Project : Pheonix. Mathew Menachery, Clement Oigbokie, Courtney Seals, and Brandon Shaver

Transcription

1 Project : Pheonix Mathew Menachery, Clement Oigbokie, Courtney Seals, and Brandon Shaver April 27, 2009

2 I. Abstract The purpose of this lab is to construct a Rube Goldberg device, multifaceted process that include many often convoluted steps to perform a simple task., to operate an electrically device. In our group s project, we incorporate the physic principles of projectile motion, conservation of energy, conservation of momentum, torque, and center mass. The device starts off with pendulum swinging down from an upward pointing position, and hits a small ball. This ball travels down a ramp where it collides with a weight. The weight is tied to a pulley that is tied to a partition that is holding up a second ball on another ramp. When the weight falls, the partition is lifted, and the second ball travels down a series of ramps. The ramps end at a balancing board that catches the ball. The ball changes the center of mass of the balancing board and causes the ball to roll into another series of ramps, which then leads the ball to hit a button on the calculator. This inefficient device is operating the calculator. The device utilizes potential energy. Mostly this energy is stored in the form of gravitational potential energy with the initial height of the swinging pendulum, the marbles, and the weight, and this energy is eventually operates the device.

3 II. Introduction The purpose of this lab is to construct a Rube Goldberg device, multifaceted process that include many often convoluted steps to perform a simple task, to operate an electrically device. In this experiment we created an apparatus constructed of wood, cardboard, and foam tubes which used a pulley, rock, makeshift pendulum and two marbles to transfer gravitational potential energy to the operation of the calculator. There are six requirements of this project: the components of the device must be able to be stored in a box with a volume of one cubed meter, the device must have five steps, the device can not be interfered with after it had been started, the device can take longer than two minutes, the materials use can not cost more than $20, and the device must employ four of the principles the EF 151 class studied over the course of the semester (Projectile motion, Conservation of energy, Conservation of linear momentum, Conservation of Angular Momentum, Torque, and Center of mass)all of these requirements were fulfilled in the construction of this device. III. Design Process The design of our Rube Goldberg project, Phoenix, was decided upon over the course of a single group meeting with the understanding that changes and revisions would be made during the course of the construction process. Despite that agreement, the project design deviated very little from what the original design specified, including the additions and changes that had to be made to the final steps. This group meeting was primarily used for this design discussion. The meetings held after this point were dedicated to the building of the project. The only significant of the difficulties during our design process was the selection of an electronic device to eventually activate, and how that was going to be performed. Our choice to only have one preliminary design discussion had its advantages and disadvantages. Our approach would rely on our abilities to locate and shape scrap materials into a reliably functioning Rube Goldberg device without the complete understanding of the machines true function. This left our team with questions of uncertainty, as we were left with the ongoing task throughout the remainder of construction. On the other hand, this easily left open the opportunity to include most of our best ideas as time progressed.

4 It was difficult to theorize what we needed to do in the final few steps as the group wasn't certain what object would be used. At first, we were going to use a coffee maker and have a second track going through the project to also push a coffee cup up towards the maker. This plan proved to be more than were anticipated, so was replaced with a far simpler design to have graphing calculator display a smiley face. It was generally thought that most of the construction materials would be acquired from the scrap materials found in the workshop, which turned out to be a good, cost-effective plan. For the pieces that we were unable to find appropriate materials for, we used a sheet of cardboard of our own to shape into what was needed. IV. Device The basic structure of the apparatus is a one and half foot by two and half foot piece of plywood. To this plywood base, two wooden posts are attached using one and half inch drywall screws. These posts are approximately twelve inches apart. The posts and base compose the backbone of the device on which the other parts of the device are attached. The starting mechanism of the device is a makeshift pendulum. The pendulum was constructed with small strip of wood and a nail that was drill into one of the posts, see Figure 5. The strip pivots about the point were the nail intersects it. The pendulum is released at a height were the wood was horizontal to the ground. The pendulum accelerates in an angular direction about the pivot point. When the wood is perpendicular to the ground, the pendulum has developed some rotational energy. This rotational energy is approximately equal to gravitational potential energy at the height at which the strip was dropped see in Equation 1. Equation 1 PEgrav =KErota mgh=½iω²

5 I=Icm + mh² Parallel Axis Theorem Icm= (1/12)mL² Mass Moment of Inertia a Thin Rod. m=mass g=acceleration cause by gravity h=height of the strip ω=angular velocity I=Mass Moment of Inertia Icm=Mass Moment of Inertia L=length of the thin rod. In an inelastic collision, the pendulum hit the marble and continues through it, see Equation 2. Some momentum of the pendulum is transferred to the marble causing the marble to all off the ledge and one to the first ramp. This ramp is attached to post with screws and twist ties. The marble then rolls down the ramp and strikes the rock in another elastic collision. The momentum transfer to the rock causes it fall its ledge and can be calculated by Equation 3. Equation 2 IωXr = Iω2Xr + mv I=Mass Moment of Inertia ω=angular velocity ω2=angular velocity after collision r=radius of pendulum m=mass of marble v=velocity of marble after the collision. Equation 3 PEgrav =KErota +KEf mgh=½iω²+½mv² I=.4mr² m1v =m1v1+m2v2 Mass Moment of Inertia of a solid sphere m1=mass of marble m2=mass of the rock g=acceleration cause by gravity h=height of the strip ω=angular velocity I=Mass Moment of Inertia v=velocity of the marble at the bottom of the ramp The falling rock pulls and string attached to a pulley which is attach to a card board partition, see Figure 3. The energy transfer of the pulley system is explained by Equation 4. The partition is pulled up and releases and another marble that goes down two sections of foam ramps. These ramps were attached to the

6 post and wood support glues to the posts by twist ties. The stored energy released by the partition can be explained in Equation 3. After travel is through, the ramps ball is deposited on a balanced wood board with a cardboard section design to catch the marble. The additional mass of the marble shift the center of mass of the board, and it tilts down to release the marble down the final ramps. Finally after traversing the last two ramps the marble collides with the graph button on a TI-83 calculator causing its graphing function to operate. Equation 4 PEgrav =KErota +PEgrav mgh=½iω²+ m2gh m2=mass of cardboard partition m=mass of rock g=acceleration cause by gravity h=height of the strip ω=angular velocity I=Mass Moment of Inertia V. Results: Figure 1 Steps 1-5 Figure 2: Steps 6-8

7 Figure 3: Pulley Set Up Figure 4: Center of Mass Sections

8 Figure 5: Ramps Pendulum Varibles Values Units Vi in/sec Vf in/sec Volume in³ Height In Width In Thickness In Weight Lb Mass Slugs ICM slugs-in² I slugs-in² ωf rad/sec PEgrav in-lb Table 1

9 Marble #1 Varibles Values Units Vi in/sec Vf in/sec Volume in³ Diameter in Radius in Density lb/in³ Weight lb Mass slugs PEgrav in-lb Height in Thickness in I slugs Kef lb Table 2 Rock Varibles Values Units Density lb/in³ Mass E-05 slugs Volume 1 in³ Weight lb PEgrav in-lb Height In Before the line is taught PEgrav in-lb Kei in-lb Height In Vi in/sec Table 3 Pulley Cardboard Varibles Values Units Varibles Values Units Diameter in Width in Radius in Length in Thickness in Thickness in Density lb/in³ Density lb/in³ Weight lb Weight lb Mass in Mass in I slugs-in² PEgrav in-lb PEgrav in-lb Height in ωf rad/sec Table 4

10 Materials Cost Wood $7.00 Twist ties $0.50 Tubes $4.00 Cardboard $1.00 Screws $2.00 Pulley $5.00 Total $19.50 Table 5: Material Cost. V. Conclusion The Rube Goldberg device completes all the project objectives. The device can fit in a one cubic meter space. The device has eight steps. The device is not interfered with after it had been started. The device takes12 seconds to complete. The material cost is $19.50, and the device must employ Projectile motion, Conservation of energy, Conservation of linear momentum, Conservation of Angular Momentum, Torque, and Center of mass principles. At the completion of the device, a graphing calculator is operated.