Percent error in conservation of momentum lab confusion

[superdave]

Okay, so I did an elastic collision with Vernier carts and magnets.

The results seem pretty good.
Cart one started with -0.1205 kg*m/s ended with +0.1027 kg*m/s
Cart two started with +0.1174 kg*m/s ended with -0.1118 kg*m/s

So Total before = -0.0031 kg m/s and total after = -0.0091 kg m/s. If I use the total before as the expected value I get 200% percent error.

While true, that seems like it is missing the point. The final value doesn't actually seem that far off from the initial value. It's close to 0 before, it's close to 0 after. But tiny differences are causing big errors.

Thoughts on how to better analyze 'Was momentum conserved?'

 

[PeroK]

Okay, so I did an elastic collision with Vernier carts and magnets.

The results seem pretty good.
Cart one started with -0.1205 kg*m/s ended with +0.1027 kg*m/s
Cart two started with +0.1174 kg*m/s ended with -0.1118 kg*m/s

So Total before = -0.0031 kg m/s and total after = -0.0091 kg m/s. If I use the total before as the expected value I get 200% percent error.

While true, that seems like it is missing the point. The final value doesn't actually seem that far off from the initial value. It's close to 0 before, it's close to 0 after. But tiny differences are causing big errors.

Thoughts on how to better analyze 'Was momentum conserved?'

If your initial total momentum had been zero, then the percentage error would be infinite.

I would say you need to look at the margin of error in all your measurements and decide whether the final result is compatible with that. The error should be as a measure of the maximum error. E.g.

If you expect $-0.0031kg \ m/s \pm 0.01 kg \ m/s$ then your error is within that $\pm 0.01$ range.

 

[kuruman]

Do you have an estimate of your error bars? You will need to propagate errors and see whether momentum is conserved within your experimental error. The 200% that you calculated is not an error but a discrepancy. Regardless of that, when you calculate the % discrepancy, you are taking the ratio of two small numbers which is likely to have a large margin of error. Momentum conservation also predicts that the momentum change of the two carts should have the same magnitude. The magnitudes are 0.2232 kg⋅m/s and 0.2292 kg⋅m/s for a discrepancy of a bit less than 3%. However, as @PeroK already said and I concur, what you should consider is your margin of error not the discrepancy.

As an aside, were you extra super careful to level your track before doing your measurements? If you measured the speed of a single cart (no collisions) at two or more separate sections of the track, how close would the measured values be?

 

[superdave]

The class is a high school level course. Margin of error is beyond the scope of the class and I don't want to confuse the students too much when they already struggle with basic algebra. I might go with the % discrepancy for Δp instead, because that will reinforce the concept of conservation of momentum. I won't be doing this again for a year, but I wanted to reflect now.

Thanks

 

[kuruman]

I agree, go with |Δp₁| = |Δp₂| which you can also use to illustrate Newton's 3rd law through Δp = F Δt.