Free Fall Time of Paper Cones

1. Free Fall Time of Paper Cones Jiankun SUN, Nan CHEN, Donghui LI, Quan YUAN, Tianyang XU

2. Introduction Formal Experiment Pre-experiment Conclusion 4 3 1 3 3 2 Contents

3. Literature Review 《浅探纸锥下落快慢与纸锥大小的关系》,陆文彬 Only study free fall time of paper cones with same radius and different angles Derive a complicated equation to describe the relationship between acceleration and velocity and the impacts from paper cone properties

4. Factor Decomposition Response variable:free fall time Inputvariables:paper thickness, cone radius, centralangle, Controlvariable:height Nuisancefactor:operator performance, recording error

5. Pre-experiment Design • Purpose • Check the repeatability and reproducibility • Get a general idea of the degree of factors’ influence • Design • 3 replications for each level and each operator

6. Experiment Process At platform of stairs in the hall of Shunde Building The operator stretch out the arm horizontally and hold the paper cone with two fingers, and then release the cone without initial velocity A camera is used to record the process for time analysis

7. Analysis: Reproducibility Check whether there is significant difference between results of different operators Cannot claim significant difference

8. Analysis: Influence Degree Check which variables have influence and how much the influence is Influence from certain variables and interaction

9. Formal Experiment Design Full Factorial Design Level setting

10. Data Collection

11. Data analysis Descriptive analysis: Thickness may have influence while radius may not

12. Data Analysis Scatter Plot: There seemsto be a linear relationship between time and angel.

13. Data Analysis Main effects plot

14. Data Analysis Interaction plot No significant interaction between radius and thickness or between angle and radius. Interaction between thickness and angle.

15. General Linear Model (GLM)

16. Residual Plots The residual versus is a bowl-like curve May be due to interaction

17. Conclusion from GLM Free fall time of paper cones have strong linear relationship with central angle and paper thickness At 95% confidence level, the correlation between free fall time and cone radius is not significant

18. GLM adding interaction

19. Residual Plots

20. Conclusion from 2nd GLM Arelatively higher, and no obvious pattern in the residual versus fits At 95% confidence level, The effect of the interaction between paper thickness and central angleis significant.

21. Conclusion from 2nd GLM Arelatively higher, and no obvious pattern in the residual versus fits At 95% confidence level, The effect of the interaction between paper thickness and central angleis significant.

22. Conclusion & Explanation • Equations • thin paper: Time = 0.461408 + 0.0143581 Angle • thick paper: Time = 0.461408 + 0.00927134 Angle • Explanation • Air resistance increases with central angle. • For different paper thickness, different mass of paper contributes to different change in fall time as the central angle changes. • Wrong sign of coefficient of thickness: not significant

23. Thank You !