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Urgent Pendulum problem elastic collision

  1. Mar 21, 2012 #1
    Urgent!! Pendulum problem elastic collision

    1. The problem statement, all variables and given/known data

    An elastic ball (A) with mass m is released from a horizontal position, connected via
    a massless string to a rod. When the ball reaches the bottom, it collides with
    another elastic ball (B) of twice the mass, aslo connected via a massless string to the rod.
    How high can each ball swing, respectively? (The collision is total elastic.)
    Assume the +x direction is to the right
    a)What is the velocity of ball A after the collision? (5pt)
    b)What is the velocity of ball B after the collision? (5pt)
    c)How high will ball A swing relative to the bottom position? (5pt)
    d)What is magnitude of the tension force (T) in the string connected to the ball A at the
    moment right after the collision? (5pt)

    A picture of the problem can be found at http://www2.fiu.edu/~leguo/Site/PHY2048_files/ExtraCredit2.pdf

    2. Relevant equations



    3. The attempt at a solution

    M=Mtotal=3m
    Va= initial velocity A

    Vb= initial Velocity B

    V1= final velocity A

    V2= final velocity B

    pi= initial momentum

    pf= final momentum

    ki = initial kinetic energy

    kf= final kinetic energy



    So what I first did was I wanted to find the initial velocity ( Va) before the collision.

    To that I did: 1/2MVa^2=MgH
    Va= √2gh

    The collision is total elastic which means momentum and energy is conserved

    Pi=pf

    MaVa=Mav1+Mbv2

    Im going to solve for v2:

    MaVa-Mav1/Mb=v2

    Plugging in known variables

    m√2gh-mv1/2m=v2

    m's cancel and you get

    √2gh-v1/2=v2

    Here is where I get confused my main problem lies with h. So I want to make that h cancel

    since it is circular motion as the picture shows I try using uniform circular motion

    g=Va^2/H

    H= Va^2/g

    I want to make sure if im doing good so far. This is a problem that will be on my exam tomorrow so much help would be appreciated.
     
  2. jcsd
  3. Mar 21, 2012 #2
    Re: Urgent!! Pendulum problem elastic collision

    I'm attempting the same problem right now.

    I took a different approach after final the initial velocity.

    Since one object is stationary, I used the equations:

    vaf = (ma - mb) / (ma + mb) * vai

    vbf = (2ma) / (ma + mb) * vai

    plugging in that gave me

    (m-2m) / (m+2m) * √2gh
    = -m / 3m * √2gh = -1/3 * √2gh

    and

    2m / m+2m * √2gh = 2m/3m *√2gh = 2/3 * √2gh

    so the velocity of ball A after the collision is 1/3 the initial velocity in the opposite direction and the velocity of ball B is 2/3 the initial velocity of ball A in the +x direction

    Can someone verify if this is correct?
     
  4. Mar 22, 2012 #3

    gneill

    User Avatar

    Staff: Mentor

    Re: Urgent!! Pendulum problem elastic collision


    That looks okay :approve:
     
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