Momentum and Collisions

What’s the Big Idea‽

The following lab focuses on…you guessed it, momentum! And to that end, we’ll also be playing with the momentum of a system before and after internal collisions. Stay tuned and we’ll perform experiments that not only answer the questions “What is momentum?” and “How is it calculated?”, but also demonstrate conservation of momentum.

Procedure

Like many of our labs, this lab revolved around the low-friction dynamics cats.

That’s dynamic carts, not cats.

We set up two dynamics carts on each side of the track, behind each of which was a motion detector. As usually, a Vernier LabQuest recorded the data onto a laptop. The following photos demonstrate this described setup:

Say hi to Jill!

The motion detectors recorded how the carts’ velocity changed over time.

In addition to using the motion detectors to record the carts’ velocity, we used a scale to measure the carts’ mass.

Cart 1 Pushed; Cart 2 Not Pushed
	Cart 1			Cart 2			Total
	mass	velocity	momentum	mass	velocity	momentum	mass	velocity	momentum
before	0.52 kg	0.13 m/s	0.07 N/s	0.51 kg	-0.00 m/s	-0.00 N/s	1.03 kg	–	0.07 N/s
during		0.12 m/s	0.06 N/s		-0.00 m/s	-0.00 N/s		–	0.06 N/s
after		-0.00 m/s	-0.00 N/s		0.10 m/s	0.05 N/s		–	0.05 N/s

If we divide the difference of the final momentum and the initial momentum by the average momentum, we can find the percent difference. The first trial yields a percent difference of 15.4%, which while not fantastic, does suggest the conservation on momentum. The higher-than-expected percent difference is most likely due to precision errors incurred when rounding the measured values.

Cart 1 and Cart 2 Pushed at Same Velocity
	Cart 1			Cart 2			Total
	mass	velocity	momentum	mass	velocity	momentum	mass	velocity	momentum
before	0.52 kg	0.12 m/s	0.06 N/s	0.51 kg	-0.13 m/s	-0.07 N/s	1.03 kg	–	-0.01 N/s
during		0.05 m/s	0.03 N/s		-0.01 m/s	-0.01 N/s		–	0.02 N/s
after		-0.09 m/s	-0.05 N/s		0.12 m/s	0.06 N/s		–	0.01 N/s

Similarly to the last trial, we can find the percent difference. However, this trial yields bizarre results because the average momentum is zero, making it impossible to find the percent difference.

Cart 1 and Cart 2 Pushed at Different Velocity
	Cart 1			Cart 2			Total
	mass	velocity	momentum	mass	velocity	momentum	mass	velocity	momentum
before	0.52 kg	0.40m/s	0.21 N/s	0.51 kg	-0.30 m/s	-0.15 N/s	1.03 kg	–	0.06 N/s
during		0.39 m/s	0.20 N/s		-0.29 m/s	-0.15 N/s		–	0.05 N/s
after		-0.24 m/s	-0.12 N/s		0.33 m/s	0.17 N/s		–	0.05 N/s

The percent difference of the third trial is 18.2%, which is worse than expected. Again, I believe this is due to precision errors.

Takeaways

Although the data isn’t fantastic, it roughly shows us how momentum is conserved with at least some degree of certainty. Before the collision, the total momentum of the system can be calculated as the sum of the carts’ individual momenta (as momentum is a vector quantity). And in the same manner, the total momentum of the system can be calculated to determine the difference between the momenta before and after the collision.