PHY221 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.

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Momentum conservation and KE conservation equations

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Equations in CM frame

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Equations in CM frame

So we have shown that, IN THE CM 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!!):• the initial and final SPEEDs of the objects m1 and m2 are the same: v1i=v1f

and v2i=v2f • 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 d and applications: ball bounce and grav sling shot effect

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2 d General comments

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1d example

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