Differences between revisions 2 and 3
 ⇤ ← Revision 2 as of 2012-08-29 16:27:12 → Size: 3466 Editor: srnarf Comment: ← Revision 3 as of 2012-08-29 16:28:16 → ⇥ Size: 3440 Editor: srnarf Comment: Deletions are marked like this. Additions are marked like this. Line 43: Line 43: ***Modify for elastic collisions*** Line 47: Line 46: v,,1,,' = (m,,1,, - m,,2,,) * v,,1,, / (m,,1,, + m,,2,,) v,,2,,' = 2 * m,,1,, * v,,1,, / (m,,1,, + m,,2,,) v,,1,,' = (m,,1,, - m,,2,,) * v,,1,, / (m,,1,, + m,,2,,)           v,,2,,' = 2 * m,,1,, * v,,1,, / (m,,1,, + m,,2,,)
 [:PiraScheme#Mechanics: Table of Mechanics Demonstration] [:MEEquipmentList: List of Mechanics Equipment & Supplies] [:Demonstrations:Lecture Demonstrations]

# Air Track Totally Elastic Collision, 1N30.33

Topic and Concept:

• Linear Momentum, [:Linear_Momentum#Collisions1D: 1N30. Collisions in One Dimension]

Location:

• Floor Item: ME, South Wall attachment: mainPhoto

Abstract:

A moving glider collides with a stationary one, both having bumpers.

 Equipment Location ID Number Air Track Floor Item: ME, South Wall Air Track Carts ME, Bay A4, Shelf #3 Red Clay Double Steel Door Bin Cabinet [:RedWhiteGasCart:Red & White Gas Carts] In Lecture Halls 2103, 2223, 2241

Important Setup Notes:

• N/A

Setup and Procedure:

1. Place air track on lecture bench, and connect the compressed air supply from the [:RedWhiteGasCart:Red & White Gas Cart] to the track using an air hose.

2. Make sure that the gliders to be used have clay on one side and that the clay juts out a little off center (see photo).
3. Place two gliders on the track, one on an end of the track and the other roughly in the middle.
4. Turn on the air supply.
5. Give the glider on the end a good push toward the glider at rest to create a collision.

Cautions, Warnings, or Safety Concerns:

• Make sure you are using compressed air and NOT methane gas which is extremely flammable!

Discussion:

In conservative systems, momentum is always conserved. In the lab frame, one glider is in motion and one is at rest. Thus, the total momentum of the system is P0 = m1 * v1 where m1 is the mass of the glider in motion and v1 is its speed. In an perfectly elastic collision, there is no loss of kinetic energy. Invoking conservation of kinetic energy and momentum then, the velocities of each glider after the collision can be determined in terms of their respective masses and the speed of the first glider. The result is this:

v1' = (m1 - m2) * v1 / (m1 + m2) v2' = 2 * m1 * v1 / (m1 + m2)

From this result, it is easy to predict the outcome of a collision. The second glider will always obtain a velocity in the same direction as the first glider was moving. Its speed depends on the masses of both gliders and the initial speed of the first one. If the first glider is more massive than the second one, both gliders will move in the same direction. If the first glider is less massive than the second one, it will bounce back in the opposite direction from which it came. In either of those two cases, the first glider will always move at a slower speed than it was initially.

 attachment:ElasticGliders-01-250.jpg attachment:ElasticLargerGliders-03-250.jpg attachment:ElasticShortGliders-04-250.jpg attachment: photo

Videos:

References:

[:Instructional:Home]

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