Download Water Balloons Weapons of Mass Destruction?

Water Balloons
Weapons of Mass Destruction?
Stan Jones
Department of Physics and Astronomy
The University of Alabama
AAPT 2011W
Setting the Scene
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From an attorney:
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From the Internet:
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Can a launched water balloon cause serious
injury?
You bet
From simple physics:
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This can be modeled
The weapon itself
Duck!
Used this as basis for an ongoing
project in introductory class
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Range formula
Stopping distances and average force
Terminal velocity
Trajectory
Experimental test
Range formula
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Manufacturers claim ranges of 100, 200,
even 400 yards.
What launch speed might accomplish this?
Assume 45o launch, no air resistance
Range (m)
Vo (m/s)
Vo (mph)
100
31.3
70
200
44
98
400
63
140
Force of Impact
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Can use F = DK/Dx, where K = ½ mv2.
Problem is to estimate stopping distance.
For a balloon, assume Dx = radius of balloon.
Then F = mv2/D, where D = diameter of
balloon.
Example forces
Assume 3” diameter balloons
V (m/s)
Dt (s)
F (N)
F (lbs)
P (psi)
20
0.004
1215
273
38.7
40
0.002
4862
1094
155
“Force of 900 N for 0.006 s will break a cheekbone”
Terminal Velocity
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From general considerations:
Fair ≈ ½ CrAv2
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C = drag coefficient ≈ 0.4
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F ≈ 1.1 x 10-3 v2 Newtons for 3” balloon
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Let Fair = mg to find:
Vterm = 45 m/s
Trajectories
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In 2 dimensions, calculation best done
numerically
Using VPython, found trajectories for typical
launch parameters
This graph actually for a baseball
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“No one can throw a baseball from centerfield wall
to home plate on the fly!”
Experimental Test
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Height of building = 12.6 m.
V(final) = 15.7 m/s; air not important
Predicted force about 750 N
Measured force 600 N, roughly comparable.
Aim is important…takes many trials.
Conclusions
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Water balloons are fun, but launchers can be
dangerous
One can estimate a force when a reasonable
estimate of stopping distance is available
Air resistance is a fact of life, and can be a
worthwhile subject for introductory students
All in all, the project generated interest and
students had fun