Elastic and Inelastic Collisions: The Case of the Happy and Sad Balls

Steve Shropshire, Idaho State University

This material is replicated on a number of sites as part of the SERC Pedagogic Service Project

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This activity has benefited from input from faculty educators beyond the author through a review and suggestion process as a part of an activity development workshop. Workshop participants were provided with a set of criteria against which they evaluated each others' activities. For information about the criteria used for this review, see http://serc.carleton.edu/sp/compadre/devactivities/reviewcriteria.html.

Initial Publication Date: July 29, 2007

Summary

This activity highlights the differences in impulse delivered during elastic and inelastic collisions. Students are expected to have read introductory material on momentum, momentum conservation, and collisions. They are tested on this reading with a short online quiz prior to class. In class, students are asked a question regarding the ability of balls of different restitution (happy and sad balls) to knock over a block of wood. After initial responses are presented, discussion groups are formed to achieve consensus and provide justification of conclusions. This is followed by a confirming demonstration. Follow-up quantitative demonstrations or labs with dynamics cart or air tracks with motion and force sensors are suggested.

Classical Mechanics | High School (9-12), College Lower (13-14)

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Learning Goals

Students should improve their understanding of momentum conservation and learn that a recoiling object in an elastic collision will transfer more impulse than if it collided inelastically.

Context for Use

Educational level: Introductory Physics, all levels.
Setting: High school or college, all class sizes. This in an Interactive Lecture Demonstration classroom activity.
Time required: 20 to 30 minutes.
Special equipment: Recoil Again apparatus, dynamics cart or air track, motion and force sensors connected to a computer or calculator, overhead or lcd projector, and an audience response system.
Pre-requisite knowledge: Basics of forces, Newton's Laws, momentum, impulse, and conservation of momentum during collisions.

Description and Teaching Materials

Prior to instruction students are expected to read introductory material in their text on momentum, impulse, and collisions. After this reading and at least one hour prior to class, students should be encouraged to take an online quiz on momentum and impulse based on the reading assignment. The lesson should start with a short introduction to momentum and collisions. The level and depth of this introduction should be determined by the results of the online reading quiz and the level of the class.

For discussion in class, pose the globular glue ball concept test question as a peer instruction activity, preferably with an audience response system. Divide the class into discussion groups to arrive at a consensus, and have each group present their answer and reasoning.
Present and describe the recoil demonstration and ask the students to predict the results. The rubber bullet concept test taken from Thinking Physics by Epstein works well for discussion and peer instruction.
Follow-up demonstrations or labs using a dynamics track or air track with force and motion sensors interfaced with a computer or calculator are useful to cement conceptual understanding and to develop mathematic descriptions for momentum conservation and impulse in elastic and inelastic collisions. Replacing one of the dynamics carts or air track cars with a force sensor to study the impulse delivered during elastic vs. inelastic collisions is especially useful.

Sample questions for pre-lecture reading quiz or survey: Momentum Quiz (Acrobat (PDF) 101kB Jul16 07)
Globular glue ball concept test question: Concept Test (Acrobat (PDF) 48kB Jul16 07)
Rubber bullet concept test question: Concept Test 2 (Acrobat (PDF) 32kB Jul16 07)

Teaching Notes and Tips

If the happy and sad balls are frozen, as in a freezer, their behavior is reversed.

Most students will initially think that bringing the sad ball to a stop will provide more impulse since the happy ball is still in motion. The argument that "not only does the wood apply a force to stop the happy ball, it applies additional force to push it in the opposite direction, reversing its motion" is most effective in reversing this attitude.

Video clips of movies or tv shows where momentum conservation during collisions is violated are worth showing and ridiculing.

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Assessment

Both concept tests are worth repeating on exams. Numerical calculations of collisions from the follow-up demonstration or lab with the dynamics carts or air track work well as exam questions.