These are general guidelines for a lab report on collisions. There were various methods and experiments.

**Abstract:** Remember to include and summarize the ENTIRE report. Write this at the end, but put it at the beginning. Key results are how energy is conserved versus how momentum is conserved. Or if you are doing the two dimensional report how direction affects things. You do not need to include every single result, but summarize the trends.

# Introduction:

You need not explain position, velocity, acceleration.

Do Explain the concepts of collisions, kinetic energy, inelastic collisions, equal and opposite reactions, conservation of momentum, elastic collisions, momentum , conservation of energy, include historical elements. If you are working with the touch table, also emphasize the vector nature of momentum. You may have noticed that the order of these concepts in the above sentence makes so logical sense. It is my hope that this will dissuade you from writing a list-like lab report which means you actually have to think about how to integrate all of these ideas together into a cohesive story.

Provide the equations such as p = mv, the elastic and inelastic collision equations (show derivations of these equations from conservation of momentum), kinetic energy.

# Procedure:

Be inclusive and have diagrams. Mention the computers, motion sensors, carts, rails, magnets, velcro, launchers, index cards (for motion sensors if you used them), black bricks, Touch Table, strings, clay balls, LEGO balls, marbles etc. Most of the dynamics cart sources can be found in the Galileo Report information. The newer carts are by Vernier, the silver carts by PASCO.

# Data and Analysis:

You do not need to include every single graph (although you may do this in the appendix if you so wish) but you should show one example of each kind of graph (such as one elastic and one inelastic). You should be able to cut and paste this into your microsoft word document as opposed to using a scanner.

You should have a table with just the data, which is the mass and velocities for all experiments. Make sure you explain the table.

You should have a second table with the momentum and kinetic energy of each object calculated before and after each collision. Make sure you explain the table.

Another table with the net momentum and energy before and after for each collision. Make sure you EXPLAIN!!!!!

And finally…a table which tells us how much momentum and energy were conserved in each experiment.

Compare your final results to what theory tells us:

Theory tells us that in all experiments, momentum should have been 100% conserved.

Theory tells us that in elastic experiments, kinetic energy should have been 100% conserved.

In inelastic experiments, kinetic energy will not be conserved. Here are some samples of how much should be conserved.

Theory tells us that in the an experiment with equal masses (1:1), you should have had only 50% KE conserved.

If a 500g car inelastically collides with a 1000g car, you should have only 33% KE conserved.

If a 1000g car inelastically collides with a 500g car, you should have only 66% KE conserved.

If a 500g car inelastically collides with a 1500g car, you should have only 25% KE conserved.

If a 1500g car inelastically collides with a 500g car, you should have only 75% KE conserved.

The above are examples. Your mass ratios will not be exact.

From these values, you can calculate a percent error for each of the six experiments.

In the text of your analysis, explain your observations of all experiments. Tell what happens (they bounce or stick together). What direction each cart goes after the collision. Discuss the transfer of momentum. Discuss the loss of energy. Where does the mechanical energy go? Why was momentum not 100% conserved?

If you are going for that A+ with the bonus points, other things you could do.

Show why these amounts of kinetic energy are what you should have conserved (instead of taking my word for it).

Peer Data: Make sure you compare your results to at least one other group. Not only present their results, but compare your results to theirs. Do the have the same general results (amount conserved) or not? Why? How are their methods different?

### Simulations/Modeling:

There is a link to the simulation you should use on Visual Classrooms. You should model several of your trials as close as possible using the simulation and present the data, and compare it to your actual results.

## Conclusions:

Summarize it all, and think how the experiment could have been improved. How could you eliminate your sources of error. Have realistic solutions. Think about what led to inconsistencies in your experiments.

Remember to include an appendix with bibliography, pictures, sample calculations, derivations etc.

By sample calculations, I mean one example of every calculation that you did (which you did for six different experiments) to generate your tables.

# Primary Sources

So what kinds of primary sources are out there for this report? There are 3 articles posted in the documents section of Blackboard. The rest are either on Google Books or in the BU Library. Most e-journals you can access from the BU Library online using your Kerebos Password.

The easy route is Newton, which momentum and the third law and the Principia.

1. Principia p 92 from PDF COROLLARY III. States the Conservation of Momentum

Definition 2

In the second law, change in motion means momentum. You can find this in the Physics Great Hall.

2. Leibniz Philosophical papers and letters; a selection translated and edited, with an introd., by Leroy E. Loemker Mugar B2558 .F56~ v. 1& 2

P 296 available on Google Books p 435 also of interest

Now, energy was not a solid idea until the 19th century. However, in a primative form, it was a competing idea to Newton. Leibniz came up with a concept called vis viva. Note, this is not energy as we have learned it in class, but it led to the idea.

3. George E. Smith, The Vis Viva Dispute: A Controversy at the Dawn of Dynamics”, Physics Today 59 (October 2006) Issue 10 pp 31-36.

This is actually a great and easy to read article. You can access it through the BU library e-journals. There is also a copy in the Physics Great Hall.

4. Wallis Scott, J. F. (Joseph Frederick) The mathematical work of John Wallis, D.D., F.R.S., (1616-1703) / by J.F. Scott with a foreword by E.N. da C. Andrade. In Mugar this is QA29.W3 S3 1981 Also available on Google Books. Start with p 97-99, and again on p 102-105

5. Coriolis Gaspard-Gustave Coriolis Both Coriolis and Poncelet published in 1829; the paper by Coriolis being Du Calcul de l’effet des machines. (“Calculation of the Effect of Machines”) The contribution of Coriolis, Poncelet, and Navier to the concept of ‘work’ is examined in detail. I Grattan-Guinness, Work for the workers : advances in engineering mechanics and instruction in France, 1800-1830, Ann. of Sci. 41 (1) (1984), 1-33. Mugar Q1 .F36~ v. 41 1984 This is by special order.

6. There is an article from the Journal of British History by Hall posted on Blackboard by Rupert Hall. This goes into a lot of detail about the experiments by Wallis with Pendulum type collisions.