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2D Momentum Collision

  1. Feb 17, 2016 #1
    1. The problem statement, all variables and given/known data

    One car of mass 1400 kg is travelling at 45km/h when it collides and becomes entangles with another car mass of mass 1300 kg travelling at 39km/h[E]. What is their velocity after collision

    So MA = 1400 kg
    VA = 45kh/h

    MB = 1300 kg
    VB = 39 kh/h [E]

    and After Collision:
    MAB = 2700kg


    2. Relevant equations

    P = mv
    ∑P = ∑P'

    PA + PB = PAB'

    3. The attempt at a solution

    so I've always been told to solve momentum first so since car A is going South that means it only has a verticle momentum? so
    that means PAY = m⋅v
    so PAY = 63000kg⋅km/h

    similarly for B

    so only a horizontal momentum
    so PAX = 50700kg⋅km/h [E]

    so now im stuck on what to do, i tried to find the momentum of Pab in the x and y direction then find pab and solve for v but that doesnt work when i tried it. Pab in the x direction just turns out to be the same as pb in the x direction and pab in y direction turns out to be pa in y direction and then using pythaguras theorum to find the hyp and hence find Pab i get 37396 kg⋅km/h and then solving for V by diving the Pab by the total mass of both of the cars together gives me a velocity of 13.85km/h but the answer is 30.0km/h so i think i messed up after solving my momentums for before the collision but idk what i did wrong
     
    Last edited: Feb 17, 2016
  2. jcsd
  3. Feb 17, 2016 #2

    NascentOxygen

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    Staff: Mentor

    Check your Pythagoras calculation again. Show your working.
     
  4. Feb 17, 2016 #3

    DrClaude

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    Staff: Mentor

    This number is not correct.

    Edit: NascentOxygen beat me to it.
     
  5. Feb 17, 2016 #4
    okay so
    PABY' = 63000kg⋅km/h and PABX = 50700 kg⋅km/h [E]

    so

    c2 = a2 + b2
    so
    c2 = 630002 + 507002
    c2 = √630002 + 507002
    so c = 37396.6576 kg⋅km/h so this is PAB '

    now i need to find the velocity after collison so i took the combined mass and divided it with 37396.6576kg⋅km/h
    and my v ends up being 13.85 km/h but the answer is 30 km SE
     
  6. Feb 17, 2016 #5
    i do not understand hot i
    it is? i dont understand how because i did
    507002 + 630002
    and since 63000 is actually in the negative direction i basically did

    507002 - 630002
    and then square rooted it. do i not assign that negative direction? but its going south?
     
  7. Feb 17, 2016 #6

    NascentOxygen

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    Staff: Mentor

    The negative sign isn't applicable here. You use Pythagoras to calculate magnitude.
     
  8. Feb 17, 2016 #7

    DrClaude

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    What if A was going North instead? Do you expect a different result? Making a diagram of the situation would help.
     
  9. Feb 17, 2016 #8
    my calculator is fine, i've used it for all my courses and im in 2 other math courses so its not broken, but i took ur advice and tried it with another one and still getting the same answer
     
  10. Feb 17, 2016 #9
    oh wait, so since im looking for the overall momentum of Pab after the collision, i dont need to consider negative and positives? since im not going in a specific direction, rather im going in 2 directions not one?
     
  11. Feb 17, 2016 #10

    DrClaude

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    Staff: Mentor

    NascentOxygen said that because
    is not correct. But this is not what you calculated, as you stated in a subsequent post.
     
  12. Feb 17, 2016 #11
    and im basically looking for the sum of 2 vectors so it would be that the cars are going S of E not just S or just E so doing what i did earlier would have made the direction be just south right?
     
  13. Feb 17, 2016 #12

    DrClaude

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    Staff: Mentor

    You already have the sum of the two vectors. What you are looking for is the magnitude of the resultant vector.
     
  14. Feb 17, 2016 #13
    that is the Pab not the velc
    OH so since im looking for the magnitude i dont need to consider their directions so it would just be

    c2 = 630002+ 507002
    c2 = √630002 + 507002
    so c = 80867.11 kg⋅km/h ??

    so then velocity would be 80867.11 kg⋅km/h / 2700kg
    so v = 29.9 km/h! thank you! that makes so much more sense!
     
  15. Feb 17, 2016 #14

    NascentOxygen

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    Staff: Mentor

    You are adding two perpendicular quantities. The hypotenuse will be longer than either of the perpendicular components.
     
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