Problem №8 “Domino amplifier”

1. Problem №8 “Domino amplifier” Alex Krotov Yekaterinburg Team of Russia

2. Statement of the problem A row of dominoes falling in sequence after the first is displaced is a well known phenomenon. If a row of "dominoes" gradually increases in height, investigate how the energy transfer takes place and determine any limitations to the size of the dominoes. Slide 2

3. Key objectives • Construct a set up. • Observe the phenomenon. • Analyze energy transfer. • Investigate and check limitations for elements. Slide 3

4. Hypothesis • A big part of mechanical energy is converted into heat during collision and friction. • The greatest dependence is on the initial distance between dominoes Slide 4

5. Experimental set up • Wooden dominoes of different height • Abrasive paper • Dynamometer • Rail cart with domino imitation • Railroad with small inclination Slide 5

6. Experimental plan Triggering the fall of the row and video-record Setting the initial distance between dominoes Finding the way rolled by the cart Derivation of energy, transferred to cart Slide 7

7. The way made by cart is as longer, as closer dominoes stay to each other initially. The energy transferred grows while the distance between dominoes reduces. The main results 14,5 см 20см Slide 8

8. …When initial distance is too little In some occasions dominoes do not fall, when current element cannot trigger the fall of the next one. It may also happen to elements of equal height. Slide 9

9. Qualitative dependence of way made by cart on the initial distance between tiles. Slide 10

10. A pattern of movement Slide 11

11. Theoretical estimationEnergy, converted from potential (1) (2) (3) (4) Slide 12

12. Counter of energy transfer 1 2 3 α L Slide 13

13. Energy loss calculationSequential subtraction 1 1 2 Slide 15

14. Ratio between energy loss and change of potential energy • Collision and friction between tile (1) and the cart: • Whenheight of elementis h=5 cmηmin=57% • As the height grows h=7.5cmηmin=59% The fraction of loss grows with the height of domino 1 2 3 Slide 17

15. Ratio between energy loss and change of potential energy • Collision and friction between (1) and (2) • Whileh1>h2, ηmin=62% • The loss grows with the height difference between dominoes 1 2 3 Slide 18

16. Ratio between energy loss and change of potential energy • Impact and friction between (2) and (3) • The minimum is reached whenh2=h3: ηmin=77% 1 2 3 Slide 19

17. Energy transfer conclusion • Major part of kinetic energy is converted into heat during collision. • Maximal energy transfer happens when the dominoes stay in the closest way to each other while being able to fall. init push init push Strong transfer Weak transfer BUT • When considering non-last-in-the-row element, it should stay tightly to the next one. Great difference Little difference • The first element in the row is the most important Slide 20

18. Collision 1 ω10 h2 ∆h1 h1 s1 Slide 23

19. Size limitations h w ∆l Slide 26

20. Common equation ω1 h2 h1 s1 Slide 27

21. Research product Observed the phenomenon Investigated energy loss experimentally: Approximately 70% of total energy of dominoes is converted into heat. The dominoes should stay tightly, while being able to fall in order to achieve maximal energy transfer. The main idea of amplifier is the ability to trigger the fall of the highest elements Investigated different size limitations, generalized by common equation. Slide 28

22. References • http://en.wikipedia.org/wiki/Domino_effect • http://en.wikipedia.org/wiki/Plywood • http://en.wikipedia.org/wiki/Domino • Физические величины справочник // А.П. Бабичев, Н.А. Бабушкина, А.М. Братковский и др.; Энергоатомиздат, 1991. • Физика 10 класс // Мякишев Г.Я., изд. Дрофа, 2001 Slide 29

23. Thanks for your attention Slide 30