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Homework Help: How do I solve elastic collisions?

  1. Oct 18, 2015 #1
    • Member warned to use the formatting template for homework posts.
    A 2-kg ball is moving at 3 m/s toward the right. It elastically collides with a 4-kg ball that is initially at rest. Calculate the velocities of the balls after the collision.

    I know that kinetic energy is conserved in elastic conditions, but I don't know how to use that to calculate this. I tried solving this using the conservation of momentum, but i ended up with 2(3) + 4(0) = 2vf1 + 4vf2 and I can't solve for both variables. I know PE = mgh and KE = (1/2) mv2
  2. jcsd
  3. Oct 18, 2015 #2


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    Yes, in all collisions, in which there is no external force, momentum is preserved and that is what your equation, 2(3)+ 4(0)= 6= 4vf1+ 2vf2 or, dividing through by 2, 2vf1+ vf2= 3. And, as you say, in an elastic collision, kinetic energy is conserved. Since this doesn't involve change in height, the "potential energy" equation is irrelevant. And, as you say, kinetic energy is "[itex](1/2)mv^2[/itex]" the total kinetic energy before the collision is [itex](1/2)(2)(9)+ (1/2)(4)(0)= 9[/itex]. After the collision, with speeds vf1 and vf2, the kinetic energy is [itex](1/2)(2)(vf1^2)+ (1/2)(4)(vf2^2)= vf1^2+ 2vf2^2[/itex]. Since the kinetic energy does not change, [itex]vf1^2+ 2vf2^2= 9[/itex].

    Solve the two equations [itex]2v1+ vf2= 3[/itex] and [itex]vf1^2+ 2vf2^2= 9[/itex] for vf1 and vf2.
  4. Oct 18, 2015 #3
    Thank you so much. I follow all of your work and understand it!
    Last edited: Oct 18, 2015
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