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Homework Help: Dynamics - Collision Question

  1. Mar 23, 2008 #1
    1. The problem statement, all variables and given/known data

    http://img138.imageshack.us/img138/9476/phyus3mu7.jpg [Broken]​
    [/URL]

    2. Relevant equations

    Conservation of momentum
    Conservation of kinetic energy

    3. The attempt at a solution

    I really have no idea. I dont know the velocity of A before the collision and i dont know the speed of A after the collision. So i cant use the conservation of momentum. I also know its not an elastic collision because im told "the restitution is e=0.5". Should i have been told some kind of equation to allow me to work this out or am i missing something?

    James
     
    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Mar 23, 2008 #2

    Shooting Star

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    Homework Helper

    Both. In short, (don't feel like using latex), if co-eff of restitution is e=1/2, then,

    relative velo after collision = vb - va_f = (1/2)va_i = relative velo before collision.

    Using consvn of mom, ma*va_i = ma*va_2 + mb*vb.

    All velos are +ve to the RHS. Solve for va_f. The masses and vb are given.
     
    Last edited: Mar 23, 2008
  4. Mar 23, 2008 #3
    Hi shooting star, i really appreciate the help but im still a little stuck, would you mind answering a few more questions for me?

    Is this correct:
    ma = Mass A = 1kg
    va_i = Velocity of A initially = Unknown
    va_2 = Final velocity of A? = Unknown
    mb = Mass of B = 10kg
    vb = Final Velocity of B? = 0.876m/s

    --------------------------------------------------------------------

    Im also a little confused by this equation. Does that mean that in effect relative velo after collision is equal to -relative velo before collision?

    Or was it meant to read like this:
    -------------------------------------------------------------------

    Finally, am i meant to rearrange this equation
    to make vb the subject and then factor it into the conservation of momentum equation you gave me? I only ask because i still have two unknowns at this point, va_i and va_f.

    Again thank you for the help, sorry i have to ask more questions.
     
  5. Mar 23, 2008 #4
    The coefficient of restitution between to objects (1 and 2) is given by
    [tex]C_r = \frac{V_{2f}-V_{1f}}{V_{1i}-V_{2i}}[/tex]

    If A is object 1 and B is object 2, then this simplifies to:
    [tex].5 = \frac{V_{Bf}-V_{Af}}{V_{Ai}}[/tex]
    Since the initial velocity of B is zero.

    And then you have
    [tex]M_{A}V_{Ai} = M_{A}V_{Af}+M_{B}V_{Bf}[/tex]
    I think Shooting Star may have meant solve for [tex]V_{Af}[/tex]. Looks like you can do it with those two equations.
     
  6. Mar 23, 2008 #5

    Shooting Star

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    Homework Helper

     
    Last edited: Mar 24, 2008
  7. Mar 23, 2008 #6
    Thank you both for the help. For some reason or another i wasnt given these equations. Ill give it a go tomorrow and see how it goes.
     
  8. Mar 23, 2008 #7
    That worked :D
     
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