The Light Weight
April 29, 2010
Team 5
Benjamin Word, Stewart Chase, Jordan Nguyen, Elliott Steen
C-1
Abstract
Our Project’s ultimate goal was to turn on a light using the initial gravitational potential energy
of a weighted eight ball in the most complicated way we could think of. With this approach in mind our
Rube Goldberg device design approach was doubly named the Light-Weight, due to a weight activating a
light! Our design process while probably simplified drastically from our initial drawings took on a life of
its own once we started building. Our eventual goal of the device was accomplished in five primary steps
and four concepts of physics that are listed below:
Introduction
The objective of the team project was to build a Rube Goldberg machine that successfully
turned on an electrical device. In order to complete our goal EF-151 concepts, group work, and openended problem solving were required. For the project, our Rube Goldberg machine design was required
to perform at least five steps. Another requirement included the use of the following principles: torque,
center of mass, projectile motion, conservation of energy, conservation of linear motion, or angular
momentum in at least four of the design steps. Each team was also limited to a twenty dollar budget.
Design Process
The design process began with brainstorming and the development of rough sketch ideas from
within the group. These ideas were based on the concepts we chose to concentrate on for our project:
center of mass, conservation of translational energy, projectile motion and torque. After we arrived on
a consensus for the device we would trigger (a lamp), we developed a plan for the set of steps involved
in turning it on. We then set out to gather the materials proposed for building the machine. After the
actual start of the building process we soon realized that some of these ideas were unrealistic and
needed to be tweaked or completely changed all together. The projectile motion element that we had
incorporated into our original idea, we found to be very inconsistent and hard to control. Due to these
problems we completely discarded the idea and developed a feature that used the principal of
conservation of energy in its place. The whole building process involved a lot of trial and error. We had
the ideas of what we wanted to do but in the process of implementing the plan we found easier ways of
accomplishing the same result. For instance, we had a box fall off a platform into a basket which
activated a lever but we found that the box was having trouble landing in the basket. We then came up
with the idea of tying the box directly to the lever so when it fell it had the same effect but with much
more dependable results. Our final design turned out much differently from our original design but we
found these changes necessary for a more reliable and consistent Rube Goldberg machine.
Device Description
Our device, the Lightweight, was constructed
out of the scrap wood and other findings in Estabrook
13. It was constructed on a base of .8m x .5m wood,
and along a wall .5m high. Our foundation was found in
the workshop, along with the ramps, popsicle sticks,
nails, plastic cups, pulleys, and twine. Even though we
found so many materials to use we still had to purchase
other supplies.
Our devices starts with one pull of a string.
Once the string is pulled it releases the billiard ball
which rolls down the ramp. At the end of the ramp is a
mailbox, which is balanced on its center of mass, and
the ball rolls into the box and is knocked off its beam and lands into a basket. The box is also attached
to a string, so when it falls down it pulls on the string, which pulls down the see-saw, which activates the
next see-saw. When the second see-saw is pulled up by the first, the thread connected to the end of it
is pulled down. The strand is wound through a pulley. It is tied to the gate holding our wooden sphere
in place. As a result, the gate is opened, releasing the ball when the string is pulled. It is then free to roll
down the ramp and knock into the rotating disk’s peg. The disk spins into a line of dominoes and causes
the final reaction. Once the dominoes fall down it triggers the mousetrap at the end. The mousetrap
has a string tied to the lamp switch. So when it is triggered, it snaps back and turns on the light! Some
of the concepts we used were:
Analysis
While the Lightweight consists of numerous concepts of engineering physics our project has four
main ones which transfer the proper amount of energy into the system. These concepts are
conservation of translational energy, center of mass of an object, torque, and conservation of angular
momentum in collision. The following analysis covers these four main concepts and is based on the
presumption of friction being very little to interfere with calculations and that all energy in the system in
virtually conserved.
Conservation of translational energy
The first part since it basically a place being placed on a ramp can be expressed in the
conservation of energy equation.
Height of
2.75in.
Figure 1, Eight ball released down ramp
Assuming that the friction of the wood has no affect on the balls velocity the equation can be
seen as shown
1
1
𝑚𝑔ℎ = 2 𝑚𝑣 2 +2 𝐼𝜔2
The mass moment of inertia of the ball is calculated as a solid sphere with its mass being
170.097 grams.
2
𝐼 = 5 𝑚𝑟 2
With these equations the theoretical velocity at the bottom of the ramp just before it collides with the
mailbox is 3.24 feet per second.
Center of Mass
The eight ball from above then hits a mailbox balanced on its center of mass, thus upsetting it
and activating the next step. This center originally took some trial and error, but originally we tried to
calculate it using the equation below.
𝑋𝐶𝑚 =
𝑚1 ∗ 𝑟1 + 𝑚2 ∗ 𝑟2 + 𝑚3 ∗ 𝑟3
𝑚1 + 𝑚2 + 𝑚3
The center of mass in calculated ended up being 1.87 inches from the left. In actuality do to duct
tape and a small bolt holding the flag in place it was about 1.6 inches from the left.
Torque
Mass of mailbox=
27 grams
The Torque is exerted from the weight of the mailbox on one side in order to lift the other and
since the mailbox attached to the see saw at roughly a 40 degree angle the amount of torque can be
calculated as shown.
ℑ = 𝐹𝑟𝑠𝑖𝑛Θ
Thus the torque exerted from the mailbox’s weight is 510.76 N-m.
Conservation of Angular Momentum
For this final concept a second ball is released to collide with a piece of wood attached to a discus that
then turns to hit domino’s with a certain velocity that can be expressed in these two equations.
1
1
𝑚𝑔ℎ = 𝑚𝑣 2 + 𝐼𝜔2
2
2
`
Equation for balls velocity of 1.95 feet per second when it hits wood discus
𝐼𝑏𝑎𝑙𝑙 ∗ 𝜔𝑏𝑎𝑙𝑙 = 𝐼𝑑𝑖𝑠𝑐𝑢𝑠 ∗ 𝜔𝑑𝑖𝑠𝑐𝑢𝑠
The second equation calculates the velocity at which the discus activates the next step, and
since the ball virtually stops when it hits the discus we calculated this as if all the energy from one was
being put into the other. Thus the calculated angular velocity of the discus was 13.34 radians per
second.
Bill of Materials
2 small craft spheres ($2.99)
pipe cleaners ($.99)
basket ($.50)
thread ($2.65)
2 foam sheets ($.70)
3 wooden pillars ($1.00)
Staples/nails ($2.00)
Arenett, our dinosaur ($1.99)
Totaling—$18.51
Some of the materials used, we had in our own possession, like the rotating disk, billiard ball,
dominoes, and lamp. When we finally assembled all of these parts together, the Lightweight was
created.
Results
One of the biggest concerns we had was positioning the basket and see-saw to make sure that
the mailbox would land into the basket, and pull it down. So it could then activate the see-saws. Since,
initially we suspended the basket by the see-saw. But the problem arose that the basket would tip
forward when the box flew in, not activating the rest of the device. We fixed that by tying the twine to
the mailbox instead. We had problems with the releasing of the eight ball as well, but fixed it with a
little jerry-rigging. We fixed everything through trial and error and chose the best path that would lead
to consistency, and succeeded.
Conclusion
Over the course of our project we made several changes and encountered many different
problems. Some of these problems were fixed easily with a little help from duct tape; however other
problems involved a little more time and problem solving. We realized that some of our original designs
where not dependable. We improvised and ended up with a Rube Goldberg that was consistent and
reliable. Our team was proud of the final product.