1. Water Balloons Weapons of Mass Destruction? Stan Jones Department of Physics and Astronomy The University of Alabama AAPT 2011W

2. Setting the Scene From an attorney: – Can a launched water balloon cause serious injury? From the Internet: – You bet From simple physics: – This can be modeled

3. The weapon itself

4. Duck!

5. Used this as basis for an ongoing project in introductory class Range formula Stopping distances and average force Terminal velocity Trajectory Experimental test

6. Range formula Manufacturers claim ranges of 100, 200, even 400 yards. What launch speed might accomplish this? Assume 45 o launch, no air resistance Range (m)V o (m/s)V o (mph) 10031.370 2004498 40063140

7. Force of Impact Can use F =  K/  x, where K = ½ mv 2. Problem is to estimate stopping distance. For a balloon, assume  x = radius of balloon. Then F = mv 2 /D, where D = diameter of balloon.

8. Example forces V (m/s)  t (s) F (N)F (lbs)P (psi) 200.004121527338.7 400.00248621094155 Assume 3” diameter balloons “Force of 900 N for 0.006 s will break a cheekbone”

9. Terminal Velocity From general considerations: F air ≈ ½ C  Av 2 C = drag coefficient ≈ 0.4 F ≈ 1.1 x 10 -3 v 2 Newtons for 3” balloon Let F air = mg to find: V term = 45 m/s

10. 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!”

11. 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.

12. 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