Download Heads or Tails

Heads or Tails
Robert Ballow, Jim Baxter, Barrett Hachey, Walt Lee
EF151 Final Project
Fall 2006
Tuesday, December 05, 2006
Created on 12/4/2006 1:08:00 PM
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Table of Contents
Overview ............................................................................................................................. 2
Process ................................................................................................................................ 3
Apparatus ............................................................................................................................ 3
Analysis............................................................................................................................... 4
Bill....................................................................................................................................... 5
Conclusions ......................................................................................................................... 5
Overview
The purpose of this project was to create a device that performs a simple task and
demonstrates three individual energy conservation processes. Our machine is engineered
to perform the simple task of flipping a coin. Our apparatus consists of a short Newton’s
cradle made out of wiffle balls, an incline and baseball, an upright text book, and a spoon
and fulcrum. The device is initialized in static equilibrium with gravitational energy
stored in the system. When the device is started, a small displacement in the Newton’s
cradle causes the baseball to roll down the incline and knock the book over which hits the
spoon, causing it to flip the coin. Our apparatus, through several energy conversion
processes converts the initial displacement of the wiffle ball as well as the gravitational
potential energy stored in the device into the energy required to flip a coin.
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Process
Often in life we find ourselves in need of making a decision between two possible
choices. It is of common human practice to flip a coin when faced with such decisions to
represent a 50-50% random phenomenon in order to make an unbiased decision. It is for
this reason that we have decided to build a device that can flip a coin in a relatively
consistent and verifiably random manner.
In designing the device we tried to keep it as simple and resourceful as possible.
We wanted a mechanism that anyone could recreate with household items. Our device
was intended to cleanly demonstrate energy conversion and conservation in the process
of flipping the coin.
Our original plan included a series of erect objects intended for a domino effect.
We removed this step from our apparatus in order to maintain the simplicity and low cost
of the device.
Apparatus
The “Heads or Tails” coin flipping device consists of three energy conservation
processes. The first is the famous Newton’s cradle demonstrating conservation of energy
and momentum (sketch 1). This portion is made from wiffle balls hanging from PVC
tubing supported by binders. The final wiffle ball collides with a baseball at (a). This
causes the baseball to roll down an incline mounted on an old stool and wooden supports
(sketch 2). Finally the ball gains enough kinetic energy to knock a standing book over
(b), which again gains kinetic energy, and falls on a spoon (c) that flips a coin (sketch 3).
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Analysis
(calculations attached)
Newton’s laws are known to describe motion and forces that cause motion. When
we generalize Newton’s laws we find that in a closed system (no external forces act on
the system) the quantity energy is constant. The mechanical energy of a system can be
written as the sum of the kinetic and gravitational potential energies of the system.
Emech = Ki + Ui
(1)
Where K and U are the kinetic and gravitational potential energies, respectively, and can
be represented by the quantities,
K = ½ m v2
(2)
where m is the mass of the object we are describing and v is its velocity, and
U=mgh
(3)
Where, again, m is the mass of the object, g is the acceleration due to gravity equal to
32.2 ft/s2, and h is the object’s height with respect to some frame of reference.
When generalizing Newton’s laws we also get that the quantity momentum is
conserved in collisions in a closed system.
0= Δp = Σmfvf - Σmivi
(4)
Knowing these things we can analyze the energy conversions in our machine. Our
Mechanism begins with an initial displacement of the first waffle ball in the Newton’s
cradle (sketch 1). When the ball is displaced it gains gravitational potential energy
proportional to the height it is displaced (3). This energy is converted into kinetic energy
as the ball swings down (1). In the Newton’s cradle energy and momentum are
transferred from the first waffle ball to the last, so the last ball swings outward, colliding
with the baseball. The small displacement of the baseball disturbs its static equilibrium
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causing it to roll down the incline. The baseball also gains a small amount of kinetic
energy in the collision as it gains velocity (2,4). As the height of the baseball decreases its
gravitational potential energy decreases and its kinetic energy increases (1)(graph 1). The
ball gains enough energy to displace the upright book from static equilibrium, causing it
to fall over, as well as adding a small amount of kinetic energy from the collision (2,4).
As the book falls, it too gains kinetic energy equal to the gravitational potential energy it
looses (1)(graph 2). Lastly, the book falls onto a spoon, causing it to transfer energy to
the quarter in the upward direction, giving a consistent unbiased flip.
Bill
Item
Lunch Tray
Binder
Wiffle ball
Stool
Pvc(6ft)
Baseball
Srting
Duct tape
Wood
scraps
Quarter
Spoon
Old Book
Cost($)
1
1.25
0.5
3.5
1.5
2.5
0.5
0.6
0.25
0.25
1.4
2
qty.
1
4
3
1
1
1
1
1
total
1
5
1.5
3.5
1.5
2.5
0.5
0.6
1
1
1
1
Total
0.25
0.25
1.4
2
20
$
Conclusions
The Heads or Tails apparatus successfully flips in a regular random manner while
effectively demonstrating energy conversion processes. The simple design of the device
ensures its effectiveness and consistency.
Stability was a difficulty when initializing and preparing the device. Several parts
of the device depend on unstable static equilibriums, such as the baseball resting at the
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top of the incline, and the upright book. These systems are difficult to keep stable as
minor displacements disturb these equilibriums. This is partially due to the lack of
rigidity in the support structure; we used duct tape to hold the structures, which works
fine, however a more rigid substitute such as nails, glue or clamps would have certainly
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offered more stability in our design.
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