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!

2D elastic collision

  1. Aug 5, 2016 #1
    1. The problem statement, all variables and given/known data
    A 2D elastic collision:
    Two pucks (masses m1 = 0.5 kg and m2 = 0.3 kg) collide on a frictionless air-hockey table. Puck 1 has an initial velocity of 4 m/s in the positive x direction and a final velocity of 2 m/s in an unknown direction, θ. Puck 2 is initially at rest. Find the final speed of puck 2 and the angles θ and φ.

    I get stuck at the end of this problem when I have to use the two equations to solve for 2 unknown angles. If someone could show me how to do that last step that would be great. Thanks in advance!
    2. Relevant equations


    3. The attempt at a solution
    Since the collision is elastic I found the final kinetic energy using Ei = Ef and it equals 4.47 m/s

    Then conservation of the x and y components of total momentum:

    X DIRECTION: Pi = Pf
    m1v1 + m2v2i = m1v1 + m2v2f
    (0.5)(4) = (0.5)(2cosθ) + (0.3)(4.47cosφ)
    2 = cosθ + 1.341cosφ

    Y DIRECTION: Pi = Pf
    m1v1 + m2v2i = m1v1 + m2v2f
    0 = (O.5)(2sinθ) -(0.3)(4.47sinφ)
    0 = sinθ - 1.341sinφ
     
  2. jcsd
  3. Aug 5, 2016 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Hint: cos2θ + sin2θ = 1

    (Your work looks good so far.)
     
  4. Aug 5, 2016 #3
    So I solve the first equation for cosφ and the second equation for sinφ?
    1.341cosφ = 2-cosθ
    and
    -1.341sinφ = sinθ

    then square each term:
    1.3412cos2φ = 22-cos2θ
    and
    -1.3412sin2φ = sin2θ

    then I added them but I'm still a bit lost/don't know the next step :/

    1.3412cos2φ + (-1.341)2sin2φ = 22-cos2θ + sin2θ
     
  5. Aug 5, 2016 #4
    Take another look at (2-cosθ)2. It doesn't look right. Also, I thought it might have been a little simpler to solve for sinθ and cosθ, then square, then add the equations and then implement TSny's hint.
     
  6. Aug 5, 2016 #5

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Note that (2 - cosθ)2 ≠ 22-cos2θ. In general (a + b)2 ≠ a2 + b2.

    In order to use the trig identity cos2θ + sin2θ = 1, you could solve the first equation for cosθ. You already have an expression for sinθ, except I believe you have a sign error in -1.341sinφ = sinθ.
     
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: 2D elastic collision
  1. 2D Elastic Collision (Replies: 9)

  2. 2D Elastic Collisions? (Replies: 1)

  3. 2D Elastic Collisions (Replies: 1)

  4. 2D Elastic Collision (Replies: 4)

Loading...