrong with that run of the experiment. It wasn't any of the things you are looking at. It may be hard to find after the fact. Perhaps somebody bumped a marble while it was in flight.

If it is repeatable, you may be able to find it by systematically checking the kinds of things you have looked at. In that case, you might look for something this group is doing that is different from other groups.

• While we were in the lab, the groups results were repeatable. I and another TA were able to replicate their data. If I go back into the lab tomorrow and set everything back up, I don't know if I will still be able to replicate it. If I get the opportunity I will try. This is the first time I've been completely stumped by one of the results in my lab's experiments. There shouldn't be any y-momentum for the projectile by definition of our x-axis, and the target was stationary so I don't think that can be the case either. If unaccounted forces exist, I'd be really interested in what they are. Mar 27, 2015 at 11:13
• Also, the drawing paper was taped down. Mar 27, 2015 at 11:14