The Happy Gilmore Celebration

December 5, 2006

Bryan Hunter

Zack Watts

Jonathan Kahler Table of Contents

Summary: Overview of a Technological Marvel...... 3

Behind the Project: The Design Process...... 3

Device Description: In the Belly of the Beast...... 4

Energy Conversions: No Concern for Conservation...... 7

Bill of Materials: The Grocery List...... 11

Conclusions: The End of an Era...... 12

Sources: Aiding and Abetting...... 13 Summary: Overview of a Technological Marvel

The Happy Gilmore Celebration is an overly-complex compilation of mostly- random items built to accomplish the simple task of making a golf ball into a hole and popping a confetti-filled balloon in worldwide celebration. In short, the golf ball falls through a series of ramps, after which it strikes a second golf ball which falls into a cup.

The cup is attached via pulley system to a lever, which strikes two sets of dominos leading to two other golf balls. The first ball is knocked onto a ramp leading to the hole.

The other ball is knocked into a tube, at the end of which it rolls into a Dixie cup attached to a lever, causing the lever to rotate and strike another ball resting at the top of a ramp.

This ball rolls down the ramp and collides with another lever—this time, tipped with an

Xacto blade—which pops a balloon as a finale for the ball landing in the hole.

Behind the Project: The Design Process

At first, obviously, the group was somewhat intimidated by the broad range of ideas for our project. Upon finally sitting down and trying to crank out a rough design, we decided that we would have a ball roll down a series of flat inclines before being dropped onto a ramp that sloped downward and then upward, where the ball would have just enough momentum to strike another ball into a cup hanging from a string. This string would be attached to a lever which would rotate upward, popping a balloon.

Although the design seemed feasible, we quickly discarded the idea of the ball rolling down and then up a “vert” style ramp before colliding with another ball. This part of the design would have been too difficult to build with the mostly-cardboard supplies we had on hand, and it would have been even more difficult to get the ball to leave it at the right speed.

Upon completing the project up to the ball falling into the cup, we realized that our run time was far too brief for our liking. We were not satisfied with a ball going down some ramps, falling into a cup and then “POP!” So instead of having the lever pop the balloon, we decided to have it hit something else, perhaps triggering a domino effect.

We eventually decided to use to use actual dominos to achieve this desired effect. We then thought it would be cool to have the dominos split off and start two different processes. One, we knew would continue through other steps. The other, though, we thought should just be a ball rolling down a ramp. We then remembered the life- changing climax from Happy Gilmore, where Happy manages to sink the winning put in a very “Rube-Goldberg-esque” fashion. This is what gave us the use for our device, as well as the name, “the Happy Gilmore Celebration.”

Device Description: In the Belly of the Beast

The Happy Gilmore Celebration uses several steps to knock a golf ball into a hole and pop a balloon filled with confetti. In the first step, a golf ball is placed at the top of a series of cardboard ramps. The ramps are shaped with Duck tape (as is most of the device) and are built to move the ball along all sides of the rectangular central structure, a shoe-rack box. The ball rolls down five ramps, the last of which is on the side the ball began. The last ramp has a square “trap door” cut out of the end and flipped up in order to stop the forward motion of the ball, which hits the door and falls through the hole into a cardboard tube sloped downward in the opposite direction. At the opposite end of the tube, another golf ball is held in place at the other opening by friction with the walls of the tube, which is narrower at the bottom than at the top.

When the first ball reaches the end of the tube, it collides

with the second ball, propelling it into a Styrofoam cup

hanging from a string. The first ball stays in the tube

because of the opposing forces of the collision with the

second ball and because of the friction with the walls of the

tube that held the second ball in place. The second ball falls

into the cup, which is held in equilibrium by a string attached to a lever over a simple series of pulleys. The downward force of the ball falling into the cup is transferred through the string to the lever, causing it to flip upward with approximately the same velocity as the ball when it lands in the cup.

In step three, the lever collides with a

domino, which then hits two other dominos,

branching into two separate paths. At the end of

each path, the final domino collides with a golf

ball. The first ball is placed at the top of a ramp made from a foam tube that we cut in half. The other ball is placed just in front of the opening to a tube made from rolled up posters that we Duck taped together.

Ball A travels down the ramp, landing in our handy

roll of Duck tape, a.k.a. the

hole. Ball B travels down

B the poster tube, at the end

A of which it hits a Dixie cup

attached to yet another hinged lever. As the ball hits the bottom of the Dixie cup, the lever rotates about the hinge, causing the bottom of the lever to raise and strike another golf ball resting at the top of another foam ramp.

In the final step, the

golf ball travels down

the foam ramp and

collides with a cardboard lever hinged to the base by

Duck tape. At the tip of the lever lies an Xacto blade.

The ball hits the lever, causing it to rotate about the hinge bringing the Xacto blade into contact with the confetti-filled balloon.

The ball is in the hole, and the balloon is popped. Now it’s time to clean up!

Energy Conversions: No Concern for Conservation

Although the machine is inefficient by definition, all steps except for the final steps do not account for ELoss. This is because we are unable to quantify the specific forces that resist motion and cause inefficiency. Therefore, all of the theoretical velocities are calculated to be 100% efficient, and are likely to be higher than the actual velocities.

For the first step, the ball rolls down five ramps, experiencing a dramatic loss in energy each time it moves from one ramp to the other. The change in height from the start of each ramp to the end is approximately 0.5 inches.

Assumptions: The force of friction is negligible. The initial velocity at the beginning of each ramp is 0.

2 mgh0 = .5mvf

2 2 (32.2 ft/s )(0.5in)(1ft/12in) = .5vf

 The velocity of the ball at the bottom of each ramp: vf = 1.64 ft/s

For the second step, the ball begins by hitting the “trap door” and then falling through the hole in the ramp into the cardboard tube, at the end of which it collides with another golf ball held in place by friction with the walls of the tube. The change in height from the top of the tube to the bottom is approximately 6.5 inches. The second ball then falls into a cup hanging under the tube. The change in height from the bottom of the tube to the bottom of the cup is approximately 5.5 inches.

Assumptions: The initial velocity of the first ball is 0. The force of friction on the second ball is just enough to hold it in place, and does not significantly affect the collision. The coefficient of restitution is 1.

2 mgh0 = .5mvf

2 2 (32.2 ft/s )(6.5in)(1ft/12in) = .5vf

 The velocity of the first ball at the end of the tube: vf = 5.91 ft/s 1 = (v2f-v1f)/(v1i-v2i)

1= v2f/(5.91ft/s)

 The velocity of the second ball after the collision: v2f = 5.91ft/s

2 2 .5mvi + mgh0 = .5mvf

2 2 2 .5(5.91ft/s) + (32.2ft/s )(5.5in)(1ft/12in) = .5vf

 The velocity of the second ball when it hits the cup: vf = 8.03ft/s

As the ball hits the cup, it applies a downward force to the Styrofoam cup being held in equilibrium by a string directly attached to a hinged lever lying in the horizontal position. The energy transfers directly through the string, over four pulleys in place to reduce friction, and pulls the lever vertically about the hinge. As the lever rotates upward, the cup is pulled down 1.5 inches.

Assumptions: The friction holding the empty cup in equilibrium is not significant enough to affect the transfer of energy as the ball hits the cup. The mass of the cup, as well as its resistance to the free fall of the ball, is negligible. The velocity of the lever is the same as the velocity of the ball after the cup has moved down 1.5 inches.

2 2 .5mvi + mgh0 = .5mvf

2 2 2 .5(8.03ft/s) + (32.2ft/s )(1.5in)(1ft/12in) = .5vf

 The velocity of the ball and cup after the cup has moved down 1.5 inches:

vf = 8.51ft/s

 Therefore, the velocity of the lever as it has become completely vertical:

vlever = 8.51ft/s

The third step of involves the lever colliding with a domino, which starts a chain reaction as that domino hits two others, branching off into two separate paths of dominos. At the end of the third step, the final dominos of the two chains strike two golf balls placed at the top.

Assumptions: The first domino hits the second with a speed of 8.51ft/s, and velocity remains constant throughout the chains. The mass of a domino is approximately one half that of the golf ball. The coefficient of restitution between the domino and golf ball is 1.

mv1i = mv2f

.5v1i = v2f

.5(8.51ft/s)= v2f

 The velocity of both golf balls after they are struck by the dominos:

v2f = 4.26ft/s

In the fourth step, the golf balls are both pushed into their respective inclines.

The change in height experienced by ball A, traveling down the foam ramp, is 9.5 inches.

The change in height for ball B, traveling through the tube, is 2 inches.

Assumptions: Friction between the balls and their inclines is negligible.

2 2 .5mvAi + mgh0 = .5mvAf

2 2 2 .5(4.26ft/s) + (32.2ft/s )(9.5in)(1ft/12in) = .5(vAf )

 The velocity of ball A at the bottom of the ramp: vAf = 8.31ft/s

2 2 5mvBi + mgh0 = .5mvBf

2 2 2 .5(4.26ft/s) + (32.2ft/s )(2in)(1ft/12in) = .5(vBf )

 The velocity of ball B at the end of the tube: vBf = 5.37ft/s

In the fifth step, ball A reaches the end of the ramp and is stopped in the hole.

Ball B reaches the end of the tube and is caught by a Dixie cup attached to a hinged lever. The lever then rotates about the hinge and nudges another golf ball, ball C down a ramp.

The change in height from the top of the ramp to the bottom is 4 in.

Assumptions for ball A: Friction is negligible. The final velocity of ball A is zero. The mass of the golf ball is .0459 kg ~ .00315 slug

mvAi = mvAf + ELoss

(.00315slug)(8.31ft/s) = ELoss

 The energy lost after ball A comes to a rest in the hole: ELoss = .0261lb-s

Assumptions for ball B: Friction is negligible. The velocity with which ball B enters the Dixie cup remains constant as the lever rotates about the hinge. The angle of the lever when it makes contact with ball C is approximately 45° below the horizontal.

The velocity transferred to ball C from the lever is the instantaneous horizontal component of the lever’s tangential velocity. The mass of the lever itself is negligible, and only the mass of the golf ball in the Dixie cup should be considered. The coefficient of restitution between the cardboard lever and the golf ball is approximately 1.

vLever = 5.37ft/s

vLeverx = 5.37ft/s(cos45°) = 3.80ft/s

mvLeverx = mvci

 The initial velocity of ball C after being hit by the lever: vci = 3.80ft/s

2 2 .5mvi + mgh0 = .5mvf

2 2 2 .5(3.80ft/s) + (32.2ft/s )(4in)(1ft/12in) = .5vf

 The velocity of ball C at the bottom of the ramp: vf = 5.99ft/s

In the final step, ball C rolls into a hinged lever which pops the balloon. The collision

with the hinged lever brings the ball to a stop. Assumptions: Friction is negligible. The final velocity of ball C is zero. The

mass of the golf ball is approximately .00315 slugs.

2 .5mvi = ELoss

2 .5(.00315slug)(5.99ft/s) = ELoss

The energy lost after ball C is stopped by the lever: ELoss = .0565lb-s

Bill of Materials: The Grocery List

 Hinge x 2 = $2

 Pulley x 2 = $3

 String = $1

 Duck Tape = approx. $2

 Wood base = $4

 Dominos = $4

 Various cardboard scraps (modified) = approx. $1

 Balloons = $1

 Confetti = $1

 Cardboard tube (modified) = $0.25

 Styrofoam cup (modified) = $0.25

 Screws = $0.10

 Washers = $0.10

 Golf ball x 5 = No cost

 Poster x 2 = No cost  Foam tubing = No cost

 Xacto blade = No cost

 Shoe rack box = No cost

 Priority Mail box = No cost

 Toaster box = No cost

 Duck tape roll (used for hole) = No cost

o Total = $19.70

Conclusions: The End of an Era

Although our device did not turn out exactly as we had planned, we can only consider it a resounding success. Our device changed a lot throughout the course of the design process, but we always found a way to make it work the way we wanted. All it required was a little imagination. In fact, the largest problem we faced had nothing to do with building the device; rather, the only bumps in the road came when we realized the difficulty inherent in trying to describe the processes we had engineered mathematically.

However, we are more than satisfied with our effort on this project, and we hope that everyone will join us in the celebration that ensues after the golf ball drops and confetti is dispersed into the atmosphere. Sources: Aiding and Abetting

The name and concept was derived from the movie Happy Gilmore. We would like to thank Wal-Mart and Lowes for supplying us with our purchased items. Also, we would like to thank the Architecture department for their contribution of a cardboard tube and Xacto blade, without which we would have been unable to precisely cut many components of our device. Another “thank you” goes to Estabrook room 13, which generously supplied us with a Priority Mail box, as well as a Toaster box and a

Styrofoam cup. Without these precious items, the Happy Gilmore Celebration would not be the astounding marvel of brilliance and ingenuity that it is.