George Mason
Engineering Team Project
David Quarterman
Jared Sullivan
Overview
This project is a Rube-Goldberg device, a machine that performs a simple task in multiple steps.
The device highlights the change from kinetic energy to potential energy back to kinetic energy
in several steps utilizing the roll of a billiard ball through hills, springs, and loops and finally,
ringing a bell at the end. We were given a budget of $25 for supplies and a few weeks to
complete the device.
Design Process
Originally, we knew that one of the easiest ways to demonstrate the change from potential to
kinetic energy was to roll a ball down a hill. We took the process a step further and decided to
roll the ball down the hill and have it drop onto a flat area of track, compress a spring, launch
from the spring, collide with another ball, go down yet another hill, and flip a switch. The track
would have to be sturdy, supported by wood, and the ball would have to be heavy and capable of
staying on track while compressing the spring sufficiently. We took a trip to Home Depot and
bought a 12 ft. 2”x4” for our bracing and mounting and found that our first dilemma facing us
was not building the device itself, but trying to fit the board into the car. In the way of track, we
decided that matchbox track, supported heavily, was the way to go. Matchbox track is very
pliable and perfect for the type of hills we wanted to make. Originally we wanted to have a 1”
diameter steel ball to run the course from beginning to finish, but we decided that the steel ball
would be difficult to find, and difficult to put compression on the spring, which is also why we
decided not to use marbles either. The best solution was to acquire billiard balls to run the
course. Billiard balls are heavy and would be excellent for demonstrating compression on the
spring and would not lose an enormous amount of momentum due to friction. The billiard balls
are large, but not so large that they cannot run the track as the track forms a sort of runner on
each side underneath the ball to support the ball instead of having the ball roll on its small
contact patch. The last important piece of equipment we acquired was the spring. At 1 and a half
inches long, the spring gives moderate resistance, but is easily compressible and a fine choice for
our Rube-Goldberg device. Finally the design itself was changed dramatically as we found that
the enormous hill we had built actually gave the billiard ball too much kinetic energy as it came
crashing down to the matchbox track below, bouncing off, and comically injuring us multiple
times. However, we found the perfect balance with a hill that drops 4 and a half inches, a drop of
4 inches, and the last hill at a drop of 8 inches.
Bill of Materials:
12 ft. 2"x4" pine board
$3.47
5 pieces of Matchbox track
$2.95
1 light switch
$2.25
Set of 1.5" springs
$1.76
10 ft 2"x 2"
$2.12
Scrap pieces of wood
$1.15
Assorted nails
Approx. $1.50
Wood screws
free
Wood pillaged from Room 13 junk pile
also free
2 billiard balls
priceless
Description
The device can be best described as enormous. Since billiard balls are large, the project itself
needed to be large to handle the size of the ball, and we built it accordingly. Since the guidelines
we were given asked us for 3 easily recognizable energy conversions, we decided to do just that
instead of aiming for obscure little conversions. The ball itself rolls on 5+ feet of track from start
to finish and starts at 25 and a half inches ending at 9 inches off the ground.
Calculations
201
2
At the starting point the ball is 25 and a half inches off the ground. However, for our
conservation of energy equation, the height is actually 4 and a half inches from where the ball is
released until the next stage of the track where another conversion takes place( we call this point
the datum). At the point where the ball is released(1), the ball has gravitational potential energy.
As the rolls down the track it gains speed and its potential energy turns to kinetic and is
expressed in the equation Mgh= M v where M=mass, g=the acceleration due to gravity, h=
height at which the ball starts to drop, and v=final velocity after the transition from potential to
kinetic energy. Using this equation we find the
theoretical velocity to be 4.91 ft/s as the ball
leaves the track. However, the ball leaves the
track at 20 below the x-axis (2) and so carries
only y acceleration with x velocity remaining
constant. The calculated x velocity in this case
251
82
is 4.6 ft/s and does not change as the ball makes contact with the track 4 inches below. The
ball continues to roll approximately 1 foot before colliding with a spring at point 3. At this point
the kinetic energy of the ball transfers to potential energy as the spring absorbs the energy of the
ball. This time we use a different equation to calculate the potential energy: M v = k xwhere
k=the spring constant and x=the distance the spring compresses or stretches due to the energy.
From the package the spring came in, we find the spring constant to 6.84 lbs. at its maximum
compression point. Conveniently, the spring being 1 and a half inch long compressed to a half
inch giving us 6.84 lbs/in. From this equation we calculated that the spring should compress just
over of an inch theoretically. From this point the ball is launched from the spring with the same
energy it enacted on the spring due to the conservation of energy. At point 4, the ball collides
with another ball of the same mass. Assuming a totally elastic collision, the second ball leaves
the collision with the same speed as the first ball and the first ball stops. Also at point 4, the
second ball reaches yet another hill of 8 inches. This time the ball has both kinetic energy and
potential energy. Using the formula Mgh + M v= M vwe find that the theoretical velocity at the
bottom of the hill is 8 ft/s and the work done on the light switch is a measly .003 ft/lbs. However,
since engineers work in the real world, they must take into account friction, air resistance and
internal energy loss. From measuring the compression of the spring we find that the compression
the ball puts on the spring is one/tenth of an inch, much less than the of an inch the theoretical
value suggests. Using this value we find that the ball has already lost 84% of its energy as it hits
the spring. Our team assumes the loss to be a myriad of causes from friction over the 2 feet of
track to the impact of the ball on the drop and the energy taken in the bounce. We found the
overall efficiency to be 16%. Interestingly enough, the ball from the theoretical scenario and the
actual scenario arrives at the light switch at nearly the same speed due to the fact that the kinetic
energy in the 3rd equation is so insignificant due to the square root of the terms that it is almost
negligible, but not quite.
Conclusion
All in all, the project was a success. We worked many hours just bracing the wood for the track
and found that nails, though worthy when building fences or large objects, are terrible at odd
angles and high stress levels without other nails. Halfway through the project we decided that we
were not going to use nails anymore because the screws were holding far better than the nails.
The second main problem we had was just getting the ball to make contact with the track and
avoid bouncing or bouncing off. This we remedied by cutting the hill by 60% and introducing
side bracing for the point where the ball would most likely bounce off. However, once we
shortened the hill, the bracing was needed very little but it compliments the overall design. We
also found that the ball coming off the spring exerts just enough force to send the second ball
over the hill while slowing just enough to stop due to friction before the hill. Initially we had
planned to run only one ball but decided that the second ball would add more to the project and
its easily recognizable conversions. If we were to do this project over again, we would create a
longer, less sloped hill, a longer, more easily mountable spring, and we would not use nails.