HARRY - HERE
DEREK - HERE
-Discussed materials to use
Counterweight Dumbbell weights
Base Square
Arms Tetrahedrically connected to base
Trigger Cam be observed later
-Discussed some physics behind a 25 foot throw
Water balloon is on average about 3.15 inches in
diameter and .227 kilograms
Kinematics are involved
The ideal 45 degree throw to get 25 feet is
26.4 meters per second
Centripetal/Circular motion involved
Confusing, due to there being two systems
that interact dynamically with each other
Development of simulation suggested
-Discussed the use of Calculus
can be advantagous to development
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MEETING SUMARRY 10-MAY-2014, 10:00 AM TO 4:00 PM
HARRY - HERE
DEREK - HERE
Because this was only our first out-of-school
meeting, both of us knew that we had to get cracking if we
wished to complete the trebuchet within our allocated time.
To make matters worse, we spent many of our hours trying to
figure out a bunch of equations we didn't need, such as how
the acceleration due to gravity accumulates to velocity as
the position of the arm changes. After a clarification of the
rules, we found out that the requirements for the physics
applications simply calls for an explanation of force and
energy, not applied equations. However, we did apply calculus
to derive kinematics into a dandy equation that gives how
velocious an object needs to be in order to reach a certain
distance, given that the projectile's initial direction is 45
degrees above the horizontal. Here's the derivation (Please
note: "V" is the initial velocity in both dimensions):
⌠t
δy = │ (V - 9.8u) du
⌡0
or, δy = Vt - 4.9t²
δx = Vt
Vt = 4.9t² + δy
V = 4.9t + δy/t
V = 4.9(d/V) + δy(V/d)
1 = (4.9d/V²) + δy/d
d = (4.9d²/V²) + δy
d - δy = (4.9d²/V²)
4.9d²/(d-δy) = V²
____________
V = √4.9d²/(d-δy)
So now we have V, which is both the X velocity and Y
velocity. The actual tangental velocity is that number times
the square root of two:
____________
Vtangental = √9.8d²/(d-δy)
Once we store 9 meters into the distance-to-fly d value and
-1.5 meters into the change-in-y δy value, we get the speed
our water balloon needs in order to fly a grade-winning
distance: 8.695 meters per second.
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MEETING SUMMARY 14-MAY-2014, 2:00 PM TO 4:30 PM
HARRY - HERE
DEREK - HERE
Today, the both of us actually knew how to work
efficiently on the content of the project; as such, we were
able to get more stuff done, such as completing the written
portions of the physics applications of Force and Energy;
that leaves just Projectile motion left.
In addition, we devised many possible solutions to
some building restrictions. Through the use of pencils and
playdough, the both of us could much more easily explain our
ideas to each other. Several great ideas arisen from this.
For example, building the frame of the trebuchet in the shape
of a pyramid (rather than a prism) allows for much more
structural stability. Also, we decided that the use of
implementing a piece of skateboard would most certainly help
with the question of what our swinging arm will use to
actually swing.
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MEETING SUMMARY 18-MAY-2014, 12:30 AM TO 8:30 PM
HARRY - HERE
DEREK - HERE
This day saw our longest meeting to date, ranging an
entire eight hours from start to finish. Derek's father,
Norman Goodwin, aided in certain phases of construction that,
theoretically, are too dangerous for a pair of inexperienced
11th graders to try, but for the most part, we accomplished
most of the non-powertool-related building. After a good read
of a few more catapult videos from Youtube, we tried to aim
the ratio of L1 to L2 at roughly 2 to 5.
After seven hours of long, hard, sweaty work, the
catapult was finally ready for fine tuning. Unfortunately, we
ran into two problems with our catapult in doing this. For
one thing, we did not have a half-pound test ball; we had to
use a full-pound ball comprised of sand to test our
contraption, leaving us to guess if our balloons can
withstand the G-forces of our sling. For another, our
catapult could only throw our projectile about six feet.
What's worse, the reasons for the failure to launch remained
unclear until we reviewed the footage of the launch. With a
camera set to shoot frames at 80 Hz, we estimated that the
ball at launch farted out at 5.3 meters per second, a far cry
from the 8.7 meters per second we need. At the very least,
our angle of launch wound up almost perfectly correct, at
about 44 degrees from the horizon.
There are two possible reasons why our mechanism
malfunctioned:
• The counterweight wasn't heavy enough. To fix this
problem, we'd have to add extra mass onto the counterweight
to provide maximum centripetal acceleration.
• The sling's ropes were too long. Because of the
shape of the counterweight, L1's angle stalls at about 60 to
70 degrees below horizon from .7s to 1s after launch. To
maximize centripetal acceleration increasing the speed rather
than changing the angle, we would want our projectile to
launch exactly when the arm starts stalling. Instead, our
projectile takes until 1s to launch, destroying some much-
needed inertia just to get to a 45 degree angle. Shortening
the lengths of the ropes would most certainly solve this
problem, since the entire sling would swing around faster.
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MEETING SUMMARY 21-MAY-2014, 3:50 PM TO 8:10 PM
HARRY - HERE
DEREK - HERE
Because this was our last day to finish anything, we
worked more vigorously during this meeting than any other
meeting. Harry and Derek completely finished the trebuchet,
with the most noticeable modification (other than the paint)
being the counterweight's gain in mass; now, the catapult's
counterweight appears disorganized, but is actually extremely
sturdy. Dubbed the "CataPortal", our trebuchet juts out its
projectiles a whopping 32 feet.
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