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Creating a Numerical Model for a falling Ball

  1. Nov 1, 2014 #1
    1. The problem statement, all variables and given/known data
    A ball was dropped through a known vertical distance with the time of drop also recorded. The aim of the task is to create a numerical model in excel in order to approximate the drag coefficient.

    2. Relevant equations
    This is my method.

    1. FBD for the ball falling. (assume forces only acting in y direction)
    APviUjM.jpg
    (note approx range for Cd (drag coefficient) may be wrong as a different ball was used.

    2. Spreadsheet.
    jfoLkcm.jpg
    The aim is here that we use calculate the values for v,a,Fd and t for the 0.01 intervals of y.
    Since we use small intervals for y we can use constant acceleration equations.

    3. The attempt at a solution
    Originally I tried some of these constant a equations although I seemed to overlap and could not work out the next values. I then tried to start at the end however this also did not work. The aim is to work out a value for Cd (drag coefficient) where tend = 0.5.

    Looking at some material on the web it claims to use time intervals although we have been instructed to use y intervals (distance intervals).

    (NOTE: It was suggested we adjust Cd value until estimated time is close to actual time.)
     
  2. jcsd
  3. Nov 1, 2014 #2

    haruspex

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    It's hard to comment if you don't show what you actually did.
     
  4. Nov 1, 2014 #3
    I think I may of finally got it. So here is my attempt attached and the formulas I used.

    D0DrHM8.jpg
     

    Attached Files:

  5. Nov 2, 2014 #4

    haruspex

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    You're not supposed to post handwritten equations as images. Images are for diagrams and printed text. Much better for those trying to read and comment to type in your working.
    Anyway, it looks ok except you've forgotten something in the vi+1 line.
     
  6. Nov 2, 2014 #5
    Sorry I forgot to square root the entire RHS right?
     
  7. Nov 2, 2014 #6

    haruspex

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    Yes.
     
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