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The
Bungee Omelet
A Freshman Engineering Design Project
Developed by Dr. Ron Roedel, Arizona State University
Instructions to
Students
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1. |
Project
Description
Bungee
cord jumping attracts those persons who like the strong
feeling of danger mixed with their entertainment. Jumps
have been made from high bridges, tall cranes, and hot
air balloons. Bungee cord jumpers step, dive, fall, or
are pushed off these high perches with only one end of
an elastic cord fastened to their bodies. The other end
of the cord is supposed to be fastened to the device
from which the jump is made.
During
the first part of the jump, jumpers are pulled toward
earth by gravity, accelerating in free fall, much like a
sky diver. For the jumper, this free fall is related to
the quality of the jump - the desire is to free fall for
as long as possible and to reach a speed that is as high
as possible. But, the free fall continues only as long
as the bungee cord remains slack. When the slack is gone
and the bungee cord begins to stretch, the cord applies
an upward force that begins to decelerate the jumper.
This decelerating force increases as the bungee cord is
stretched farther and farther. If all goes well, jumpers
are brought to a stop before the space between them and
the ground shrinks to zero.
The
sport of bungee cord jumping is now on the wane,
partially due to the rise in legal cases as a result of
injuries and partially due to the fad running its
course. However, physics, math, and engineering are
involved in successfully designing a "good" bungee jump
so that is what this lesson is going to teach you to do.
The purpose of this project is to integrate these three
disciplines together to understand better how they
relate to one another.
In
this project your team will be expected to develop a
bungee jump design using theory coupled with
experimental measurements of the parameters or variables
necessary for accurately modeling. Your team's first
prototype will be the one which is actually used in the
competition, to be described later. This is in keeping
with the new decision paradigm which says that to be
globally competitive, one must strive to model the
complete artifact and its manufacturing process so that
the first one manufactured can go to the customer.
The
goal of this project is to design a quality bungee cord
experience that will allow a delicate object to come as
close to the ground as possible without damage. Damage
can be incurred by:
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actually impacting the ground, or
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decelerating the object too rapidly
The
bungee designs will be demonstrated in a competition to
see which team's design performs the best. During the
competition, visual and video tape evidence will be used
to judge the closeness to the ground and to determine
the maximum deceleration of the payload.
For
this project, the "jumper" will consist of an
uncooked egg and the jump will be from the top of
Sun Angel Stadium. The egg is vulnerable - if it
strikes the ground, it will experience the HD syndrome.
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2. |
Performance
Modeling
Your
team's performance model should aid you in picking a
design that best meets the constraints and objectives of
this project. The model will contain a variety of
variables and parameters which your team must specify.
Modeling the physics of the jump
There are several variables of importance in the jump.
At this stage in your physics education, you have
learned about Newton's Laws of Motion. This project will
provide you an excellent opportunity to apply these laws
in an engineering context.
To
model the physics of the jump, your team must begin with
Newton's Second Law applied to the jumper. The forces in
this equation will be somewhat complicated, since the
force applied by the bungee cord will act only when the
cord is stretched. But, at this stage of your
mathematics education, you have learned about the use of
Excel spreadsheets to solve a variety of problems, so
here is an excellent opportunity to apply this knowledge
(and the the use of some new Excel functions) in an
engineering context, again.
A
quantity of importance is the maximum deceleration
encountered by jumpers as the bungee cord stops them. If
this deceleration is too great, it may cause damage to
the jumper. The maximum deceleration is reached when the
net force on the jumper is a maximum. The force must
not exceed three times the weight of the jumper.
Modeling the properties of the cord
Elastic materials such as rubber consist of long chain
molecules that deform when stretched and recover when
released. The processing of these materials determines,
among other properties, the relationship between the
amount of stretch and the force causing the stretch. The
number of cross-links formed through covalent bonding
between the long chain molecules can be increased, for
example, to decrease the amount of stretch for a given
force. Elastic materials with few covalent bonds can
easily stretch in one direction to three or four times
their original length without damaging the material.
Rubber materials change their properties over time
and with use as the bonds change.
The
bungee cord enters into the modeling equations of the
previous section through the relationship between the
force used to stretch the cord and the amount it
stretches. It is quite common to use the model of a
linear spring having a constant "spring constant" which
is the proportionality between the force causing the
stretch and the amount of the stretch. This linear model
is known as Hooke's Law. However, rubber is not truly a
linear substance and you will want to describe fully the
functional relationship between the force and the
displacement (stretch). Your modeling must include this
functional relationship.
Your
team must make a series of measurements on one or more
of the one meter lengths of cord which will be provided
to you. You should use a variety of weights to apply
static loads to stretch the cord being tested to find
the functional relationship between the force and the
stretch. A weight (or weights), which act as the
stretching force, is (are) to be tied or fastened to the
samples of latex cord, as depicted in this
figure. The unstretched lengths are measured, then
the stretched lengths for various values of the force
are measured so that the functional relationship is
deduced. This
spreadsheet may assist your team in carrying out
this portion of the design process.
Solving the models
Your team will combine the physics model and the bungee
cord model into one model that you will solve with an
Excel spreadsheet. You are to use Euler's method to
solve the equations, which is the method employed in
Model #3, in solving Newton's Law of Cooling. Additional
help will be provided in class. |
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3. |
What You Are
to Design
The release device
Your
team must design a device that will hold the egg on the
end of the patented Foundation Coalition Bungee Omelet
Swingarm. The design and dimensions of this swingarm
will be given to your team; a picture of the swingarm is
shown
here. Your release device must allow you to release
the egg from rest, remotely. Complete sketches of your
design must be approved by the engineering instructor
before you build it. The release device must then be
built according to your plans and will be used by your
team in the bungee drop competition. It must be
compatible with the FCBO Swingarm and be installable in
five minutes or less.
The cord
The
principle design variables that you will ultimately have
to specify are:
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The
unstretched length of the cord that you will use in
the competition, including the extra length needed at
the ends for fastening
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The
number of strands of the cord you will use
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4. |
Important
Guidelines
From
previous experience the engineering instructors have
discovered that:
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You
should not over-stretch the strands given for testing.
That is, you should not stretch the samples to more
than three times their original length. In fact,
exceed two times their original length as infrequently
as possible.
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You
should avoid touching the strands with your bare
hands. Oils on your skin have a deleterious effect on
the latex strands. Gloves will be provided for
handling the samples.
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You
should keep the samples out of contact with the air -
keep them in the brown bag provided.
Although you should stretch each cord a few times before
testing, do not put a lot of test cycles on the long
strands given to you for testing. |
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5. |
Competition
Day Deliverables
On
competition day, you will need to have ready:
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The
number of strands and their length
An
operational release mechanism, including a plastic bag
to reduce the HD factor |
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6. |
Written
Report
See
Report Guidelines for specifics regarding the team
written report. |
Lesson
| Instruction
to Students |
Report Guidelines |
Important Parameters
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