Galilean+Cannon


 * Lab Title:** Fire the Galilean Cannon!


 * Primary Authors:** Megan, Paul, Anna, and Lindsay


 * Abstract:** The goal in this lab is to find the combination of factors which maximize the height of the top ball on the Galilean cannon. To do this, balls of different mass, size, and material are needed to be able to test which balls maximize the height of the top ball.

media type="youtube" key="L6SKQYfpqHc?fs=1" height="385" width="480" Credit: user- sqfield, video- Galilean Cannon
 * Background Information:** A Galilean Cannon is a device which demonstrates conservation of energy. It comprises of a stack of balls with the largest, heaviest ball on the bottom and the smallest, lightest ball on the top. The idea is that the balls can be dropped and all the kinetic energy in the lower balls will transfer to the top ball, causing it to rebound to many times the height of its original drop. The device actually wasn't invented by Galileo Galilei, contrary to belief, but rather gets its name from the region of Galilee for unknown reasons. [Information from wikipedia.org]

The masses of the balls used were as follows: Basketball- 577 grams Volleyball- 261 grams Tennis Ball- 55 grams Blue Bouncy Ball- 24 grams Medicine Ball- 2721.55 grams


 * Topics Explored:** Kinetic energy and potential energy. Energy transferred from ball to ball.


 * Introduction:** The Galilean Cannon starts out with an initial velocity of zero. meaning it has no initial kinetic energy. That means it only has potential energy, being held at a certain height to be dropped and accelerate due to gravity. Once it falls and hits the ground, it no longer has potential energy because its height is zero; however, it has kinetic energy right before it hits the ground and this kinetic energy is transferred to the top ball when the bottom ball does work on the top ball. This is the reason why the top ball shoots upward and reaches its maximum height.


 * Methods:** For this lab there were many different balls used in order to test which balls work best to achieve the tallest height. The lab was set up in the hallway and the carpet was used as the base that the balls would hit. This area was chosen because it is better to drop a large ball (such as a basketball) on the ground than on a table. Also the height of the top ball might hit the ceiling if it is dropped on a high table and therefore the height could not be measured. The balls were dropped from the same height each time and there was no controlled acceleration or force on the ball except for gravity. Two balls were used each time, one on top of the other. A meter stick was placed vertically so that the person dropping the balls could ensure that they were at the same height each time they dropped the balls. Also, a video camera was used to videotape the balls dropping and bouncing in order for the action to be analyzed and the height to be measured in the program Logger Pro by setting a scale against our meter stick, then tracing the height of the ball frozen in the video frame of its topmost position. Logger Pro then could analyze the ratio between the scale and the height to determine the maximum height the ball reached.


 * Expectations:** From prior knowledge and research, it was concluded that the larger mass and sized ball must always be on the top position in the Galilean Cannon, otherwise the kinetic energy transferred to the top ball from the bottom ball would not be large enough to cause the heavier top ball to rise higher than its original position, in this case, one meter. There was the expectation that the bigger the bottom ball, the higher the smaller top ball would reach. Additionally, the blue bouncy ball would go higher than the tennis ball because of the rubber material out of which it was made. Therefore, the combination of the basketball on the bottom and the blue bouncy ball on top would go the highest.


 * Results:** In reality, many of the combinations of balls that were tried did not have the expected effects. Certain bouncy balls simply fell off the top of the larger ball or rolled and bounced off at an angle that made it difficult to measure, ending up traveling essentially sideways. Therefore, several of the balls that were intended to be used ended up not giving recordable data, thus were eliminated from the experiment. If it was possible to ascertain that the top ball traveled straight up, it would have been easier to measure all of our data with more accurate results.

1. Total Mass of Set-Up (kg) 2. Maximum Height of Top Ball (m) 3. Energy Transferred to Top Ball After Impact with Ground (J) [KEi=PEf]

Tennis Ball/ Volleyball: .316 kg 2.141 m 3.097 J Blue Bouncy Ball/ Volleyball: .285 kg 2.399 m 2.793 J Tennis Ball/ Basketball: .632 kg 3.260 m 6.194 J Blue Bouncy Ball/ Tennis Ball: .079 kg 1.752 m .774 J Blue Bouncy Ball/ Medicine Ball: 2.745 kg .9619 m 26.901 J


 * Conclusion:** From the data-- both collected and calculated-- the top ball would be expected to travel much higher than it actually did; however, the decreased maximum height is probably attributable to air resistance and the fact that the ball didn't always shoot off of the bottom ball directly upwards. Even going on a small angle would change the height significantly. The combination which traveled the highest was the tennis ball and basketball cannon, which was only half of the original prediction. Both basketballs and tennis balls are meant to be bouncy because of the nature of their purpose: in sports. Basketballs are dribbled on courts while tennis balls are bounced and hit off a springy racket, so both of those balls are designed to bounce and transfer energy well. Perhaps due to the lighter weight causing instability as the cannon was dropped, the blue bouncy ball did not end up being in the experiment which reached the highest distance. Instead, the tennis ball bounced higher, maybe as a result of its materials. This could also explain the reason why the medicine ball was the only ball in a cannon which caused the top ball to reach a lower height than its original 1 m. A medicine ball is meant to be heavy and difficult to lift, therefore its material is not very bouncy and must thus absorb the energy which should have been transferred to the top ball.


 * Final Reactions:** Overall, this experiment was more difficult to conduct than originally expected. There were many more unforeseen obstacles than originally predicted and the outcomes were also not easy to predict. In some ways, the Galilean Cannon can defy the logic of physical knowledge by reacting to uncontrollable outside forces, greatly skewing answers. Also because of the fact that the cannon is dropped by human hands, which can unknowingly exert small amounts of force or angle on the set-up, human error factors into the results of the experiment. Despite its shortcomings, this experiment really made it much simpler to understand exactly how conservation of energy is utilized in everyday life by giving us a clear visual of it in action.