Elastic Collision Derivation FINAL

# Elastic Collision Derivation FINAL - which will help...

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1 Derivation of the Final Velocities of Two Objects in an Elastic Collision ( KE and p are both conserved) (situation in which object B is initially at rest and both objects do not stick) GOAL: To get two equations for and , the final velocities of the two masses just after the collision. p conservation; Equation 1 KE conservation; Equation 2 Notice in Equation 2 that the term is a FOIL of the binomials and . Thus, Equation 2 can be rewritten as follows; A B A B Before After

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2 New Equation 2 The trick is to now divide the New Equation 2 by Equation 1 so that all one simpler equation can be found
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Unformatted text preview: which will help determine the final speeds of A and B ; New Eq. 2 divided by Eq. 1; Equation 3 Nearly done! Now, the next trick is to substitute Equation 3 back into Equation 1 to first eliminate so you can obtain the equation for . After that, rearrange Equation 3, solving it for so that you can then insert it back into Equation 1 once again, but this time to eliminate to solve for . Once you’ve done this, you will now have the two velocities of both objects right after they collide, again, assuming a perfectly elastic collision....
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