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Connected Particles

  1. Mar 5, 2007 #1
    1. The problem statement, all variables and given/known data
    Two bodies A and B of equal mass m, connected by a light inextensible string, are placed on a smooth horizontal table with the string just taut. A is projected with velocity U at 45 degrees to the direction AB. Determine the impuslive tension in the string when it becomes taut.

    2. Relevant equations



    3. The attempt at a solution
    Well, following from previous examples i tried to find the momentum in direction AB and perpendicular to AB.

    Momentum in direction AB

    mu + mu = U cos45
    2mu = Ucos45
    u = (Ucos45) / 2m

    Momentum perpendicular to AB
    mv = U sin45
    v = (Usin45)/m

    Impulsive Energy at A
    T = mu
    = (Ucos45)/2
    = (U * 1/root2)/2


    I think i've gotten it wrong. answer should be 1/4 m U root 2. can anyone help me out? I don't know if it's an algebra problem or (most likley) a method problem.
     
  2. jcsd
  3. Mar 5, 2007 #2
    try expressing the cos 45 as sqrt(2)/2, subbing that= u*sqrt(2)/4
     
  4. Mar 5, 2007 #3
    annoyingly i've lost an 'm' somewhere, but otherwise the answer checks out :)

    i didn't know cos 45 could be expressed as root(2)/2 ? or have you done some mathmatical jiggery-pokery that i have missed?
     
  5. Mar 5, 2007 #4
    no real trickery, just dividing or multiplying both top and bottom by sqrt(2).
     
    Last edited: Mar 5, 2007
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