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How to find the unknown mass of an object in a 2d collision?

  1. Nov 10, 2011 #1
    1. The problem statement, all variables and given/known data
    I have two pucks colliding. PUck 1 has a mass of .545 kg. Puck two has the same puck mass, but also has a weight added onto it. I need to find the mass of puck two.

    Velocity before and after for puck 1:
    V1i = 2.0m/s[19°Below the Horizontal]
    V1f = 3.0m/s[31°Above the Horizontal]

    Velocity before and after for puck 2:
    V2i = 4.33m/s[19°Above the Horizontal]
    V2f = 3.36m/s[16°Below the Horizontal]

    2. Relevant equations

    Conservation of momentum:

    [itex]\vec{Pi}[/itex] = [itex]\vec{Pf}[/itex]


    3. The attempt at a solution


    m1[itex]\vec{vi}[/itex] + m2[itex]\vec{vi}[/itex] = m1[itex]\vec{vf}[/itex] + m2[itex]\vec{vf}[/itex]

    m1[itex]\vec{vf}[/itex] - m1[itex]\vec{vi}[/itex] = m2[itex]\vec{vf}[/itex] - m2[itex]\vec{vi}[/itex]

    m2/m1 = (v1f - v1i)/(v2f-v1i)

    Now, I am supposed to draw vector diagrams for this but after that I get stuck. What do I do once I have drawn the vector diagrams for (v1f - v1i) and (v2f-v2i) ? I dont need someone to give me a full solution or anything, I just need some help to continue on the right track. I really appreciate any help!

    Here is what I am getting by the vector diagrams by the way:
    (v1f - v1i) = 2.3m/s [83° Above the horizontal]
    (v1f - v1i) = -2.5m/s [78° Belowthe horizontal]
     
    Last edited: Nov 10, 2011
  2. jcsd
  3. Nov 10, 2011 #2

    gneill

    User Avatar

    Staff: Mentor

    Hmm. One would expect momentum to be conserved in the collision. In fact, momentum in the x-direction and momentum in the y-direction should be conserved independently. Since you have the vectors for both objects before and after collision, you can write the momentum equations for both components.

    When I do so and solve for the mass of the second puck I get different results for that mass from the x and y component equations. Furthermore, both results are LESS than the mass of the puck 1.

    I would expect some variation due to experimental error, but the results seem to be a bit wonky even so. Can you check your data to make sure that you transcribed it correctly?
     
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