Purpose 
Apparatus 
Calculations 
Proceedure 
Measurements 
Conclusion 
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.
3 sticks (48 inches, 46 inches
and 23 inches)
2 golf ball (Spalding, Topflite 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 
Angle(in degrees) 
Dist. Between the Ball and the Cup(in inches) 
Height of the Cup(in inches) 












Angle(in degrees) 
Dist. Between the Ball and the Cup(in inches) 
Height of the Cup(in inches) 












Angle degrees 
Base length (B) inches 
Length of top board (H) inches 
Ballcup distance (X) inches 
































Actual working differences between ballcup 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
The ball, when sitting on the propped up topboard, 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 freefalling. One end of it is already on the ground. As the starting angle between the ground and the topboard decreases, the board's rate of acceleration will approach (but never quite reach) 9.8 meters per second squared. The topboard 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 topboard'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 topboard.ÝIf the topboard 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 topboard 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 topboard, the height of the cup is the most important factor for determining the range of angles for the test to work. If the topboard 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 topboard 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!