Collisions

Activity

The focus of this activity is designing a set of experiments to test an idea, and clearly communicating the results. Well-presented graphs are the focus of this activity!

You have two carts and a track. The carts have velcro so they will stick together (if the collision speeds are low enough). You have 2 motion sensors, one on each end of the track. You have masses you can add to the carts. Your goal is to design experiments to verify or contradict the following 2 statements:

1. Total momentum of both carts is always conserved in collisions, i.e. \(m_1 \vec{v}_{1,i} + m_2 \vec{v}_{2,i} = m_1 \vec{v}_{1,f} + m_2 \vec{v}_{2,f}\)
2. Total kinetic energy of both carts is always conserved in collisions, i.e. \(\frac{1}{2}m_1 v_{1,i}^2 +\frac{1}{2}m_2 v_{2,i}^2 =\frac{1}{2}m_1 v_{1,f}^2 +\frac{1}{2}m_2 v_{2,f}^2\)

Things to consider before you begin:

For each statement you need more than one scenario. Things you can control include the mass ratio, and the initial velocities. It can sometimes be helpful if you rewrite the question you are investigating. For example, you might decide to answer the question “How does the final energy compare to the intial energy after a collision of equal-mass carts?" You will want several such questions.

You must repeat each scenario more than once (3 to 5 should be enough). One set of data is not as reliable as many. Not every collision is good. If the collision causes a cart to go off the tracks or jump up and down a lot you should probably ignore that experiment. Note: slower collisions are less likely to go wrong. Think about what criteria you might use to decide when to ignore the data from a trial.

This being physics (not mathematics) you cannot prove (e.g.) momentum conservation with absolute certainty. You can, however, do careful experiments that check whether or not your results are consistent with momentum conservation. Recall the general rule: you can claim that you results are consistent with a statement or a prediction if the discrepancy between the prediction and your measurements is small compared to your measurement uncertainty. Also remember that a good measurement has small total uncertainty.

Think about how you wish to present your final data. Your final data is whatever you use to justify your claim of confirming or contradicting the statements. One of the most crucial decisions you have to make when communicating the results of your experiment is how to present your results as efficiently, as comprehensively, and as clearly as possible. In general, graphs (with data points and a fitted trend line) are your best bet. Your dependent variable (the quantity you controlled) is always on the horizontal axis. In this case, one good way to graph all your data is to plot final kinetic energy (of both carts) as a function of initial kinetic energy. According to statement 2, the data should be a straight line with a known slope. Where possible you should combine different scenarios onto the same graph. This is especially true if your data supports the original statement. You should be able to combine all your data into just 2-3 graphs.

Make sure you have a clear conlcusion, explicitly backed up by your graphs, about each of the statements you tested.