1 Steel balls Topic 3 Taiwan Representative

2 Outline Question Experimental set up: Vertical collision Materials: Paper, Plastic, and Metal sheets Experimental results: Hole size v.s materials, height… What we learned & discussion Conclusion

3 Question Colliding two large steel balls with a thin sheet of material (e.g. paper) in between may "burn" a hole in the sheet. Investigate this effect for various materials.

4 Experimental Setup: vertical collision 1 m H Sheet

5 Materials 1. Paper (Burning point: 130 o ~232 o C) Reference: _is_the_Burning_point_of_paperhttp://wiki.answers.com/Q/What _is_the_Burning_point_of_paper 2 mm 5 mm

6 Inflammable materials Paper A thin piece of material left on the ball Greatly heated Burned O2O2 Greatly heated Burned O2O2

7 Materials 2. Plastic (Melting Point: 106~114 ℃ ) (Soften temperature: 80~98 ℃ ) 3 mm 4 mm

8 Non-flammable materials Plastic Compressed Into thin layer Melted Wrinkles Cooled down

9 Materials 3. Aluminum foil (Melting point: 660  C) 5 mm 6 mm

10 Non-flammable materials Aluminum foil Concentric circles wrinkles Melted Compressed

11 Materials 4.Copper foil (Melting Point: °C) Reference: 5 mm 2mm

12 Non-flammable materials Copper foil Concentric circles wrinkles Depends on condition Compressed Melted ??

13 H PlasticPaper  = 7.6 cm

14 Height v.s. Materials

15 Height v.s. Materials

16 Height v.s. Materials

17 Height v.s. Materials

18 Estimation of physical parameters during collision The highest temperature T max. = ? Duration ∆t = ? Collision area A=? Average pressure P = ? Conducted heat ∆Q = ? Adiabatic process? i.e. ∆W >> ∆Q

19  We can melt Al foil. Melting point of Al = 660 ℃. T max. = ? Cooled after melted

20 Duration ∆t = ? Our high speed video: 230 μs/frame

21 Material t=0 Dropping ball Fixed ball Edge of pillar

22 t=230μs Material Dropping ball Fixed ball Edge of pillar

23 t=230μs x 2 Material Dropping ball Fixed ball Edge of pillar

24 t=230μs x 3 Material Dropping ball Fixed ball Edge of pillar

25 Duration ∆t = ? 1. Our high speed video: 230 μs/frame  ∆t < 230 μs 2. From reference our m ball =287 g R. Hessel, A. C. Perinotto, R. A. M. Alfaro, and A. A. Freschia, Am. J. Phys. 74 3, 176 (2006). We can conclude : ∆t < 230 μs

26 Collision area A=? Al foil Diameter ~ 1.6 mm Estimate A from the melted Al foil. Diameter: 1.58± 0.08 mm

27 Average pressure P = ? m=287 g, H=50 cm, g=9.8 m/s 2, A< π (0.8mm) 2, ∆t < 230 μs

28 Work ∆W=? Pressure P > 1.2 x 10 9 Nt/m 2 Collision Area A= π r 2 ~ 2x10 -6 m 2 Thickness of sheet ∆d= m Conducted heat ∆Q=? ∆T < 1000 ℃ A= π r 2 ~ 2 x m 2 Air0.026 Al237 Cu401 Fe80.4 Steel46 Water0.61 Wood0.11 σ

29 Heat produced Using the lowest production of work, Increase ofΔT, => Higher than melting point of Al: 660

30 Adiabatic process?? Work done during collision ∆W > 3.9 ×10 -1 (J) Heat conducted during collision : ∆Q < 2.9 ×10 -4 (J) ∆W >> ∆Q  Adiabatic process T high T low

31 Conclusion Height: Diameter of holes increases as height increases Collision Area:  Burning  Melting

32 Colliding process P T

33 Burning O2O2 O2O2

34 Melting

35 Conclusion Height: Diameter of holes increases as height increases Collision Area:  Melting  Burning Adiabatic Process is the main reason holes are burned because:  Δt is small  Area is small  Pressure is high

36 Conclusion Height: Diameter of holes increases as height increases Collision Area:  Melting  Burning Adiabatic Process is the main reason holes are burned because:  Δt is small  Area is small  Pressure is high