 Physics Practicals

# Collisions

PHY180 Module 4 - PHY180 Student Guide April 18, 2023, 2:27 p.m.

## 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.