Problem №8 “Domino amplifier”

Alex KrotovYekaterinburg

Team of Russia

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.

Statement of the problem

Slide 2

Key objectives

Construct a set up.

Observe the phenomenon.

Analyze energy transfer.

Investigate and check limitations for elements.

Slide 3

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

Slide 5

Wooden dominoes of different height

Abrasive paper Dynamometer Rail cart with domino

imitation Railroad with small

inclination

Experimental set up

Setting the initial distance between dominoes

Triggering the fall of the row and video-record

Finding the way rolled by the cart

Derivation of energy, transferred to cart

Experimental plan

Slide 7

The main results

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.

20 см

14,5 см

Slide 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

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

Slide 10

A pattern of movement

Slide 11

Slide 12

Theoretical estimationEnergy, converted from potential

hmgE

thicknessl

lh

lh

lh

lh

h

p

)4(22

)3(2

3

2

)2(2

)1(22

(1)

(2)

(3)

(4)

Counter of energy transfer

cartAlossA

i piE

mgAFA

gLmmgA

cartfrictcart

cartcart

)(18.0)(

sin)(

L

31 2

α

Slide 13

Energy loss calculationSequential subtraction

1

1 2

1

11

1

11

p

cartp

p

cartlosscart E

AE

E

A

21212 cartppcartloss AEEA

cartlosscartlossloss AAA 112122

1212

p

loss

E

A

on... so AndSlide 15

Ratio between energy loss and change of potential energy

Collision and friction between tile (1) and the cart:

When height of element is h=5 cm ηmin=57%

As the height grows h=7.5 cm ηmin=59%

The fraction of loss grows with the height of domino

ii

loss

E

A

31 2

Slide 17

Ratio between energy loss and change of potential energy

Collision and friction between (1) and (2)

While h1>h2,

ηmin=62% The loss grows with the height

difference between dominoes

31 2

Slide 18

Ratio between energy loss and change of potential energy

Impact and friction between (2) and (3)

The minimum is reached when h2=h3:

ηmin=77%

31 2

Slide 19

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.

When considering non-last-in-the-row element, it should stay tightly to the next one.

The first element in the row is the most important

initpush

initpush

BUT

Weak transfer

Strong transfer

Little difference

Great difference

Slide 20

Collision

h2

h1

ω10

s1

1

∆h1collision ofmoment at theenergy kinetic -

22

: thatstates,energy kinetic of definition The

10

21

21

22

1

1110

1

k

k

E

shlhh

hgmE

10

10~

kheatheat

kheat

EA

EA

heatintoconverted

energykinetic ofPart

%90heat

Slide 23

Size limitations

w

∆l

h

2

2

lE

mIE

hE

mIE

mIE

rise

k

rise

k

k

2

2

~

~~~

~

~~~

~~~

h

h

Δl

Δl

w

Slide 26

Common equation

222

2221

21

2211

heat

0

10

:isequation overall the90%η

part lossheat and ω oft replacemen thegConsiderin

hlhhshlhh,

h2

h1

ω1

s1

102210

fall todomino second for theCondition

EhgmE heat

Slide 27

2

12

122

110

222

220

2

1

2

1

2

12

1

shlhh

hlhh

h

h

m

m

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

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

Thanks for your attention

Slide 30