(In)Elastic Collisions

You have likely witnessed both elastic and inelastic collisions in your life. Breaking in a game of pool is a common example of an elastic collision while two cars sticking together after an accident demonstrates an inelastic collision. Being able to determine what happens during these collisions– what changes and what stays the same– is important to help engineer useful products and innovations used everyday. Sometimes, as is the case for the seatbelt, these innovations both emerge as a result of these studies as well as utilize the concepts behind collisions.

In this lab, you and your group are tasked with colliding carts in different situations (masses, velocities, etc.) and qualitatively and quantitatively determine the results of these collisions. From your observations and measurements, you will be able to determine what physical parameters – specifically kinetic energy and momentum, but any others you consider are acceptable – are conserved during collisions. From this investigation, you and your group will develop a better understanding the phenomena experienced and be able to discuss common misconceptions of forces felt during collisions.

Collisions occur in two distinct ways– elastically and inelastically. The properties that are conserved in a collision depend on which type it is. Conservation of a physical parameter implies that its initial state is equal to its final state. Using mass (m) as an example, that is to say

!“!#!$% = !”#$%

This can also be written as

= 0

implying that there is no change of mass.

Determining the parameters that are and are not conserved is a major component of this lab. Therefore understanding conservation is a key to success.While models for inelastic and elastic collisions are easily found online, it is important to recognize there are assumptions that go into those models. In this lab, it is likely that your data and analysis will not fit those simple models well. It will be your job to determine the limitations within your system and your models and assign conservation laws within those considerations.

In order to investigate inelastic and elastic collisions, it would be best to ensure your understanding of:

• What it means for something to be conserved in a natural process

• The difference between an elastic and an inelastic collision

• The parameters that determine common physical concepts, such as kinetic energy and momentum.

Part 1 – Using the Air Track

Conducting your experiment carefully will require you to utilize the air track effectively. Like many other pieces of scientific equipment, this implies that you will need to calibrate the air track to ensure it is level. With your group, determine the most appropriate ways to ensure this is true. While doing so, it may be helpful to consider:

• Why is this step important?

• Discuss how your precision with regard to a level track affects the motion of carts on the track. How could this affect data in your experiment?

• What additional things can you do to remove other uncertainties from your measurements?

• Is there a tolerance you are considering acceptable? What affect does this have on your data?

Part 2 – Observation of Inelastic Collisions

While your group will investigate both types of collisions, determining the properties of inelastic collisions will likely help support your understanding of elastic collisions. By now you all have observed a few collisions between carts on the track; continue (or start) to do so. While making observations, it may be useful to consider the state of the carts before and after each collision. Try to be thorough –you will be using these observations to help support the analysis of your quantitative results.

• How do the initial parameters (velocity, mass, etc.) of each cart affect the result of the collision?

• Do you observe any differences in how the cards collide based on the initial velocities of the carts? What does this tell you regarding how you can maintain consistency in your data?

• What parameters are you resetting between trials to create better reproducibility?

Part 3 –­ Measurements of Inelastic Collisions

Looking at the important aspects you identified in Part 2 , determine the data do you need to take in order to determine what is conserved during in these collisions (i.e., momentum, kinetic energy, etc.). If you decide time or velocity is important, decide how you will be determining these values (i.e., photogate timers, video tracking software, etc.).

Note: If you are using photogate timers, they have a number of settings that are useful. It may help to take a couple minutes to determine which settings (including the memory) are most helpful and how to best utilize these.

• What are some sources of uncertainty that are prevalent? Are there some that impact your data more than others?

• In what ways are you attempting to minimize the uncertainty that is inherent in these measurements?

• How do you compare across trials? Can you determine variables that are controlled?

Create graphical representations that demonstrate whether or not momentum and kinetic energy is conserved in these collisions.

• What are you considering as your independent variable? What is dependent?

If you have more than one variable you are adjusting between trials, how are you accounting for this when defining a single independent variable for your representation?

• How are you defining whether a property is conserved?

• How are you accounting for outside influences on your data?

Part 4 – Observations of Elastic Collisions

Exchanging the inelastic attachments for elastic, repeat Part 2 again for elastic collisions. You and your group will once again use these observations to build quantitative models for the conservation laws, so it may be useful to consider:

• What's different about these collisions, compared to Part 2?

• What parameters are important?

It is likely helpful to consider many of the same questions posted in Part 2.

Part 5 – Measurements of Elastic Collisions

Repeat Part 3 for elastic collisions. Consider the differences you observed and how those affect the value of your variables. In addition to the questions listed there, it may be helpful to consider:

• How are you defining each parameter?

• Do you need to make adjustments to the way you define your parameters?

• Are there sources of uncertainty that are appropriate to this situation that were not important before?

Create another graphical representation of what properties are conserved, especially considering momentum and kinetic energy.In addition to questions posed in Part 3 , it may be helpful to also consider:

• How do these results differ from those found in Part 3?

• Can you make sense of these differences?

• How have any new sources of error you found in Part 4 contribute to these data?

Part 6 – Applying to Everyday Life

Consider this scenario:

A car is stopped at a red light. A truck behind the car has trouble with its brakes and can't stop in time, hitting the car from behind. Which vehicle feels more force – the car or the truck?

After your group has discussed this, look at Newton's Third Law. How does that relate to your conclusion from above?

• If your answers don't agree, can you use the results in your lab to reconcile the difference?

• If your answers do agree, can you determine why the misconception is so prevalent amongst the population? How would you help another understand this common misconception?

• Can you demonstrate this phenomenon on the air track?

Part 7 – Challenge: Quantifying Uncertainties

In Part 1 , we defined a couple of assumptions that have been accepted through this experiment– for instance, that the track is frictionless and level. You should have all the tools necessary to quantify the affect of friction the cart feels as it travels and the angle of the track.

• How does a slightly unleveled track affect your data?

• Do you see this impact in the conservation laws you determined?

• What is the impact of this friction?

• How does that affect the conservation laws you determined from your data?

Considering these values you determined,

• What is the relative size of these assumptions?

• How does quantifying these assumptions affect your conclusions?

• Does considering these aspects make you change your mind on any of your determined conservation laws?

Utilizing this approach, are there other areas of uncertainty you can investigate and account for in this way?