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# Download Water Balloons Weapons of Mass Destruction?

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Water Balloons Weapons of Mass Destruction? Stan Jones Department of Physics and Astronomy The University of Alabama AAPT 2011W Setting the Scene From an attorney: – From the Internet: – Can a launched water balloon cause serious injury? You bet From simple physics: – This can be modeled The weapon itself Duck! Used this as basis for an ongoing project in introductory class Range formula Stopping distances and average force Terminal velocity Trajectory Experimental test Range formula 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 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 From general considerations: Fair ≈ ½ CrAv2 C = drag coefficient ≈ 0.4 F ≈ 1.1 x 10-3 v2 Newtons for 3” balloon Let Fair = mg to find: Vterm = 45 m/s Trajectories In 2 dimensions, calculation best done numerically Using VPython, found trajectories for typical launch parameters This graph actually for a baseball – “No one can throw a baseball from centerfield wall to home plate on the fly!” Experimental Test 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 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