- #1

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**Problem statement:**

I have a 0.0506kg bouncy ball that will I drop at 1.75m. I must predict how many times it will bounce before it comes to a rest.

**My work:**

We did a lab to predict the percent of energy "lost" from each bounce. After doing some calculations with my data, I found that, on average, 37.9% of the total energy of the ball was "lost" after each bounce. (I verified this number with my teacher and classmates) Note that when I say "lost", I mean converted to thermal energy.

So, I took a similar approach to this problem.

PE

_{g}= mgh = (0.0506kg)(9.8m/s

^{2})(1.75m) = 0.868 J

I created a table.

Number of Bounces - Total Energy of Ball (J)

0 - 0.868

1 - 0.539

2 - 0.335

3 - 0.208

4 - 0.129

5 - 0.0801

6 - 0.0498

7 - 0.0309

8 - 0.0192

9 - 0.0119

We are using the same ball for this part. I maintained my assumption that after each bounce, 37.9% of the total energy of the ball will be converted into thermal energy. However, I must predict how many bounces the ball will bounce before it stops. But since I'm taking a percentage of the previous value will theoretically always have kinetic and potential energy, ie. not all will be converted to thermal. So theoretically it would bounce forever. At what height will the bounces become so small that's its unnoticeable?

For example, after the ninth bounce, the ball will reach a height equal to:

(0.0119 J)/((9.8m/s

^{2})(0.0506kg)) = h = 0.024m... or 2.4cm.

Not sure how far I want to take it before the ball supposedly stops bouncing. I will be graded on how accurately I can predict the # of bounces.