# The Great Ball Drop Experiment

Shinichiro Sakaki and Lavell Blanchard
Physics 1999 Final Project
Mr. Matthew T. Geyman

## Purpose:

The purpose of this project is to see if the "Ball and Cup" trick outlined in our textbook (Physics; 3rd Edition; by Wilson & Buffa; Prentice Hall) truly works and if the angle of the top board and the weight of the top board will cause a change in the results of the trick, and to see if the ideas of Galileo hold true in this experiment.

## Procedure:

We took a golf ball and placed it in the ball holder at the end of the board and placed the board at the experimental angle.  We then used the carpenterís square to determine the point on the base board directly below the resting point of the ball. Then we lowered the top board, and marked a corresponding point on it ó placing silly putty on that point and placing a cup there.  This is where we believed the ball would land. After we saw that the cup was secured and steady we moved the board back to the experimental angle.  We propped the board up at that angle with a small stick.  After waiting a few seconds to see if everything was stable, we sprung the stick out quickly and watched the ball fall (hopefully!) into the cup.  We repeated this procedure, making slight adjustments, until the ball landed in the cup continuously.  At that point we measured the distance between the ball and the cup.  We then recorded the data, including the height of the cup. Then we moved on to a different angle and repeated this procedure at that angle.   We tested greater and lesser angles to determine the range of operability, each time recording the data.  Then we took clay and placed it on the board to see if the added weight would change the outcome of the experiment.  We repeated the previous step over again and recorded the data.  For the final part of the experiment we cut the cup to lower the height of the cup to see if this would change the results.  We then recorded the data of this test.

## Apparatus:

 3 sticks (48 inches, 46 inches and 23 inches) 2 golf ball (Spalding, Top-flite plus II) 2 Spring water cups cut in half carpenter's square 2 hinges silly putty clay 1 Egg exact knife video camera 2 chop sticks pen , pencil paper protractor spot light

## Measurements:

30
5.5
2.5
35
7.25
2.5
40
9.00
2.5
45
10.75
2.5

### (in inches)

20
2.5
1.5
25
3.5
1.5
 50 14 1.5 55 15 1.5

## Calculations:ÝÝ

### Ball-cup distance (X) inches

20
43.23
46
2.77
25
41.69
46
4.31
30
39.84
46
6.16
35
37.68
46
8.32
40
35.24
46
10.76
45
32.53
46
13.47
50
29.57
46
16.43
55
26.38
46
19.62

Actual working differences between ball-cup distances for 5 degree angles
7.25 inches -5.50 inches = 1.75 inches
9.00 inches - 7.25 inches = 1.75 inches
10.75 inches - 9.00 inches = 1.75 inches

3.5 inches - 2.5 inches = 1.0 inches
15 inches -14 inches =1 inch

## Conclusion:

From our calculations, we were able to create a good aproximation of  the base length.Ý

The ball, when sitting on the propped up top-board, is at a greater height than the cup that is attached to the board; still, when the stick is removed and the ball and cup are falling, the ball lands in the cup.  The ball falls in a verticle line, and the cup travels in an arc to the same spot.  Even though the board and cup are moving in a circular path, it appears that board and the cup are accelerating faster than the ball, causing the board to hit the ground before the ball ó but this would contradict the ideas of Galileo Galilei and his law of falling objects, which states that all objects fall at the same rate due to the gravitational force applied to them.  However the board, in this case, is not free-falling.  One end of it is already on the ground.  As the starting angle between the ground and the top-board decreases, the board's rate of acceleration will approach (but never quite reach) 9.8 meters per second squared.  The top-board with the cup and the ball drop at almostthe same rate of acceleration; the cup starts slightly lower than the ball, and simply arrives first due to this starting height difference alone.

In Test 2, even though we knew better, we assumed that weight would affect the top-board's falling rate before we start the experiment.Ý However, as you can see from the results, weight will not affect the falling acceleration of the top-board.ÝIf the top-board fell faster, the range of working angles would increase, but since the range of the angle did not increase in Test 2, we can say that the falling speed of the board didn't increase even though we added weights.  It means this experiment is still follows Galileo's principal of free fall ó weight has nothing to do with the rate of free fall.

The range of angles for a top-board length 46 inches with a cup height of 2.5 inches is greater than 30 degrees but less than 45 degrees.Ý If you make the angle smaller, the ball will hit the cup and will not go in. Also if the angle exceeds 45 degrees, the ball will hit the side of the cup.Ý This means that the cup is too high and needs to be shallower in order for the ball to go in.Ý When we tested with a shallower cup, 1.5 inches high, the range of angles increased, from a minimum of 20 degrees to a maximum of 55 degrees.Ý From that we can conclude that with the same length top-board, the height of the cup is the most important factor for determining the range of angles for the test to work.  If the top-board is at a much greater angle, this difference in falling acceleration prevents the ball from dropping into the cup ó the ball would end up rolling down the board.  If the top-board were at a much lower angle, the arc would not produce enough horizontal movement to move the cup under the ball, and the cup would have to be extremely short as well.

We can conclude that, within the range of operating angles (30 - 45 degrees), there is a direct relation between angle and distance between the ball and the cup; for every 5 degree change in angle, the distance must change about 1.75 inches in the corresponding direction.  Also, between the angles of 20 and 30 degrees, and between 45 and 55 degrees, the distance between the ball and the cup increases 1 inch for every 5 degrees.

There is one remaining aspect of The Great Ball Drop Experiment to be considered:  The "Coolness Proportion:"  This experiment is neat because it appearsunlikely.  In fact, the more unlikely it appears, the cooler it is.  And the way that it looks most unlikely is when the top edge of the cup is at the nearest possible height to the bottom of the ball (of course, it can never be higher).   Therefore:

For a cup of given height, the Coolness is greatest at the lowest operational angle, or  Given cH, C is inversly proportional to A until failure.

So, we determined that given a cup height of 2.5 inches, the Coolness was greatest at 30 degrees.

And finally, what we're sure you are waiting for is to see this phenomenon in action!