1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: How do I solve elastic collisions?
  1. How do I solve this? (Replies: 2)

  2. How do i solve this? (Replies: 15)

Loading...