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Bouncing ball lab

  1. Nov 12, 2007 #1
    1. The problem statement, all variables and given/known data

    Figure out the total distance traveled by a ball bouncing vertically when its dropped from a height of 6 ft above the ground and the time the ball was in motion for.

    G 32ft/s^2

    ball one dropped from 72 inches bounced back up 53 inches with a Coefficient of restitution of .736

    2. Relevant equations
    the distance i figured would be the CR of each bounce up times 2, with the initial drop the ball traveled 178inches with just one bounce.

    72 drop down + (2(53 bounce[up + down])) + (2(53xCR)) + ....

    How do i figure out how to calculate the distance without punching in the CR and calculating each bounce up and down


    3. The attempt at a solution

    I got the Coefficient of restitution for each ball tested, but im having some trouble with figuring out the time and distance problem.
     
  2. jcsd
  3. Nov 12, 2007 #2
    here are the equations that were presented with the lab.

    [​IMG]
     
  4. Nov 12, 2007 #3
    Bouncing ball distance

    edit
     
    Last edited: Nov 13, 2007
  5. Nov 13, 2007 #4

    rcgldr

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    Ignoring deformation, the ball bounces an infinite number of times, but in a finite time. What you're looking for is this sum:

    [tex]\lim_{n \rightarrow \infty} \ 72 + 2 \times \ 53 \times \ \sum_{i=0}^n \ (.736)^i[/tex]

    This sum can can be calculated with a somewhat clever method.
     
    Last edited: Nov 13, 2007
  6. Nov 13, 2007 #5
  7. Nov 13, 2007 #6
    hmmm soo how would i go about figuring out the clever method to get he sum. im just having a hard time with this, someone please help.
     
    Last edited: Nov 13, 2007
  8. Nov 13, 2007 #7
    wouldnt it be like this?? the equation
     
  9. Nov 13, 2007 #8
  10. Nov 13, 2007 #9
    i looked at the wiki page but im just having some trouble with set up of the equation. i know jeff reid set up an equation for me but i am still having trouble understanding the set up and calculating it.
     
  11. Nov 13, 2007 #10

    Shooting Star

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    The sum of an infinite geometric series with 1st term 'a' and CR 'r' = a/(1-r), if mod(r)<0. That was what Jeff Reid was talking about. Now try out the formula he gave.
     
  12. Nov 13, 2007 #11
    Starting with your
    S = 72 drop down + (2(53 bounce[up + down])) + (2(53xCR)) + ....
    and re-writing it as
    S = 72 + 2(72)x0.736 + 2(72)x0.736^2 + 2(72)x0.736^3 + 2(72)x0.736^4 ...
    = -72 + 2(72) + 2(72)x0.736 + 2(72)x0.736^2 + 2(72)x0.736^3 + 2(72)x0.736^4 ...
    -72 + a + ar + ar^2 + ar^3 ...
    where a is 2(72) and r is 0.736

    Check out the wikipedia link and you will find that the sum of
    a + ar + ar^2 + ar^3 ...
    is
    a / (1 - r)
     
  13. Nov 13, 2007 #12
    awesome, thanks guys

    would i go about the same way to figure out the total time in seconds the ball was in motion.
     
  14. Nov 13, 2007 #13
    Try it!

    What is the time for the first bounce, second bounce, third bounce ... any pattern like ar^n wher n is 1,2,3, ... ?
     
    Last edited: Nov 13, 2007
  15. Dec 6, 2007 #14
    wouldnt i just go about finding the time by first finding hte total distance in feet, then figure out the time it was in travel by the feet per second it travels.

    total distance / 32ft/s^2
    sqrt of (total distance / (32ft/s^2))
     
  16. Dec 7, 2007 #15

    Shooting Star

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    The ball does not have a constant speed...
     
  17. Dec 11, 2007 #16
    if the balls speed changes thus making it not have equal speed between bounces taking different time how do i go about figuring it out with geometric progression
     
  18. Dec 11, 2007 #17

    Shooting Star

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    Each time the ball bounces back with 0.736 of the speed with which it hits the ground. We know the time a ball takes to fall back to the ground if it's projected upward with velo v. Sum the times of each bounce-- that's also a GP. Remember, the very first time it only fell.
     
  19. Dec 12, 2007 #18
    Like I said, "What is the time for the first bounce, second bounce, third bounce ... any pattern like ar^n wher n is 1,2,3, ... ?"
     
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