Thats How Far the Ball Drops

8/2/2019 Thats How Far the Ball Drops

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Ball Drop Lab

Just how far does a bouncing ball

travel??


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Objective

Through the use of Calculus calculate the total

distance a ball travels as it is dropped from a

known height.


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Steps Needed

Step 1

Measure point to be used as reference during

experiment

Step 2

Record a ball being dropped from a known height

to include all subsequent bounces till at rest.


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Calculating Heights

Through the use of a analytical software.

Breakdown the video to measure the ball

travel every time it falls from peak to ground.

Used Kinovea Program which I downloaded

for free from www.kinovea.org


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The Video

The Next couple slides will show the

measurements I took off of snapshots taken

from the Kinovea.


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Now to develop a series

ValuesInitial 0 200.58 9=27.68

1 148.92 10=21.96

2 113.60 11=16.233 96.42 12 =13.4

4 71.6 13=11.49

5 57.28 14=8.64

6 45.86 15=6.687 37.23 16=5.73

8 31.5 17=3.82


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Determine Percentages

From 1 height to the next you must determine if

there seems to be a pattern.

By dividing the next bounce and the first bounce

down the line a pattern appears.

1/0


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Calculating r

r in our case is the percentage a number

changes as you move down the sequence.

After all the percentages are calculated the

avg. for this problem is .794 or 79.4% of

previous bounce.


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Series Identifying

0 200.58

1 0 (.794)=159.26

2 0(.794)(.794)=126.45

3 0(.794) (.794) (.794) =100.40

4 0(.794) (.794) (.794) (.794) =79.72

5 0(.794) (.794) (.794) (.794) (.794) =63.29


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Pattern

Now we see the pattern

0()

0 is the initial height

r is the change

n is the number in the sequence


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Form

=0

a is our initial height a=200.58

r is percentage of change r=.794 k is number in sequence

This is a geometric series


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Calculating infinite series

Since we have r


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Total distance

Now that we figured out the infinite series we

need to move to how far our ball actually

moved. Since we took the percentage change

from one height to the next we did notaccount for the ball travel in two directions

only in one. The ball did travel in one direction

but only for the initial drop.


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Total Calculation

Distance travelled dropping

973.69 cm

Now we double this number

1947.38

Then we subtract the extra distance for initial

since not doubled1746.8


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Answered

Thus we have answered the question, how far

does the ball bounce.

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Thats How Far the Ball Drops