Creating a Numerical Model for a falling Ball

[cavalieregi]

Homework Statement

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.

Homework Equations

This is my method.

1. FBD for the ball falling. (assume forces only acting in y direction)

(note approx range for C_d (drag coefficient) may be wrong as a different ball was used.

2. Spreadsheet.

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

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 C_d (drag coefficient) where t_end = 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 C_d value until estimated time is close to actual time.)

 

[haruspex]

I tried some of these constant a equations although I seemed to overlap and could not work out the next values.

It's hard to comment if you don't show what you actually did.

 

[cavalieregi]

It's hard to comment if you don't show what you actually did.

I think I may of finally got it. So here is my attempt attached and the formulas I used.

 

[haruspex]

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 v_i+1 line.

 

[cavalieregi]

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 v_i+1 line.

Sorry I forgot to square root the entire RHS right?

 

[haruspex]

Sorry I forgot to square root the entire RHS right?

Yes.