Creating a Numerical Model for a falling Ball

In summary, the conversation discusses creating a numerical model in excel to approximate the drag coefficient of a ball dropped through a known vertical distance. The method involves using a spreadsheet to calculate the values of velocity, acceleration, drag force, and time at 0.01 intervals of distance. Some difficulty was encountered in finding the next values using constant acceleration equations, but a solution was eventually found. The conversation also touches on the difference between using time intervals and distance intervals in the calculation.
  • #1
cavalieregi
41
0

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)
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.

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.)
 
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  • #2
cavalieregi said:
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.
 
  • #3
haruspex said:
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.

D0DrHM8.jpg
 

Attachments

  • numerical model of falling ball in air.xlsx
    12.1 KB · Views: 336
  • #4
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.
 
  • #5
haruspex said:
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.

Sorry I forgot to square root the entire RHS right?
 
  • #6
cavalieregi said:
Sorry I forgot to square root the entire RHS right?
Yes.
 

Related to Creating a Numerical Model for a falling Ball

1. What is a numerical model for a falling ball?

A numerical model for a falling ball is a mathematical representation of the motion of a ball as it falls under the influence of gravity. It takes into account factors such as the ball's initial velocity, mass, and air resistance to predict its position and velocity at different points in time.

2. How is a numerical model for a falling ball created?

A numerical model for a falling ball is created by first identifying the relevant physical principles involved, such as Newton's laws of motion and the equations of motion for a falling object. Then, the model is constructed using mathematical equations and computer algorithms to simulate the ball's motion.

3. What are the advantages of using a numerical model for a falling ball?

The advantages of using a numerical model for a falling ball include the ability to accurately predict the ball's motion under different conditions, such as changing initial velocities or air resistance. It also allows for quick and efficient analysis of the ball's motion without the need for physical experiments.

4. Are there any limitations to using a numerical model for a falling ball?

Yes, there are limitations to using a numerical model for a falling ball. The model may not account for all the factors that can affect the ball's motion, such as changes in air density or surface friction. It also relies on assumptions and simplifications, which may not always accurately reflect real-world scenarios.

5. How can a numerical model for a falling ball be validated?

A numerical model for a falling ball can be validated by comparing its predictions to experimental data. This involves conducting physical experiments and measuring the actual motion of a falling ball, then comparing it to the predictions of the model. If there is a close match between the two, it provides evidence that the model is accurate and can be used for further analysis.

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