Screwed Tubes December 4, 2008 Andreas Bastias Luis Castellanos Howard Hensley Jessica Rhyne
Abstract This project was assigned to get students to think about physics in a real life situation. The goal was to create a rollercoaster that would bring the marble to the endpoint in 15 seconds. Our group believed that the simplest way to achieve this goal would be to employ ramps and inclines of other natures, which wound up being our final design. It starts with a pulley system that creates an incline 2 cm high and begins to roll due to gravity. The marble then travels down a series of tubes inclined in opposite directions to insure the velocity would reach zero each time, making calculations easier and the speeds at the end of the ramps more predictable. After traveling through a semicircle, the ball reaches the cushioned end point. The energy in the system is all potential due to gravity and kinetic, assuming no energy loss. Our datum was reset to the bottom of each incline each time the velocity reached zero to simplify calculations. When the ball stops at the endpoint we have reached our goal of 15 seconds. Inclines are easily calculable and reliable to use in practice, which is why we were able to hit our goal so closely. 2
Introduction The goal of this project was to make a rollercoaster that transported a car (marble) to the end of the track in 15 seconds. We wanted the rollercoaster to be selfpowered, run on gravity, and somehow employ a pulley. Design Process In the first meeting of our group, we decided to use a series of vertically aligned ramps to transport the marble down the track and a vertical tube to keep time under control. This would be a simple and effective way of reaching our goal, however the system was too fast and we decided to make a construction twice as tall as the given parameters with a folding capability via hinges. We soon discussed how, by itself, this idea was too simple. Still thinking, we made our initial trip to gather materials. The idea of a pulley was introduced after construction began. We thought of having a double pulley, but there was simply not enough time. Half PVC pipes were chosen as our ramps for their curved structure, good for keeping the ball on the desired path. The problem of connecting our new ramps to the wooden back arose. We used a sander to form flat areas on the bottom of the pipes and glued them to newly constructed wooden blocks that could screw into our support. While these were being installed, we found that our system was now traveling too fast. We drilled holes into the structure and fit tubing into place to 3
keep from forming too many ramps. An endpoint, consisting of a scoop and padding, was drilled in place for the ball to finish. Device Our device is a rollercoaster that stands upright to transport the ball vertically down, as seen in Figure 1. Figure 1: The Device The first stage that the marble goes through is a pulley system. A weight of 20 grams was attached on one end of the string. The string continued over the pulley at the top of the structure to attach to a lever that holds the ball at an initial position when pulled down. When released, the marble is now on a ramp with one end at a vertical height of 2 cm. Once the marble reaches the end of the ramp, it falls down a vertical tube to the next ramp. This ramp has a height of 3 cm and distance of 25 cm and allows the ball to fall onto the next ramp, with 3 cm height and 20 cm distance angled in the opposite direction. The marble lands on another ramp of the same dimensions as the second. The next ramp is angled oppositely again and has 16 cm distance and 2 cm height. From here 4
the ball falls 12 cm down to the next ramp and rolls 30 cm horizontally and 2 cm down. A steeply inclined ramp (height 5 cm and length 7 cm) lets the ball gather speed down to another ramp. Another steep incline rushes the ball to a very long ramp (45 cm long and 2 cm high) to a tube semi-circling around the back at a height difference of 8 cm. The tube comes out to an endpoint directly below it. The budget of the project was $40. Our shopping trip was to Walmart and Home Depot. At Walmart, we bought a bag of marbles for $4. At Home Depot, we purchased PVC pipe ($6), wood ($8), hinges ($8), and screws ($5). This totals to $31 we spent on materials. For this project, we assumed no friction or energy loss. Since each time the ball would change directions, we reset the datum each time the velocity reached zero. A picture of the rollercoaster with critical points is shown in Figure 2. Figure 2: The Points 5
The velocity equation at the end of each ramp is shown in Eq. 1. mgh= ½ mv^2 Eq. 1 This simplifies down to Eq. 2. (2gh) = v Eq. 2 Each velocity is found using these equations. The first ramp had a vertical height of 2 cm from Point A to Point B, giving it a velocity of.626 m/s at B. Even though the ball drops vertically to Point C, is hits and comes to a halt. The velocity at D is only the velocity due to the current ramp, which is now.767 m/s due to the 3 cm height difference. We measured the angles carefully to make sure that each time the speeds would hit zero on each ramp and end at.767 m/s until point N is reached. At this point, the ball falls and comes to rest at Point O. At P, the speed reaches.626 m/s again due to the 2 cm height before hitting Point Q and rolling down 5 cm, reaching a speed of.99 m/s at R. At Point R, the next equation (Eq. 3) is put to use. mgh+ ½ mv^2 = ½ mv ^2 Eq. 3 And simplifies down to the next equation. (2gh + v^2) = v Eq. 4 With Eq. 4, Point S, with an initial velocity of.99 m/s and height of 2 cm, has a velocity of 1.17 m/s. The ball comes to a stop on the next incline and rolls down past Point T at 1.25 m/s. Eq. 4 is employed again, showing the marble s velocity at Point U to be 1.40 m/s. The ball comes to rest in the tube before rolling down 6 cm vertically, giving the ball a velocity of 1.08 m/s the moment before stopping at the endpoint W. 6
Results Results in testing after construction varies. It is typically very close to 15 seconds, yet it can sometimes be close to a second off. Reasons for the dissimilarity are the pulley getting slowed down due to friction with the screw, debris on the track, and human error with timing. Test Number Time from Start to Finish (seconds) 1 14.89 2 14.63 3 15.05 4 15.62 5 14.49 Table 1: Timing Results Conclusion In presentation, our team s coaster was a success more or less. We actually hit 18 seconds (something that never happened in testing) while being timed, though we were later informed that as long as we reached at least 15 seconds or more, we were fine. While being a simple rollercoaster, we fulfilled all requirements and kept the finished project neat and clean-cut. Our group learned hands-on applications of physics and that friction still exists with a marble. We faced problems with meeting times and communication, which were very difficult to get through. If we were to do this project again, we would have exchanged more than just emails and have a backup phone number to call. 7
Appendix A: Equations Eq. 1 : mgh = ½ mv^2 Eq. 2 : v = (2gh) Eq. 3 : ½ mv^2 = mgh + ½ mv^2 Eq. 4 : v = (2gh + v^2) Appendix B: Figures Figure 1 Figure 2 Figure 1: The Device Figure 2: The Points 8
Appendix C: Tables Table 1 Test Number Time from Start to Finish (seconds) 1 14.89 2 14.63 3 15.05 4 15.62 5 14.49 Table 1: Timing Results 9