Frictionless Demonstration Using
Fine Plastic Beads for Teaching
Mechanics and Wave
Kiichiro Kagawa
University of Fukui, Japan (Honorary professor)

Fukui Science Education Academy (NPO)Attitude towards Physics Education（１）Try to Separate from school textbooks（２）Try to use ordinary materials. Don’t use
commercial kits, which degrade children’s ability.
（３）Try to encourage to have logical thinking
through experiments（４）Try to use beautiful phenomena as the topicsof study (rainbow, snow crystal so on)（５）Try to encourage to repeat the experiment withcareful observation (small discovery)
Even physics education, there should be originality.

Chapter １• Frictionless Demonstration Using Fine
Frictionless
Demonstration
UsingFine
Plastic
Plastic Beads for Teaching Mechanics
Spherical Beads for Teaching Mechanics

Introduction• Mechanics is most important to understand science and technology• However, in high school mechanics is taught through training tosolve calculation problem
Most unpopular subject in high school

The reason
1) Due to the friction, we cannot demonstrate
the law itself.
2) For falling objects, phenomena finish
in a short time (less than 0.5 second).
Student cannot see carefully with enoughunderstanding

Commercial equipments forfrictionless motion

Car (1set): \21.000

Car including slope \46.000

Air slide track \210.000 (2000 US$)

Diameter isabout ０．３ｍｍ

Microscopic viewof Plastic beads
1㎜Work as ball bearing; beads are rotating

Plastic beads

Uniform linear motion
Patent: No ５２５７８７９

Almost no energy loss because themass is very small mass

Demonstration of the principle of thisfrictionless equipment for children

The plate with doll move smoothly,The Ping-Pong balls are rotating.

How to treat the beads
gause

Scatter the beads like shaking
pepper . Almost invisible for our eye.
But if you look at the surface froman oblique, it looks slightly white.

Take out the beads after
experiment using vacuum cleaner,or wipe with wet paper

Rainbow Experiment
Using Fine Plastic Beads

Beads scattered on a black paper work, same as water droplet.

Published in Journal of Physics Education

2008

iron ball bearing

Book ofNuffield “O”
level(1972),
using metal
smallball(1~2mm)
Weak points:
1) Heavy object: ~1kg2)Only horizontal surface,
No application for slope

Ａｄｖａｎｔａｇｅｓ ｏｆ Ｂｅａｄｓ Method
・Easily obtainable object of which bottom is flat(but should be light)
・Very cheap( 50 US$ for 1 bottle (700g),
one time only a few g)
・Even slope, the beads can be attached byelectrostatic force. (frictionless slope)・Systematic understanding is made because all
experiments are done using the same object on thefrictionless plate.
.Students can touch the equipment by themselves
as they like.
Small weak points: 1) In high humidity, friction increases2) Too much density increases friction

Objects used for frictionless demonstration
petridishlid
Bottom plane should be flat and less 100g

Equipments for frictionless demonstration
Size: 183 x 91 x 6 cm
Weight: 7.5 kg(Using Styrofoam,but covered by 2mm
Plastic plate)

Flatness is important

90 x 60 x2 cm, 7kg
For group experiment(ordered to professional)
We say “frictionless plate”, “ beads plate”

Children can enjoy using beads plate

PK gameMovieEven small driving force become vivid

Bead plate

High sensitive detection of magnetic force
Beads plate

The bar magnet direct to North

First Law of motion(Uniform linear motion,viewed from the top)

Strobe lighting; T=0.25s(4 Hz)

Beads plate

Pulse light source to record the track
Diode light source(red or green); Off and on , Periodically flash

Petri dishRepetition :5 Hz

Recorded using a digital camera: 1sec

Circular motion with uniform velocity
Beads plate

Normal reaction force

Cylindrical pipe
30cm

Velocity vector of Circular motion is tangent line

MovieCircular Motion and Simple harmonicoscillationProjected shadow

Using projected shadow,
We can show that circularmotion is simple harmonic
oscillation

Bright light sourceCircular Motion Using a String

Plasticlid with aholepinstring

Strobe lighting; T=0.25s(4 Hz)

If there is quite no friction, thecircular motion keeps going onlike a planet motion.

Rotation of rigid bodyCenter of gravity
Center of gravity

On the frictionless plate

Usually, to have the image of rotation of rigid
body is difficult for students

Law of conservation ofangular momentum( L = r x p )Circular motion using stringEnd of string was fixed so as to be coiled aroundthe pole; ( with decreasing r , V increase )Law of inertia
Suspended weight

Weight moves to frontward
Object at rest

Pull suddenly

It stay there;

because no transmission offorce due to no friction

F=ma(the second law)in high school textbook

Using wheel car
For students, it is difficult tounderstand that this is a general law

Qualitative demonstration for F = masailboat

Beads plate
Give force continuously with blower, the speed increases step by step.
Put a weight on the vessel, see how acceleration change.

Demonstration of second lawLED,periodical
flash ,10 Hzpulsar

Petri dishM

Accelerated motion

On bead plate

Constant force

Weight:２０ｇ

Ｍ＝53.４ｇ

V = △X/ △T

Ｍ＝153.４ｇ

F=maAcceleration

ビーズ板
Constant force(Second Law of Motion)
We can change m and F,independently.
F: weight(２０ｇ)
Under various mass
(48.8g)velocity (m/s)

M(98.8g)(148.8g)(248.8g)

time ( s )Action and Reaction Law(Third law of motion)
Repulsion force each other,
without touchingSSN

The expansion
is the sameHigh school textbook

S NS

NSSSNNNN

On the frictionless tableWe constructed “Circular magnet”
Small Neodymium
magnet are arranged
In a circular form
In a plastic lid

図8-2Compass

Demonstration
using circular magnet,
under strobe flash light

改良型
小型ネオジム磁石A

On frictionless plateBAction and reaction, using jumping frog

On frictionless plate
Usually, difficult to see the force itself

Demonstration on practice problem
On the smooth surface C, there is an object D (M kg). On the smooth slope
B, another 0bject A (m kg) is placed . Then, the object A slide down on theslope. Please assume , there is no friction on these surface.
Questions:
1) What is the acceleration of A against D ( in X, Y component)
2) What is the relative acceleration of A against D3) What is the relative acceleration of D against C

We can demonstrateusing the frictionlessplate and frictionlessslope.
Difficult for students to have the image

Free falling object

Falling object on a slope
Frictionless slope

ＭｇMgsinθ
Mg cosθ
Mｇ

Ｆ＝Ｍｇ
a=ｇ

Ｆ＝Ｍｇsinθ
a=ｇsinθ(small)Acceleration become small by using slope,
when Θ＝1°acceleration=(１/60)g

We can see the phenomena as slow motion, easy to understand.

Can measure the force tothe slope direction

Inclining frictionless table

Smooth slope

Free-fall on the smooth slope

Regardless of the mass, falling isthe same
We can see the penomena
in slow motionUniform acceleration
motion on theinclined beads platex = 1/2 g’t2

Angle of slope ：0.8o

Time vs. length

time：~3.5 sec
acceleration：0.13m/s2(g’ = g sinθ）

Measurement can be madeusing a stopwatch(very instructive)

Time vs. velocityg’m g（sinθ-μcosθ）= F
μ : Dynamic friction coefficientfor ground glass plate

m g'= Fg'＝g (sinθ-μcosθ)

Beads scattered on the surface

X =½at2
Derive g'using a stopwatch

μ = 0.013
g’

For smoothglass = 0.001

Monkey Hunting
Vertical direction motion is thesame between the monkey andthe stone

ｘ方向と、ｙ方向の運動は独立。
サルも弾もｙ方向に対しては同じ落下運動をする。

Commercial equip.
\39,000

Experiment of monkey hunting
using the inclined beads plate
One --Two--Startmonkey

Regardless of the speed
The stone can attack
The monkey

Both Monkey and stone,
the motion of
the Y direction is the same .
The Motion takes place slowlyⅹystone
10Plastic lid(regard as stone) is shot aiming
at the monkey

What angle gives the mostfar distance? (under the same initial speed)x  v 0 cos   t
1 2gt`  v 0 sin   t (ｇ`＝ｇsinθ)2gx`y  x  tan   22

2 v 0 cos  tan   2 v 02 cos x  0, x gyⅹyv02 sin 2gx max  sin 2  1  450

Chapter ２
Many Application ofFrictionless Plate

Horizontal spring vibration
T = 2π √m/kusing a big springNon-gravity (Weightlessness) demo.
beadsbeads
In a elevator, whichfreely fall.

During the falling on the frictionlessslope(~20o) , no expansion of the springCollision phenomena
AA

stop
A

stop
B

A f t e rcollision

Before collision

AA

stop
B

A
A

Before collision

ＡBB

A f t e rcollision

stop
ＢAＡ

A f t e rcollision

Before collision

m1v  m 2 v 2  m1v1'  m 2 v 2'v1'  v2'e
v1  v2ＢAHead on collision usingaluminum disk
On frictionless plate

Completely exchange

Small one is repelledMomentum conservation for
oblique collision
Head-on collision（one-dimen.） Oblique collision (two-dimen.）

From high school
textbookMomentum conservation for
oblique collision○×○×
Before collision

After collision

Using strobe light flash

Composed momentum vector is conserved

When the same mass, same size
disk collide diagonally ,VVResting disk

We can see this kind of problem in study-aid book of high school;
one exists on a table, and another come with a speed V to collide
diagonally , prove that V1’ and V2’ make always a right angle after
collision, (Using momentum conservation law and energy
conservation law)

Relationship between work andkinetic energy
VX

1/2 m V2 = f ・ X
firiction on the paper( f = μ m g)v2

Velocity and distance can bemeasured simultaneouslyXConversion from potential energy to kinetic
energy （beads are attached by electrostatics force ）Plastic sheet with fine beads

Speed meterv

Beads plate

Velocity vs. height
theorymeasurement11
mv o2  mgh o  mv 2221
mgh 1  0  0  mv 221
mv 2  mgh 12mgh 1 ｈv V 2=gh√2gh1

Fall down the slope
Smooth slope
Plastic sheet

ball

Petri dishBall is late:(energy is consumed forrotating the ball, thus kinetic
energy of motion is reduced )Elastic and Inelastic collision
CushionBound slowly （no movement of small plastic balls）

Stop
Energy change tothermal energyCollide with hard wall, plastic balls move randomlyCentifugal force and Coriolis force
Beads plate

Beads plate

rotating coordinate
Fixed coordinateBeads plateti n gatorcoteani
ord
Fixed coordinate

Centifugal force and Coriolis force

Coriolis force

Beads plate

rotating coordinate

Fixed coordinate

Centifugal force and Coriolis force

MovieApplication of Frictionless Plate
For Wave Demonstration
Usually wave propagate very fast, thus it is very
difficult to observe。
We made slowly propagating waves using thefrictionless table.

Slowly-moving wavePlastic lid (diameter 5cm, 8g) is connected using a thinrubber string for wave propagation.

Frictionless Plate(white borad)

Fine beads

Chain of thin plastic lid.
1 piece= 8g

Reflection of wave at fixed edge
Movie

Reflection of wave at free edge
Movie

Standing wave
Movie

Superimpose of Waves(+ ,+ )Textbook

Wave machineSuperimpose of Waves(+,+)
Movie

Superimpose of Waves(+, -)Movie

Two wave with different speed
MovieInternational seminar in Fukui

10 students (Syiah Kuala Univ. ,Faculty of Science)came to Fukui to attend internationalseminar under the support ofJapan Monbushou (2008).

Questionnaire survey from university students
Before demonstration

After demonstration

Inertial law

Inertial law

A little
understand

UnderstandAction and reaction

don’t
understandAction and reaction

Conclusion:

We have proved that this method is very effective
to teach mechanics and wave.

• Frictionless Demonstration Using Fine
Beads
for Teaching
Mechanics
In Plastic
order to makepopularthis demonstration

method into educational field in Japan, our NPO,
Fukui Science Education Academy, is constructing
the frictionless equipment by ourselves, and trying
to make donation for schools in Fukui prefecture.

Acknowledgement: This work has been

supported by grant-in-aid (Hokuriku Rokin Bank,2020)

①large one: 1(184 x 92 x 6cm )②middle one: 2( 120 x 90 x 6cm)
③ small one( 90 x 60 x 6cm )END
Thank you very muchfor your attention

How to make frictionless plate・軽量（約2.5 kg）で生徒のグループ実験に十分使える簡易型摩擦の装置の簡単な紹介をします。
＜材料＞•コルクボード：６０ｃｍ ｘ９０ｃｍ（平面度良好）（DCM ホールディング株式会社 （１０９７円）•サンデーシート（硬質塩化ビニール板）：５１０
青色透明 ９１０x６００x１ｍｍ （２１００円）•スタイロフォーム：３０ｍｍ厚、約 ７００円
•ブラタン： ９１０ｘ ９１０：約 ６００円
・モール、クッション
訳 １０００円
合計： 約7000円＜手順＞•コルクボードの裏側にブラタンを両面テープで貼る•さらにブラタンにスタイロフォームを両面テーで貼る•サンデーシ-トに黒太マジックで碁盤の線（１５ｃｍおきき）を入れる•簡易型ビーズ板
黒線の上に幅の狭い両面テープ（５ｍｍ幅）を貼る「。
•サンデシートをコルクボードに貼る•コルクボードの木の枠にABSモール（ELPX1222-9）を貼り、その横にクッションを貼る。

Main materials for constructing
frictionless plate (Beads plate)

Cork board

Plastic late
(2mm)

Styrofoam plate(30mm)