PHY205 Ch12: Elastic Collisions

1. Recall main points:

Using CM frame: 2. Discussion and examples• Example 1d collision. Application: Ball bounce on

ground and Grav sling shot effect.• Example 2d collision in CM frame.

PHY205 Ch12: Elastic Collisions1.

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Elastic Collisions: KE is conserved (definition)

PHY205 Ch12: Elastic Collisions1.

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Equations in CM frame:

Solution for final vel. v1f and v2f in terms of initial ones v1i and v2i

In CM Frame

PHY205 Ch12: Elastic Collisions1.

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Solution cont’d

PHY205 Ch12: Elastic Collisions1.

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Equations in CM frame for totally elastic collisions:

So we have shown that, in the Center of Mass Frame, the following describes the outcome of a elastic collision (those statements are NOT true if we don’t put ourselves in the CM frame and/or the collision is not elastic!!):• In CM frame each object retain its speed after collision :

• Since the total momentum is conserved, the final momentum remains ZERO (since the total initial momentum was zero) and thus the final momentum vectors of the 2 objects must be opposite to each other which means that they travel in opposite directions

• The angle by which the trajectories of the 2 objects are deflected during the collision is not determined by the conservation of energy and momentum. That angle will be the result of the specific type of collision (for instance if 2 billiard balls collide the outgoing velocity directions will depend on the collision geometry)

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* * * *1 1 2 2 and i f i fv v v v ��������������������������������������������������������

PHY205 Ch12: Elastic Collisions2.

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1 d and applications: ball bounce and grav sling shot effect

PHY205 Ch12: Elastic Collisions2.

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2 d General comments