Scoop-Doop-Alley-Oop. December 6, Steven Cohen. Riley Exum. Blake Vaughn

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1 1 Scoop-Doop-Alley-Oop December 6, 2008 Steven Cohen Riley Exum Blake Vaughn Each Team member contributed to this paper and approves the finished product.

2 2 Abstract This experiment was a final project for Engineering Fundamentals 151. The requirements were to build a roller coaster which incorporated the concepts learned in the class to the design. The object was supposed to finish its run in as close to fifteen seconds as possible and was required to fit in a half meter cube. To solve this problem we used conservation of energy, trajectory, and friction to get the ball through the track in fifteen seconds. Our system had a theoretical yield of seconds and a tested yield of seconds. We also obtained velocities for each section of the track. We concluded that our experiment would be easy to rebuild because it was sturdy and had specific measurements, it incorporated creative aspects, and it consistently finished runs in the allotted time.

3 3 Introduction The objective of this team project was to design a roller coaster like system incorporating many of the different concepts we learned in lecture this semester. The apparatus was to fit in a space no larger than a half meter by half meter by half meter when folded up. The device was allowed to expand, but must have done so in under thirty seconds. Projects were to be graded based on creativity of design, reliability, and repeatability. Design Process When designing our roller coaster, the Scoop-Doop-Alley-Oop, we wanted to accomplish several objectives. We wanted a creative design with several unique features, the devise to be very consistent and have a low margin of error, and we wanted a sturdy system which would be easy to transport. We concluded a frame would be necessary for our design. The next two things we determined we would like to see our coaster do is complete both a flip and a jump. We concluded the coaster would need a very high velocity to complete both of these things and decided on a fold out design. The next thing we had to determine was what materials we would use for the track. We decided to use flexible, clear, plumbing tube. Later during testing we found out the friction from the tube on our object was too much for the ball to be able to make the run we designed without stopping. This prompted a major change in our design. We decided to change our track after the jump from tube to pvc pipe. The pvc pipe has a much lower coefficient of friction; the ball ran through it faster, but our creativity was limited after the change. This required us to revise our planned track and make it longer than

4 4 expected, but after the changes on paper it looked like we could finish in the required time in the required space. Then we turned to construction. Device Figure 1.1 (Figure excludes support structures) Our devise is enclosed inside a box made of plywood. The interior dimensions are the maximum half meter sides. We used pvc pipe attached to the sides of the box with nails, as well as, a sawed off two by four as supports for our track. The extendible portion of the devise is a very large pvc tower. We screwed a three way pvc connector into the side of the box which acts as the foundation for the tower. Two pipes, which are held together by another three way connector, are then inserted into the lower connector to form the tower. The tubing is then duct taped to the top of the tower. Immediately after the drop is where the loop is located. Its diameter is small and it is practically straight up and down. The loop is held stable because it is hot glued to the two by four which it is wrapped around. The tubing is stabilized after leaving the loop because it is wrapped in a barrel roll type configuration around a pvc pipe. The tubing makes a sharp turn off the pvc pip and opens up. This is where the ball will make its jump to a funnel located directly in front of the jump. After landing in the funnel and rolling out the ball

5 5 will make the transition from tubing to pvc piping as its track. The pvc runs along the side of the box. It is held to the sides of the box by hot glue. There are four of these pvc like tunnels, one on each side of the box. After exiting the final tunnel the ball falls into a piece of pvc which is cut in half that runs diagonally across the box. This piece has been blemished using a power drill to create a greater friction force. At the end of this piece it falls off into a bottle cap, which is the end of our devise. Results The equations we used are listed below. Other items were also very important mgh=.5mv2 Eq mv2+mgh=.5mv2 Eq mv2+mgh=.5mv2+mgh Eq. 1.3 y-y0=(x-x0)tanθ-(g/2v0^2)(1+tan^2θ)(x-xo)^2 Eq. 1.4 to finding theoretical yields. The mass of the ball was.25 grams or x 10^-5 slugs. Friction was determined by solving the conservation of energy equation backwards and solving for energy lost, which was equal to 2.52 joules while in the tube. Friction of the ball and tube was assumed to be negligible. The theoretical yield for time was concluded to be seconds. Excel was used to determine the velocities of each point on the track, the total distance of each part, and the time it took to finish the track. These spreadsheets are in the appendix. Conclusions At the final trials our roller coaster finished in seconds. We were able to reassemble the coaster in 19 seconds which was well under the thirty second requirement. Our 0.88 seconds over the limit can easily be explained by human error. Our coaster will

6 6 not finish exactly the same every time, but it has an average range between 14.3 seconds and 16.1 seconds by our calculations, in pretesting trials. Our coaster has a straight forward design which can be easily replicated, but also incorporates creative elements as well, like the loop and jump. Because of the four elements of accuracy, consistency, ease of replication, and creativity we feel we created a great project.

7 7 Appendices 1. Section Angle (deg.) Ver. Dist. Hor. Dist. Vel. (ft/s) Tot. Dist. Time (sec) Total Time (sec) Drop Loop Run to Jump Jump Funnel to Wall Wall Wall Wall Wall Diagonal Drop to End Ver. Dist. Hor. Dist. Velocity Time Total Time Section Angle (deg.) (ft/s) Tot. Dist. (sec) (sec) Drop =G2/H =SUM(H2:H12) Loop =G3/H3 =(4/12)*PI() Run to Jump =G4/H4 =SQRT(D4*D4+C4*C4) 0.3 Jump =G5/H5 =SQRT(D5*D5+C5*C5) Funnel to Wall =ATAN(C6/D6)*(180/PI()) =G6/H6 =SQRT(D6*D6+C6*C6) 0.3 Wall 1 =ATAN(C7/D7)*(180/PI()) =G7/H7 =SQRT(D7*D7+C7*C7) 1.7 Wall 2 =ATAN(C8/D8)*(180/PI()) =G8/H8 =SQRT(D8*D8+C8*C8) 1.8 Wall 3 =ATAN(C9/D9)*(180/PI()) =G9/H9 =SQRT(D9*D9+C9*C9) 2.22 Wall 4 =ATAN(C10/D10)*(180/PI()) =G10/H10 =SQRT(D10*D10+C10*C10) 4.11 Diagonal =ATAN(C11/D11)*(180/PI()) =G11/H11 =SQRT(D11*D11+C11*C11) 4.27 Drop to End =G12/H