Rube-Goldberg Catapult
EF 151
Spring 2006
Craig Bowers
James Hartsig
Aaron Shannon
Rob Burgin
Overview
Our team quickly decided that we would design and construct some sort of
catapult device.
We agreed that we should keep the design as simple as
possible and that we should stick to the minimum of three distinct steps. Our first
step involves a ball bearing rolling through an inclined length of ½” PVC pipe,
triggering a mouse trap upon landing.
The energy in this process can be
analyzed from the viewpoint of gravitational potential energy changing to kinetic
energy.
The second step involves a mouse trap being triggered by the ball
bearing, which in turn pulls the firing pin of the catapult. In the second step,
kinetic energy is used to release elastic potential energy that is converted back to
kinetic energy. That kinetic energy is used to initiate the third step. In the third
step the catapult is fired. The firing pin is pulled releasing stored elastic potential
energy of two linear springs. The springs are connected to a lever that spins,
converting the stored elastic potential energy to kinetic energy.
The lever
releases a 10 gram projectile at an angle of 54 degrees from the horizontal.
Design Process
Our design process was quick, simple, and to the point. We chose PVC to build
most of our structure because it is cheap, strong enough for our application, very
easy to use, and Rob likes the way the glue smells. We chose to build our
device on wooden planks because Craig has lots of scrap wood at his house.
We considered the idea of having our projectile strike some sort of target, role
into a hole, or something else along those lines.
Upon further scrutiny, we
decided to keep the device as simple as possible, erring on the conservative side
rather than tempting Murphy’s Law. Each of the first two steps yields way more
kinetic energy than necessary to trigger the next steps into motion. Would we
change this if we had to do it over again? No, we would not. The spirit of a
Rube-Goldberg device seems to be centered on inefficiency, going through
unnecessary lengths to accomplish a simple task.
The Catapult
Our Rube-Goldberg device is fairly simple.
A ball bearing is inserted into the PVC pipe
(back right, partially obscured).
The ball
accelerates down the pipe where it is
released onto the mousetrap (back left,
holding receipts).
The mousetrap, via a
string, pulls the firing pin of the catapult. The
catapult is powered
springs.
by tandem
linear
The catapult arm swings into
Figure 1. Catapult
motion, and then stops abruptly upon reaching a stop, launching the projectile (a
10 gram, aprox. 2 cm diameter ball).
Energy Analysis
Step 1:
Step one involves rolling a 25 gram ball through an inclined section of PVC Pipe.
The gravitational potential energy associated with the ball the instant before it
begins rolling can be calculated by multiplying the mass of the ball by the height
of the ball above the finish point and by the force of gravity, Ugrav=mgh. This
value is (.025 Kg)(9.81 m/s/s)(.1588m)=.0389 Joules.
Almost all of this
gravitational potential energy is converted to kinetic energy. Some energy is lost
due to friction inside the pipe, but this amount of loss is very small, and has been
omitted from our calculations. A small amount of the energy has been converted
to rotational energy of the ball, but has also been omitted. The approximate
velocity of the ball can be calculated by setting the gravitational potential energy
equal to one half the mass of the ball times the velocity squared. Solving for
velocity gives 1.77 meters/second. The ball lands on the triggering device of the
mousetrap.
Step 2:
The triggering device of the mousetrap requires a miniscule amount of energy to
be tripped (so small that even a little mouse can do it). The .0389 Joules of
energy provided by the ball may be on the order of 100 times greater than
necessary. The spring employed by the mousetrap is torsional rather than linear.
The elastic potential energy of the cocked mousetrap can be calculated by
measuring the moment about the axis of the spring required to hold the lever still
in mid-travel. In our measurements, 8 force scales were linked together, each
reading 17 Newtons, for a total force of 136 N. The distance from the end of the
lever to the axis of the spring is .08m, so the elastic potential energy can be
calculated as (136N)(.08m)=10.88 NM or 10.88 Joules. When the trap is tripped,
most of this elastic potential energy is converted to kinetic energy. A string is
attached to the lever of the mousetrap. The string is attached to a pin, that when
pulled, triggers the catapult. The force required to pull the pin from the cocked
catapult is approximately 1.5 Newtons. This demonstrates once again that our
device is latent with excess energy to accomplish the tasks at hand.
Step 3:
The lever arm of the catapult is accelerated via two linear springs. The spring
constant, K, can be calculated by measuring the force per length deflection from
the neutral position. A force of 34.5 N is required to obtain a deflection of .292 M.
K is then equal to (34.5 N)/(.292 M)= 118 N/M for each spring. The elastic
potential energy, Uelas, of the catapult can be calculated by (1/2)Kx2 , where x is
the deflection of the spring, and multiplying by two (two springs).
Uelas=(1/2)Kx2(2)=Kx2=118N/M(.292M)2=10.06 NM or 10.06 Joules. By chance,
this is remarkably close to the potential energy of the mousetrap. Much of the
elastic potential energy of the catapult is converted to kinetic energy when pin is
pulled. The kinetic energy is that of the lever and the 10 gram ball held in the
cup at the end of the lever. All of the elastic potential energy is certainly not
transferred to the ball. In order to release the ball, the arm hits a stop, and the
ball keeps moving. Judging by the loud noise and the vibration of the entire
device when the lever hits the stop, the lever arm has much of the energy after
the ball is released. If all of the elastic energy were transferred to the ball, the
speed of the ball could be calculated by setting Uelas equal to 1/2Mv2, or
10.06J=1/2(.01Kg)v2, V=44.9 M/sec. Adding up the energy from all of our steps
we get the total energy in to be approximately 21 joules. The energy we get out
of the catapult is only about 4 joules. So when we divide the energy output by
the energy input we get a total efficiency of about 19% which isn’t very efficient
but in general nature Rube-Goldberg devices are not.
Materials
Mousetrap: $1.96
PVC and Fittings: $8.32
Dowel Rod: $2.05
Springs: $4.17
Hardware: $1.96
Total w/tax: $20.17
Recoverable Materials:
Scrap wood
Nails (if we are very careful)
Plastic can lid used to hold projectile
Conclusions
Our project is simple and reliable. One thing that we learned is that in analyzing
a system such as ours is that accounting for energy loss is the difficult part.
When
nonconservative
forces
are
omitted,
the
calculations
are
very
straightforward. We are very pleased with the way our project turned out, and
would be hesitant to change the way we addressed the problem were we to do it
again. Our team works very well together.