Physics collisions problem, need help

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Stef_11
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So, you've got a central elastic collision between two balls. The two balls have opposite momentums. Prove that the kinetic energy of ball 1 before the collision is the same as the kinetic energy of ball 1 after the collision.
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Absent Agent
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(Original post by Stef_11)
So, you've got a central elastic collision between two balls. The two balls have opposite momentums. Prove that the kinetic energy of ball 1 before the collision is the same as the kinetic energy of ball 1 after the collision.
Interesting! I would be interested to know how people would approach this.

Edit: by the way, next time post in the Physics forum:
http://www.thestudentroom.co.uk/forumdisplay.php?f=131


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username1560589
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#3
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(Original post by Stef_11)
So, you've got a central elastic collision between two balls. The two balls have opposite momentums. Prove that the kinetic energy of ball 1 before the collision is the same as the kinetic energy of ball 1 after the collision.
Does your statement include the statement that the initial momentums of the balls are equal in magnitude? If so you should make that clear. If not, the statement is not generally true, counterexample: m_1, m_2, u_1, u_2 = 1, 1, 1, -1(with relevant units).

What have you tried?
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Stef_11
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#4
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I mentioned that the momentums of the balls are opposite i.e they have the same magnitude and opposite directions. I didn't mention that the momentums are opposite INITIALLY, my bad. Anyway, in all my efforts I have made use of the following relationships: m1v1 - m2v2= -m1v1' + m2v2' and KE1 + KE2=KE1' + KE2'. I also used p1=p2 and p1'=p2'. My goal is basically to prove that V1=v1'. I used the above relationships in many different ways, solving and substituting but that doesn't lead me anywhere, only to relationships I know to be true. Any ideas?
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