1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    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



    Im going to solve for v2:


    Plugging in known variables


    m's cancel and you get


    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


    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


    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


    User Avatar

    Staff: Mentor

    Re: Urgent!! Pendulum problem elastic collision

    That looks okay :approve:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook