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With all momentum experiments it is important to consider the Total Momentum, the Center of Mass Momentum.
We expect this to remain Constant. The difference between the C.M. momentum before and after the collision should be small (compared to the Total C.M. momentum.
Dividing the motion into that OF the C.M. and that ABOUT the C.M. is important also.
Once you get to the Totally Elastic Collisions I found it useful to ‘assume’ (because we found it to be nearly always true) that each mass approaches the C.M. with the same speed that it will LEAVE the C.M. This amounts to Conservation of K.E. but since we did Momentum before K.E. we couldn’t call it this.
;-)
On Mar 12, 2015, at 4:32 PM, Bruce McKay <brumac@bigpond.net.au> wrote:_______________________________________________
I do similar experiments with my high school physics classes. The first experiment involves firing two carts apart. What is the percentage difference between initial and total final momentum? Obviously, with initial momentum zero this is nonsense so we consider the difference in the magnitudes of the change in momentum of each cart and find the percentage difference in those. In other collisions we compare total momentum before with total momentum after, unless the total is small when we again compare the difference in the magnitudes of the change in momentum of each.
Bruce McKay,
St. Ignatius’ College,
Riverview,
Sydney
Australia
On 13 Mar 2015, at 6:23 am, Bill Nettles <bnettles@uu.edu> wrote:_______________________________________________
One of my typical intro experiments involves inelastic collisions. Two carts/gliders on a track/air track heading toward each other in opposite directions, colliding and sticking together. The velocities are measured using motion sensors (most often looking at the slope of the position vs. time graph immediately before and immediately after the collision). Due to a variety of conditions, friction in bearings or a non-level track or wind shear on the air track, the momentum after is not equal to the momentum before.
My question is how to categorize the difference |delta p|=|p_a - p_b| as some fractional or percentage discrepancy. IF p_b is the result of two larger, but nearly equal, magnitudes, there will be subtractive cancellation resulting in a nearly zero p_b. For example, p_b1 = +1.00 kg.m/s and p_b2 = -0.98 kg.m/s, then p_b = + 0.02 kg.m/s. Then, if p_a is +0.01 kg.m/s, the absolute difference in the momentum is 0.01. A "traditional" error calculation would say this is a 50% discrepancy. That doesn't pass my "gut check" mainly because of the large subtractive cancellation in the p_b calculation. A small variation of the initial momenta would have huge effects on this calculation.
My first attempt to characterize the discrepancy is to average the momentum magnitudes of the initial objects, 0.5(|p_b1|+|p_b2|), and use that as a divisor of |delta p|.
Has anyone developed a measure of discrepancy tool that you like for situations like this? It's very hard to do a statistical sampling because reproducing the same initial velocities is difficult, but that might be the best thing to try.
Or is this a fool's errand? (Remember that students like to have "a percentage error", aka, "How close do we have to be?")
Bill Nettles, Ph. D.
Chair, Dept. of Physics &
Associate Dean of Arts & Sciences
Union University
Jackson, TN
731-661-6588
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