9 Water bombs Mário Lipovský.

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Presentation transcript:

9 Water bombs Mário Lipovský

Task Some students are ineffective in water balloon fights as the balloons they throw rebound without bursting. Investigate the motion, deformation, and rebound of a balloon filled with fluid. Under what circumstances does the balloon burst?

Content Motion and deformation Rebound Burst Summary Two types Angle of rebound Burst Energies in balloon Elastic Kinetic Potential Summary

How it looks

How it looks

Motion and deformation Kinetic energy Potential energy Elastic energy

Motion and deformation

Motion and deformation Water flows to the sides

Motion and deformation Maximal radius of balloon Water stopped by rubber Some energy lost - water flows

Motion and deformation Rubber is contracting

Motion and deformation

Motion and deformation

Motion and deformation Energy losses Water convection Heat

Different type of deformation The view is from the bottom of the aquarium

Different type of deformation Elongated balloon Easier to stretch

Different type of deformation Hard to stretch Easier to stretch Hard to stretch Hard to stretch Hard to stretch Hard to stretch Hard to stretch

Different type of deformation

Different type of deformation

Different type of deformation Maximal length Starts to contract

Different type of deformation Balloon jumps

“Investigate the motion, deformation and rebound…”

Rebound Jumps to the side Balloon is accelerating in horizontal way Balloon wants to rotate Jumps to the side

Jumping balloon

Jumping balloon

Jumping balloon

“Investigate the motion, deformation, and rebound of a balloon filled with fluid. Under what circumstances does the balloon burst?”

Apparatus m h Balloon with mass m Changing height h from h=0cm Find the smallest h, when it bursts Do it with many balloons m h

Height, which causes burst We can calculate the potential energy… m h

Potential energy needed to burst Kinetic energy Potential energy Elastic energy

Elastic energy of balloon Can be calculated from pressure change during inflation

Pressure measurement

Elastic energy of balloon

More measurements of elastic energy

Elastic energy of balloon with water

Total energy given to balloon Potential energy of fall Elastic energy

Total energy needed to burst (Potential + Elastic) Let’s measure the energy without losses

Compressing Parallel plates Height Scale Force

Apparatus Height-meter Compressed balloon Scale (Force)

Compressed balloon Plate Balloon Plate

Force vs. depth of compression

Force vs. depth of compression

Work done by apparatus for many balloon volumes Let’s add the initial elastic energy More than 1000 measure-points

Total energy needed for burst (Work + Elastic) Rising tendency

Big balloon Elastic energy is almost maximal Almost maximal tension

Small balloon Elastic energy is less than maximal Low tension Max tension Low tension Low tension Low tension Low tension Elastic energy is less than maximal Friction Tension at the bottom remains the same

Total energy needed for burst (Work + Elastic) max max min min Let’s compare it with the first experiment! max max max max E max max max max

Energy needed to burst trough fall & through compression

Falling balloon In graph In real life There are losses Water convection Heat Let’s assume that constant ratio of energy is preserved

Energy needed to burst trough fall & through compression

Energy needed to burst trough fall & through compression k=0,38 Very simple assumption Ratio of losses is constant (k) Remarkable result!

What we have We can derive approximately the velocity of throw needed to burst a balloon

Approximate velocity needed for burst

Summary Motion and deformation Rebound friction

Summary - Burst m

Summary - Burst m k=0,38

Thank you for your attention!

Appendices

Energy needed to burst trough fall & through compression k=0,38

Rubber stretch at rebound

Rubber stretch at rebound

Adding air

Other liquid

Elastic energy of the balloon Stretching a piece of rubber, surface tension In terms of pressure inside:

Spherical shape: Elastic energy