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Displacement-Time Graph of a bouncing ball

  1. May 10, 2016 #1
    1. The problem statement, all variables and given/known data
    Does anyone know how to plot a displacement-time graph that will give the average velocity of a bouncing ball? The ball bounces 5 times and I would like to know it's average velocity. What equations would I use?

    2. Relevant equations
    0.5mv^2=mgh?

    3. The attempt at a solution
    I simply plotted displacement vs time graph but I get a quadratic (or exponential) function. I just want to confirm if I am doing this right. Thank you.
     
  2. jcsd
  3. May 10, 2016 #2
    the bouncing ball is a repetitive event and in between the bounces the speed increase -goes to a maximum and then reverses its path. so the displacement time graph should be quadratic in nature.
    what is meant by average velocity -i fail to understand but if you take the slope of displacement time graph at various points of time , then a graph of velocity and time can be plotted and one can try to get average velocity.
     
  4. May 10, 2016 #3
    So what can I do to my graph to make it a linear function?
     
  5. May 10, 2016 #4
    a displacement can depend linearly on time only in case of motion with uniform velocity- so the physical event of bouncing ball is not a system having uniform velocity.
    therefore how one can force the system to change its action.

    however if you plot displacement with square if time - artificially one can show a linear dependence- and for that to happen the initial velocity must be zero.
     
  6. May 10, 2016 #5
    Can you explain why squaring the time would result in a graph where the gradient is the velocity? Also, would displacement be displacement^2 or stay displacement?
     
  7. May 10, 2016 #6
    well one should look at the physical event -
    say a ball falling on floor from a
    height say h initial velocity =0
    so write down equation for displacement - it should be a function of t^2;
    again after hitting the floor and bouncing back with finite velocity the displacement will be a function of time and time square.
     
  8. May 10, 2016 #7
    Ok so basically, if I graph time squared and displacement, I WILL get the velocity from the gradient is what you are saying?
     
  9. May 10, 2016 #8
    yes, thats my hint.
     
  10. May 10, 2016 #9
    But then I have an equation t^2=2s/a ... so where is the velocity?
     
  11. May 10, 2016 #10
    for velocity you have the displacement -time graph and if you take slope i.e. rate of change of displacement with time then only you can get velocity -
    from any other graph you do not get it as velocity is unique.
     
  12. May 10, 2016 #11
    Then what happened to the time squared? I want to find the velocity of a bouncing ball as it bounces 5 times. What do I do?
     
  13. May 10, 2016 #12
    initially you talked of average velocity-
    now you say the velocity which can bounce five times.
    so clarify your question again.
     
  14. May 10, 2016 #13
    My question is what is the average velocity of a ball after 5 bounces?
     
  15. May 10, 2016 #14
    then you have to work with displacement -time quadratic curve.
    if however you have an ideal ball and ideal collision -elastic the one can predict the velocity after any number of bounces as the linetic energy is not lost in bouncing-
    i.e. if it is dropped from a height h
    the final velocity before the hit will be mgh =1/2 . m v^2 ; so v= sqrt(2.g.h)
    and after elastic collision its speed will be same in opposite direction.
    so after 5th bounce also it should have the same velocity.
     
  16. May 10, 2016 #15
    Yeah but my ball is not elastic, it jumps to around 0.5 of its initial height. What do I do to this quadratic curve to get a straight line whose gradient is average velocity?
     
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