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