Project 2

Engr 120

1.  Overview

Your Company is designing a new golf ball. The boss has decided that he's tired of his ball rolling down off the green into the water hazard, so he wants a ball that will stop rolling! Your mission is to determine what the coefficient of rolling resistance (more commonly known as friction) between a golf ball and the green is, and to build a model for designing golf balls that will determine what coefficient of friction is required to keep a bowl from rolling given the incline.

You may work individually or in teams of two on this project.

2.  Assumptions

  1. The coefficient of rolling resistance between the carpet in this room and a golf ball is roughly equivalent to that of the ball and the green

  2. Golf balls can be constructed with any coefficient of RR needed, without changing the mass. How isn't a concern.

  3. All the forces that act on the golf ball to oppose gravity will be lumped into ``friction'' (i.e. air resistance, the fact that the ball isn't round, dirt on the ball, etc., will be neglected).

  4. The weight of a golf ball is 1.62 oz.

3.  Theoretical Model

You need to determine the equations for a ball rolling down a hill. We will go over this in class.

First of all, let's consider a ball rolling on a flat surface at constant velocity. Ideally, no force would be required to keep this ball rolling at the same speed. However, a force is required to overcome the effects of rolling resistance. The rolling resistance is proportional to the weight of the ball. The figure below shows all the forces acting on the ball:


W is the weight of the ball, R is the effect of rolling resistance, and P is the force required to keep the ball moving at constant velocity. r is the radius of the golf ball, and b is the coefficient of rolling resistance (distance from the point of contact with the ball and the ground to the point where the effect of rolling resistance is presumed to act). You can find the force P by summing the moments about the center of the ball, a technique those of you in ME or CE will become intimately familiar with. The result of this technique is the following equation:

Pr = Wb

So given W, r and P, determining b is a simple task. However in our case, things are a little more complicated. This ball will be rolling down an incline, so the weight must be separated into two components, the force acting down on the center of the ball, and a force pulling the ball down the slope, as show below.


The two components of the force can be determined from simple trigonometry:

Wx = Wsinq

Wy = Wcosq

Wy will contribute to the rolling resistance force. Wx will cause the ball to accelerate. The ideal acceleration can be determined using F = ma. You will measure some acceleration which is smaller than this. The reason for this is that some of the Force will be needed to overcome the rolling resistance. You can compute the part of Wx used to accelerate the ball by determing:

Faccel = maactual

The force used to combat resistance will therefore be:

P = Wx-Faccel

4.  Experimentation

  1. Determine the angle of the incline in the floor in McAdams 100.

  2. Using a stopwatch, time the amount of time it takes the ball to roll from a dead stop to 5', 10' and 15' down the incline. To minimize measurement error, repeat each measurement at least 3 times.

5.  Data Analysis

Enter your experimental data into Excel and produce a plot of it. Use Excel and/or your calculator to fit a curve to your data. Determine the best possible model. Compare this equation to your ideal equation. The difference in the acceleration values should be due to friction. Calculate the force due to friction, and from this force determine the coefficient of friction.

6.  Simulation Model

Write a Matlab program which will simulate the golf ball rolling down an incline. Let the inputs to the program be the coefficient of RR for the ball and the angle of the incline. Plot distance and velocity vs. time for a 10 foot roll. Write a second program which, given an angle of incline, will calculate the minimum coefficient of RR to keep the ball from rolling. You may be able to reuse some functions between the two programs.

7.  Report & Presentation

Write a detailed report outlining the goals of the project, the procedures you followed and any problems you encountered. Include all of your data, plots, equations, program code, and demonstrations of your simulation. Refer to your Technical Communication book for information on format of a technical report. All parts of the report should be typed. One written per group will suffice. Prepare a five minute presentation demonstrating what the project was, how you went about it, and what your results were. All group members must speak during the presentation.

File translated from TEX by TTH, version 0.9.