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Stacked ball drop

  1. Apr 5, 2016 #1
    1. The problem statement, all variables and given/known data
    A tennis ball has a mass of 75 g that is placed above a basketball has a mass of 590 g. Both are stationary and They were dropped from a height about 1.2 m ( The collisions are perfectly elastic)
    1) Calculate the speed of the basketball when it reaches the ground
    2) Calculate the height that the tennis ball will reach

    2. Relevant equations
    P = m v
    F t = m dv

    3. The attempt at a solution
    Okay, so part one is pretty easy
    1) sqrt(2 g 1.2) = 4.89 m/s (Use g as 10)
    Now for the 2nd part, It is common that the ratio is 3 ( The speed of the tennis ball is 3 multiplied by the initial speed of it)
    However I didnt get that through my calculations ( 2.55)
    Here is my solution:
    V1: Speed of the basketball
    V2: Speed of the tennis ball
    1 = v2 -v1/u1 - u2
    u1-u2 = v2 -v1
    (Without needing to extract this equation through kinetic energy and momentum)
    Now the basketball will rebound with the same speed (assuming it is instantaneous) but moving upward
    And it will now have a collision with the tennis ball that is moving downward with the same speed
    So
    4.89--4.89 = v2 - v1
    9.79 = v2 - v1
    v1 = v2 - 9.79
    Now Substitute that in the momentum equation
    M* 4.89 - m * 4.89 = M * (v2 - 9.79) + 0.075 v2
    Place the value of M and m
    and V2 ( Velocity of the tennis ball) will equal to 12.48 m/s.
    For the ratio, 12.48/4.89 = 2.55

    http://hyperphysics.phy-astr.gsu.edu/hbase/doubal.html
    Here is the site for a reference about the ratio.
    I assume that the mistake might be in that they assume if the top ball hits the bottom one, the bottom one's velocity doesn't change which is a mistake.
    And according to my calculations, A ratio of 3 will only result if the m of the tennis ball is 0 which cant happen... Weird

    There are various of ways to solve this question, and all of them yield in the same result
     
    Last edited: Apr 5, 2016
  2. jcsd
  3. Apr 5, 2016 #2

    haruspex

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    The analysis at that link assumes the lower ball is much more massive, and it gives the speed ratio 3 as the limit value as the mass ratio tends to infinity. It will never quite equal 3.
     
  4. Apr 5, 2016 #3
    Hmm so I got an equation for this type of problems.
    V(small ball) = v(initial) ( 3M -m ) / (M + m)

    So what they assumed that the M is massive so that the m of the small ball wouldn't affect the ratio that much. So it is basically near 3.
    Alrighty, Thanks
     
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