# Bouncing Ball Problem

1. Mar 26, 2005

### flower76

I'm working on a lab of a bouncing ball. I have been told to fit each free-fall interval using the quadratic equation which will give the values of a,b and c for y=ax^2+bx+c. Then I am to related this equation to the one for motion of a falling object y = yo + v0t + 1/2gt^2 and interpret the meaning of each parameter.

Based on this a is the acceleration due to gravity, b is the initial velocity, and c is the initial height.

But looking at the actual data collected for the ball bouncing, the numbers for b, and c are increasing with each bounce. This doesn't make sense since they should be decreasing if they represent initial velocity and height. I know I'm missing something here, but can't figure out what.

Any suggestions?

2. Mar 26, 2005

### whozum

You are probably modeling the height of the bounce as distance from the peak of the fall. As the ball bounces more and more, it loses height, thus its distance from the peak of the fall increases.

Initial velocity should be zero for each bounch though..

3. Mar 27, 2005

### flower76

I think I see what your saying about the height, but I'm not sure thats it. The numbers for height of the final peak work out to somthing like 55 m. Which is definately not a possibility any way you look at it. I think that past the first peak the values of b and c no longer represent the initial velocity and height. But I don't know what they are now.

Also in my lab it says that it should be expected to see the values of b increase. But it doesn't say why.

Any suggestions?

4. Mar 27, 2005

### whozum

I couldn't tell ya, sorry.

5. Mar 28, 2005

### plusaf

why?

where does the concept of "the initial height increases" come from?

empirically, if you bounce a ball, the "free fall" part of the bounce, which i'll take to mean, "from the apex of each parabolic arc until it hits the ground", the apex would be lower each time because of air resistance (which we could neglect as a first-order effect) and also due to momentum lost by the inelastic collision of the ball with the "ground" at the bottom of each bounce.

if the first drop of the ball fits the equations, on the first bounce it will rebound to a lower height (i.e., lower energy level) due to the lost energy of the collision with the ground. therefore, the highest point of the next arc must be lower than the height of the initial drop. when the first bounce completes and the ball hits the ground again, it loses more momentum/energy and bounces again to another lower max height.

if you can determine from the experimental data, the maximum height of each subsequent bounce, you can easily determine how much energy was lost upon the previous contact with the ground.

but again, that's probably a nice, but irrelevant, exercise. if your experimental data show the height of the peak of each bounce, from each of those max-height instants in time, the same equations will determine the y and x positions of the ball!

help ME! what am I missing?!

6. Mar 28, 2005

### whozum

its a funky experiment