Transcript NC Science Olympiad

NC Science
Olympiad
Coaches Institute
Trajectory
Division B & C
The Trajectory Event
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Teams will design, construct, and calibrate
a device capable of launching a projectile
into a target area and collect data to
develop a series of graphs relating launch
configuration to target distance and height.
Rules
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Read the rules
Discuss the rules
Read the rules
Copy the rules
Have the students copy the rules
Read the rules again
Highlight the rules
Understand the rules
Rules
Event Parameters
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Team size, Max of two (2)
Must wear eye protection. (ANSI Z87+)
Impound event (What does this mean?)
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The launch device, graphs, and all materials
teams will use must be impounded (checked in at
the event) prior to the competition.
After all devices are impounded the target
distance and heights will be announced.
Design
Construction
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The Launching force MUST be supplied by
non-metallic elastic solids. (rubber, wood,
plastic, bungee cords, rubber tubing, etc.)
Size: everything must fit inside a cube
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Division B – 70cm cube
Division C – 60cm cube
Construct
Construct
Design
Construction
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Triggering device is not part of the device:
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It may be Battery
It may not be radio controlled
It may not pose a danger
Construction
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Trigger
This can be simple or complex
Arrow
Release
Pelican
Hook
Panic
Snap
Construction
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Trigger
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You can use eye hooks and a cotter pin
You can use screen door hooks that have been
altered.
Design
Construction
Teams
will provide
unmodified projectile.
Projectile
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Tennis Balls
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Racquetballs
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Ping-pong balls
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Practice Golf Balls
Video
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Catapult in action:
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http://www.sciencenc.com/Tournament_info
rmation/Event_rules_nc/Trajectory.cfm
Catapult Science
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Math behind the event:
http://www.open2.net/diyscience/mangonel/
catapult_download.pdf
Catapult Science
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We must calculate the Force (N) exerted
by the throwing arm.
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To do this we need to know the velocity at take
off calculated in meters per second (m/s)
We also must work out how fast the arm
accelerates. Acceleration describes changes in
velocity (m/s2).
The force comes from the elastic bands
attached to the arm.
Catapult Science
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If we know how long it takes to go from
take off to landing we know it takes gravity
X seconds to slow from take off speed to 0.
Gravity will accelerate any object at 9.8
meters per second per second.
Now we want to figure the Vertical Velocity.
Catapult Science
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Vertical Velocity
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Vv = The final component of velocity in the
vertical direction = 0
Uv=The initial component of velocity in the
vertical direction= (This is what we are looking
for)
Av=The component of acceleration in the verticle
direction (-gravity)
T = time taken
Catapult Science
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So our formula is:
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Vv = Uv + AvT
We know Vv is 0, we are going to assume the
time (T) is 1.6 seconds
Therefore: 0 = Uv + (9.8 X 1.6) solve this
equation and we have
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Uv = 15.7 meters/second This is our Vertical
Velocity we will use it again later.
Catapult Science
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Ok, so the projectile does not just go up and
down.
We must look at Horizontal Velocity
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There is a component of velocity Vx in the horizontal
direction.
This is because they take off at angle theta (Θ) not
vertically
Since Vy and Vx can be treated as vector quantities the
velocity of take off can be calculated from trigonometry.
Catapult Science
Catapult Science
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Vt = Velocity (this is what we are looking
for) It will be the hypotenuse of this triangle.
Vy = Vertical Velocity (15.7 m/s)
sin = sine – ratio of the height to the
hypotenuse.
Θ = theta – symbol to describe how big the
angle is in degrees.
Catapult Science
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So our formula is:
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Vt = Vy /sin Θ
We need to know what the angle is
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The distance the projectile travels depends upon
the point it leaves the arm.
If the angle of trajectory is Θ to horizontal then
the projectile travels 90 – Θ when being thrown.
Catapult Science
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The circumference of a circle is 2pr
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In our case, r is the length of the throwing arm.
We will estimate 50 cm.
So if the arm traveled a full circle it would travel
(2 X 22/7 X 50)cm or 314.3 cm
So 90 – Θ means our arm moves 314.3(90Θ)/360 cm. (assume 45)
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The arm must travel 39.3 cm.
Catapult Science
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The load needs to leave the arm before it
reaches 90 or there is no vertical velocity.
(the force of the arm drops off) You
probably will max out at 70.
We used 45. We will work from here.
So Velocity V is 15.7 / sin45 = 22.2 m/s
Catapult Science
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We now know how much the arm accelerates with
a final velocity Vf = 22.2 m/s. We will use this to
calculate the forces.
V2 = U2 + 2as
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V = final velocity (22.2)
U = initial velocity (0)
a = acceleration (what we are solving for)
s = speed assuming constant acceleration over the
distance moved we calculated the distance moved as
314.3 X 45 / 360 = (39.3 cm)
Catapult Science
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V2 = U2 + 2as
22.22 = 0 + 2 X a X 39.3
a = 22.22 / 78.6
a = 6.27 m/s2
Catapult Science
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To work out the forces we will use Newton’s
First Law.
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F = ma
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F stands for the net force
m is the mass of the projectile
a is acceleration
Catapult Science
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If the mass of a racquet ball is 39.7 grams
And our acceleration is 6.27 m/s2
F = 39.7 X 6.27
F=.2489 Newtons (Km/s2)
If you use this much force and the ball
stays in the air 1.6 seconds the ball should
travel over 35 meters (115 feet).
Target Area
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Two target areas
will be placed in
front of the launch
area centered on
an imaginary line
that bisects it.
Target Area
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The nearest target will be
elevated above the floor,
up to 1m for Div. B; up to
2m for Div. C in 1 cm
intervals, measured from
the floor to the top
surface of the impact
area.
The furthest target shall
be at floor level.
Target Area
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The targets will
be either circle
(1 meter in
diameter) or
square (1 meter
on each side)
with a rim no
higher than 3cm.
Target Area
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The impact
area will
contain sand
or cat litter
~1cm deep.
Projectile
impact
location
Target Area
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The center of the
areas will be
marked so that the
distance between
them and the
center of the initial
projectile impact
location ma be
measured.
Scoring
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The winner will be the team with the lowest
Final Score.
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To get the score you add:
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Lower Close Target Area score + Lower Far Target
Area score – Graph Score + Penalties – Bucket
Shot Deductions = Final Score
Scoring
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Teams will be ranked in tiers based upon;
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Devices meeting all specifications (Tier 1)
Devices not meeting all specifications (Tier 2)
Tiebreakers are:
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1st Lower total of the sum of the two scored shots (to
reward consistency).
2nd closest shot overall
3rd non-scored shot at the far target
4th non-scored shot at the far target
Scoring
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Scoring the toss (Students must indicate which
target they are aiming to hit.)
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The close target area score shall be the distance in mm
from the center of the initial projectile impact location to
the center of the target area. (outside the target area or
failure to launch scores 800 mm.)
The far target area score shall be the measured similarly
but measured to the impact location if outside the target
area. (failure to launch measures from the front of the
launch area to the center of the far target in mm.)
Scoring
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If you hit the target!!! (on the first attempt)
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A bucket shot may be requested. A 1-5 gallon
bucket will be placed on the course. Hit the
bucket but not staying in is a 50 pt. deduction.
Hit and stay in the bucket is worth an additional
100 deduction points.
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Teams with bucket shot attempts will not have a
third and/of fourth tie breaker and are scored
behind those that do.
Penalties
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Ouch!
A 100 point penalty will be added each time
any of the following occurs:
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Not wearing eye protection
Is in or in front of the launch area (when a launch
occurs)
Does not give a warning prior to launch (Fire in
the Hole!!!!!)
Any part of the device is outside the launch area.
Collect Data
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The purpose of data collection is to provide
students with an understanding of test and
result.
Determine what data you can collect
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Distance thrown
Length of action
Number of bands
Etc.
Graphs
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Each team starts out with 400 graph points
These can be reduced by turning in four
different graphs and data tables.
Each of the 4 selected graphs may reduce
the Graph Score by 100 points.
Graphs
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Any number of graphs can be impounded but the
students must indicate which four will be used to
determine the graph score.
Graphs:
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Computer or hand drawn
Graph/table together on a single (same) side of paper
Labeled
 All variables
 Units identified
 Team name
Graphs
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One of the four graphs, Selected by the event supervisor,
will be scored as follows:
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20 point reduction for completed data table
20 point reduction for graph
20 point reduction if graph matches data table and is on the
same side of the page
40 point reduction for proper labeling
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Title
Team name
X & Y axis variables
Increments with units
The score of the scored graph will be multiplied by the
number of graphs turned in (up to 4).
Construction
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Measure carefully
Use smooth action on the moving parts.
Attach your elastic solids for force securely.
Some rubber will wear with use. Be sure
you calculate wear as you practice.
Weight is not an issue.
Metal angles will work in many cases.
Construction
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Make sure your boards and angles are square
and tight.
Be sure the projectile holder does not restrict the
release of the projectile.
Use plywood for stability
Use solid construction with screws and or nails
 Hands
on Review of
Catapults.
Instructor
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Jim Roberts
[email protected]
Worked with Science Olympiad since 1998.