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Introduction

The objectives of the Engineering Fundamentals 151 team project was to create a model

roller coaster spending less then 40 dollars in materials, building the model in a 0.5 meter by 0.5

meter by 0.5 meter maximum size limitation, and consistently executing a minimum of a 15

second trial roller coaster run. Our team had very little problem satisfying the parameters of the

material costs and size dimensions, but the time limit wound up being the toughest objective to

complete. The roller coaster we created was very inconsistent at first with problems in the tubing

and speed. When we first started building the coaster, the circumference of the tubing was larger

making the speed of the marble be faster. This made our roller coaster too fast and hindered our

goal of meeting the minimum time limit. As the days went by in the construction of the roller

coaster, the circumference of the tubing slowly decreased to the point of making the marble have

such a low velocity that it would come to a complete stop. Using all of our basic knowledge of

Physics taught to us by Professor Schleter and Dr. Arazi and brainstorming, we were able to fix

these problems and create a very successful model of a roller coaster.

Design Process

The engineering design process is a specific process in which a problem is derived from a

need, and after large amounts of research, brainstorming, and adjusting of the product a solution

is made. The problem defined for this project was to build a roller coaster that is simple in built,

reliable in execution, and consumes around 15 seconds during its run time. Each member already

had their own ideas of what to use for track and how to make the roller coaster so the next step

would be brainstorming. The group came together with different sketch ideas, all revealing the

ideas of several spirals and a jump in order to take up 15 seconds and yet still have a fun

conclusion to the roller coasters run. After the group decided on one specific idea it was time to

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actually build the project. As the project grew the ideas for how it should be built changed with

each new problem that presented itself until the final design was complete, similar to the original

idea but perfected through the experienced gained through trials and error.

Device

The Rocking Roller Coaster that Symbolizes the UT Football Season’s original design

was one of simplicity devised to do the two things that were specified in the project layout, to be

simple and consume as close to 15 seconds with its run as we could. Our team’s first idea was to

make a rather high, main post to support a long track of tubing that would spiral down at an

increasing angle until the ball plummets to a ramp. Our idea was to use undone wire hangers

secured to the main post to hang the spiraling tubing. It soon became evident that the size of

tubing we needed to use would weigh too much to be held up by just the wire, and the set up

time it would take would inevitably exceed the allotted 30 seconds specified in the project

guidelines, so a new idea was introduced. The group agreed on sticking with the long spiral idea

ending with a jump, and rather than using the hangers as support we decided to split the main

post half way up and set it up like a field goal post in order to have a sturdy support post on each

side of the loops.

As the group came closer to finishing the roller coaster several problems began to come

up. One main issue was that the tubing being used had a tendency to pinch down on the ball in

several areas slowing the ball down and occasionally stopping it altogether. The first idea to

remedy this problem was to use splints to pinch the tubing the other way, but with the tube

constantly spiraling the splints would just get in the way. The next idea was to use duct tape to

squeeze down on the tubing in a way that it would hold it in a rounder position. A similar

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problem was of the tube kinking at the points where it rounded the support arms as we added on

more spirals to the project. This problem was solved by using the left over wire hangers, left over

from our first idea, as support for the tube’s integrity at these critical points. The wire was bent

into coils the size of the tube and then placed at the critical points to support the tube at the

problematic pressure points. The rest of the project fell together as it came closer to being

finished. Wood platforms, cut for a 45 degree angle, were used for the ramp and a funnel was

used to catch the ball at the end to catch the ball, and send it through more tubing to its finish, a

Mellow Yellow can. With the project near completion timing became a real issue. How the

project was designed at this point it was running at a max of 13 seconds, something more needed

to be added, but the ball had no more energy after jump to go through more loops and we were

out of tubing. The only idea that seemed possible would be to add tracks to the top that were

slightly slanted, just enough so that the ball could roll from one side of it to the other. In the end,

two tracks were added to the top of the roller coaster and the device was timing out at just over

15 seconds.

After we built our roller coaster, we ran several test runs to determine the distance that

the ball travelled through the air after the jump. After we determined how far the ball would

travel, we decided to determine the ball’s velocity as it left the ramp. To do this, we made all of

the necessary measurements and used the trajectory equation to solve for velocity.

Eq. 3-36

Next, we decided to determine the theoretical velocity that the ball would have if it did

not have any energy losses due to friction. To do this, we used the conservation of energy

equation.

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Eq. 7-9

Then, we used the conservation of energy equation again with the actual recorded

velocity in order to determine how much energy was lost to friction.

Eq. 7-9

When it came to the graphs we used in Matlab, we used the trajectory equation to create a

graph of the distance versus time plot (Figure 1).

Eq. 3-36

Then, we used constant acceleration equations to create the y-component velocity graph

and the total velocity graph (Figures 2 and 3).

Eq. 2-21

Eq. 2-23

Here is our parts list with prices:

Parts List

10ft. sch40 PVC ¾ in. $ 2.19

2 sch40 elbows ¾ in. $ 0.58

1 sch40 tee ¾ in. $ 0.33

20ft. vinyl tubing ⅝ in. $ 8.00

Duct tape $ 3.00

Hardware $ 1.00

Wood $ 5.00

Hot glue $ 1.00

Coat hangers $ 2.00

2 Ball bearings $ 0.50

Mello-Yello can $ 0.10

Funnel $ 2.00

Spray paint $ 3.44

Can of compressed air $ 8.00

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Total $37.14

Results

0 0.2 0.4 0.6 0.8 1 1.2 1.40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Bearing Trajectory

Distance (ft)

Heig

ht

(ft)

Figure 1. plot of the trajectory of the ball with distance as the x-axis and height as the y-axis

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0 0.05 0.1 0.15 0.2 0.25 0.3 0.350

1

2

3

4

5

6

7

time (seconds)

speed (

feet/

second)

Y-Component Speed Time Plot

Figure 2. plot of the y-component of the speed with respect to time

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0 0.05 0.1 0.15 0.2 0.25 0.3 0.354

4.5

5

5.5

6

6.5

7

7.5

time (seconds)

speed (

feet/

second)

Speed Time Plot

Figure 3. plot of the total speed of the ball with respect to time

Conclusion

The design of our roller coaster seemed simple enough, however, while building it we ran

into unforeseen problems and delays. The total time we spent building the roller coaster added up

to about 12 hours, which was much more than we had expected to spend on it. The project was

frustrating at times due to the problems encountered, but it was a nice change from the usual

classroom environment. This project was useful in providing us with real world application of

the concepts learned in EF 151 and served as a grand finale to the semester.

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References

Fishbane, Paul M, Stephen G Gasiorowicz and Stephen T Thornton. Physics for Scientists and Engineers.

3rd Edition. Upper Saddle River: Pearson Prentice Hall, 2005.

Pgs.: 41, 69, and 187

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Appendices

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