Team Shananigans: The Funnelcoaster 12 2 08 Presented by: Leslie Roberts, Ben Hemphill, Ryan Burnett, Cori Crenshaw, Austen Webber
ii Abstract: This project was assigned so that students could work together as a team to use the mathematical concepts taught during this semester and apply them to construct a roller coaster. The roller coaster must be designed to utilize the balls gravitational potential energy and kinetic energy throughout the track, so as to allow the ball to complete its run in fifteen seconds. Once the ball began its run on the track students were not allowed to touch it or influence its movement. Our team designed a roller coaster using of a series of angled PVC pipes, attached to a wooden frame, which allowed the ball to roll down one PVC pipe and empty into an adjacent PVC pipe located slightly lower than the first. By consecutively placing the PVC pipes in an angled downward position, we allowed the ball to travel from pipe to pipe using only gravitational potential energy and kinetic energy. The final design of our roller coaster consisted of four PVC pipes, leading to a funnel, which then dropped the ball into a final PVC pipe that ended at a second funnel, where the ball spun around and stopped at the bottom. We used the conservation of energy equation to calculate the velocity of the ball at each intersection. This allowed us to position the PVC pipes so that when the ball hit the next PVC pipe it stopped and then began rolling down. By stopping the ball at each intersecting PVC pipe, we made the ball lose all kinetic energy, and thereby allowed the ball to complete its run in 14.679 seconds. Our design was successful in meeting the requirements for the project.
1 Introduction: The objective of this project was to build a roller coaster that could move an object using gravitational potential energy as well as kinetic energy. We were allowed to spend a maximum of forty dollars on all the supplies needed to build the roller coaster. The device had to be an original idea and built from the materials purchased. The finished product had to be able to fit into a.5 x.5 x.5 meter box when folded up. The device had to be folded and unfolded in thirty seconds. The object the roller coaster would carry could be a ball, a toy car, or anything that would run along a track. Our coaster had to allow the object to be in motion for approximately fifteen seconds without stopping. Team members were not allowed to touch the object once it was on its run. This project required us to work together as a team and create the roller coaster. We applied the concepts we learned from the semester to calculate the appropriate dimensions needed for our roller coaster to operate smoothly.
2 Design Process: The final design of our roller coaster was the product of much trial and error. First, we considered the materials we were going to need to build the roller coaster. Initially, we utilized the free materials available to us in Estabrook 111 and decided to use a few pvc pipes and some old plywood. Our design using those materials involved a series of slightly slanted pvc pipes attached to pieces of plywood that would make the.5 x.5 x.5 meter box. The ball would be dropped into the first pvc pipe which would dead end into a second pvc pipe with a hole cut into it. This way the ball could easily make the transition from pipe to pipe and eventually complete its run at the bottom of the box. We began building our support box out of the plywood and quickly realized that it was not going to work. The plywood was too thin to hammer nails into it. We made a quick trip to Lowes and decided to go with thicker wood that could support the pvc pipes. While we were there we came up with a few new design ideas for the roller coaster. We bought two funnels to add to the track, some gorilla glue, a foam tube, and a few pieces wood. Our second idea involved a funnel at the top of our wooden box that would drop the ball into the series of pvc pipes that ends in a second funnel. We encountered several issues with that design as well. We tried a few different ways to position the pipes so as to meet the time requirements and found that we needed to angle the pipes downward at five degrees. We also decided to place the two funnels toward the bottom of our roller coaster, which allowed the ball to spin around a few times in each funnel. Overall, we found that calculating the expected time for the ball to complete each part of the run, and implementing those calculations into our design, to be the most useful in designing our roller coaster.
3 Device: The materials we used to build our roller coaster include wood, nails, pvc pipes, plastic straps, plastic funnels, duct tape, and glue. The support structure is made of wood, with a 19 x 19 inch square as the base of the roller coaster. Four 19 inch pieces of wood are nailed to the inside corners of the base and stand straight up. One piece of wood is placed between the two posts on opposite sides of the box and one piece of wood is nailed in the middle of the square base of the structure. A series of four pvc pipes are attached along the outside of the wooden structure. The first three pipes are approximately 16.625 inches long. Each pipe is angled downward at five degrees, which causes a change height equal to one and a half inches per pipe. The fourth pipe is approximately one inch long and is angled downward at twenty degrees. All the pvc pipes have holes carved into them so that the ball rolls from one pipe, drops into the second pipe, and rolls down. They are attached by plastic straps which are nailed to wood on either side of the pipe. The ball is then dumped into a small funnel where it spins around a few times. The funnel is nailed to the wood and empties into a fifth pvc pipe located in the middle of the wooden structure. This pipe is also attached by plastic straps, and is nailed to the piece of wood in the middle of the base. The pipe drops the ball into a medium sized funnel located at the base of the structure. The ball spins around the funnel and eventually stops at the bottom. A picture of the design of the roller coaster can be seen in Figure 1 on page four.
4 Results: From the beginning to the end of its run, the ball undergoes changes in velocity, gravitational potential energy, and kinetic energy. At the top of the roller coaster the ball is dropped into the first PVC pipe. It travels 16.625 inches through the pipe falling a vertical distance of 1½ inches. Using the conservation of energy equation, the final velocity of the ball at the end of the pipe is 3.48 feet per second. ½mv02 + mgh0 + ½ k(x0)2 + Win= ½mvf2 + mghf + ½ k(xf)2 + Eloss Eq. 3.1 Because the ball changes direction upon entering the second PVC pipe, all of the forward energy is lost and in effect, the ball resets. Therefore at the end of each pipe, the ball is traveling about 3.5 feet per second. After exiting the third long PVC pipe, the ball enters a 1 inch long PVC pipe that drops the ball 0.5 inches in height and directs it to a 4 inch tall funnel. The ball exits the short pipe at 1.64 feet per second into the funnel. After spinning for a few seconds in the funnel, all of the initial potential energy that exists at the beginning is converted to kinetic energy, and the ball exits the funnel with a final speed of 4.91 feet per second. The ball falls into the final PVC pipe and again loses most of the energy when it makes contact with the pipe. The 12 inch pipe drops 2 inches and empties the ball into the final funnel. Upon entering the funnel, the ball is traveling at 3.28 feet per second. The ball spins around the funnel and ends its run sitting on the ground.
Figure 1. Overhead view of the Funnel Coaster 5
6 Conclusion: Team Shananigan s roller coaster project was a huge success. Our team came closest to the target time of fifteen seconds with a remarkable time of 14.697 seconds. We only needed one run to achieve this time. There were no problems with assembly before the run. The main point we learned was that the key to success was to keep the design simple, therefore making it less prone to problems. We used a very simple design to achieve the task as best we could. Since the device was easily made, repairs and adjustments could be made hassle-free. Our main problem was getting the marble to roll freely though the pvc pipes while still maintaining a time close to fifteen seconds. The two funnels we placed on the roller coaster also caused some problems. It was hard to calculate the rate at which the ball would spiral down each funnel. However, with many adjustments and many tests we obtained a smooth and well working machine. Based on our time, there are no other adjustments we could have made. The simplicity of our design provided our team with much success.