Strange Trajectories of Superballs - Slow Motion Analysis1

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Exploding balloons, deformed balls, strange reflections and breaking rods: slow motion

analysis of selected hands-on experiments

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F E A TU R E S

www.iop.org/journals/physed

Exploding balloons, deformedballs, strange reflections andbreaking rods: slow motionanalysis of selected hands-onexperiments

Michael Vollmer and Klaus-Peter M öllmann

Microsystem and Optical Technologies, University of Applied Sciences Brandenburg,

Magdeburgerstraße 50, 14770 Brandenburg, Germany

E-mail: [email protected]

AbstractA selection of hands-on experiments from different fields of physics, whichhappen too fast for the eye or video cameras to properly observe and analysethe phenomena, is presented. They are recorded and analysed using modern

high speed cameras. Two types of cameras were used: the first were ratherinexpensive consumer products such as Casio Exilim cameras operating atframe rates of up to 1200 Hz for reduced image sizes and the second werehigher quality research cameras, which allow much higher frame rates atlarger image sizes. In this first article, examples are presented from explodingballoons demonstrating retardation in mechanics, karate hits, deformationsassociated with the bouncing of balls, strange trajectories of ‘superballs’ aswell as the breaking of spaghetti.

S Online supplementary data available from stacks.iop.org/physed/46/472/mmedia

Introduction

Quite often simple-to-perform hands-on exper-

iments are utilized in the teaching of physics

for motivation and sometimes deepening of the

learning process [1]. Besides the fact that,

unfortunately, the phenomena are sometimes quite

complex, they often happen too fast for proper

observation with either the naked eye or video

cameras. In the past, high speed recordings

of experiments were in principle possible, but

the camera systems were too expensive for most

schools and only a few universities used them

for introductory teaching. Hence quantitative ex-

planations of even the simplest experiments wereoften not possible or had to rely on assumptions

about the hidden physics.

This situation has improved considerably

within the last few years. The huge advances

in microelectronics and microsystem technologies

has led to modern high-speed cameras which—

in the low price segment—are now affordable for

schools [2]. As a consequence, consumer product

cameras for less than 300e can nowadays be used

in the teaching of physics [3]. Within the last

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Exploding balloons, deformed balls, strange reflections and breaking rods

0 1 2

6 8 10

Figure 1. A green laser burns a hole into the skin of a red balloon (diameter ≈ 49 cm). Within a few milliseconds,the balloon explodes (numbers correspond to time in milliseconds).

two years, we have developed a series of teacher

training seminars dealing with high speed imaging

which were successfully tested in Switzerland,Austria and Germany. Besides explaining the

physics and technology of the camera systems,

we have performed a large number of simple

to perform, but fast hands-on experiments. In

the following a selection of such experiments,

partly with a detailed analysis, partly only with

qualitative reasoning, will be presented. For better

image quality, most experiments were recorded

with our NAC camera [2]. However, an example

with the EX F1 camera will also be given below

to allow comparison with cheaper camera systems

and, in particular, to prove that such experiments

can be performed with them. The primary goals

of this work are first to make teaching materials

available by providing multimedia supplements

on the web (available at stacks.iop.org/physed/46/

472/mmedia). Second we hope that this selection

of experiments may serve as an overview of how

high-speed imaging can be used in the teaching

of physics. It will hopefully stimulate interest in

such cameras for physics teaching and thus may

lead to widespread use and many more studies of

interesting experiments.

Retardation

Retardation is a common phenomenon in physics:

it describes the fact that disturbances only propa-gate with a certain velocity and therefore conse-

quences of the disturbance happen later at greater

distances. Very well-known phenomena involving

finite propagation velocities are retarded elec-

tromagnetic fields and potentials in electromag-

netism. In mechanics, retardation effects can be

easily detected with sound waves and experiments

with large distances; think, for example, of an

echo. Demonstration experiments for retardation

with small distances as well as those involving

non-gaseous objects are, however, much more

difficult to observe. It has been proposed touse falling bars and springs to observe that the

lower end starts to fall later than the upper end,

which was initially fixed [4]. Unfortunately,

the retardation effect is somehow hidden in the

theoretical analysis since, during the fall due to

gravitation, the spring forces lead to a vertical

shortening of the initially stretched spring.

We propose a very simple retardation exper-

iment which can be more easily analysed using a

high-speed camera. Figure 1 depicts a series of

images (a video of a balloon explosion is available

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M Vollmer and K-P M öllmann

at stacks.iop.org/physed/46/472/mmedia) of the

explosion of a standard red balloon. Initially it

was inflated with air, sealed and kept fixed byhand near a metal bar. In order to destroy the

rubber skin without inducing forces and hence

movements, a green laser (frequency doubled

Nd:YAG at 532 nm, 150 mW) was directed onto

the balloon. Absorption of the green laser light

by the balloon usually burns a small hole into the

red rubber skin within less than 50 ms, the exact

time depending on the balloon material and the

degree of expansion of the rubber skin. Once an

initial hole is created, a fast rupture of the skin

occurs, which can be heard as a loud bang. During

this ‘explosion’, retardation manifests itself very

nicely.The individual images of figure 1 were

recorded at 1000 fps (frames per second) and an

integration time of 1/1000 s. At the centre of

the first image (0 ms), one readily observes two

large reflection spots from the white light sources

used for illumination as well as a smaller intense

reflection spot due to the green laser. This green

laser reflection gets dimmer as a hole starts to form

within the rubber skin.

Once the hole is created, a rupture develops

and propagates very fast. After 6 ms the ‘outer’

skin in the front nearest to the observer hasvanished and white light reflections can now be

seen nicely at the surface of the still stretched

‘inner’ skin, far away from the observer. Within

the next images, the reflection starts to become

fuzzy and it finally vanishes, when the skin is no

longer stretched. This behaviour can be explained

by retardation: the information that there is a

rupture in the skin can only propagate with a

maximum the speed of sound in the skin material

(some up-to-date research focuses on materials

where rupture cracks may propagate at higher

speeds). The information that the balloon has

already been destroyed has not yet arrived at theback part of the balloon, which is therefore still

stretched as if the balloon were intact.

For a semiquantitative analysis, one may

estimate the speed of sound in rubber, which

is given by v =

E ρ

, where E is Young’s

modulus and ρ is the density. Typical densities

of rubber range between 0.9 and 0.92 g cm−3,

however, in a balloon they will also depend on

the degree of inflation, since the skin gets thinner

upon stretching. Unfortunately, it is not easy

to get an accurate number for Young’s modulus.

It depends on temperature and more importantly

on the degree of vulcanization (the degree of interlacing of the chain molecules, induced by

sulfur). For example, E can reach values of the

order of 107–108 N m−2 for T = 20 ◦C and a

sulfur content of 20%. Therefore speeds of sound

in rubber would be expected to range between 100

and 330 m s−1. Larger degrees of vulcanization

can lead to even larger speeds of sound. Note that

although values are close to the speed of sound in

air, these are speeds in rubber!

From the images of figure 1, we experimen-

tally deduced that the rupture propagates across

about half of the circumference within 6 ms,

leading to a speed of sound of about 120 m s−1.Tests with other balloons and stronger inflation

could produce experimental maximum speeds of

rupture of about 300 m s−1. Sometimes, two

different speeds are observed, e.g. the rupture may

propagate at more than twice the speed in one

direction compared to the perpendicular one. This

was also observed in the beginning of the balloon

explosion of figure 1. The third image clearly

shows that the rupture initially propagated much

faster horizontally than vertically. Since this effect

depends on the type of balloon, it may be due to

anisotropies induced during manufacturing of therubber skin.

Karate demonstration: translation androtation of rods

A typical example of a hands-on experiment which

is performed very fast, such that details of the

physics behind it are sometimes difficult to grasp,

dates back to the 16th century and it has belonged

to the standard repertoire of hands-on experiments

since the 19th century. A wooden rod (which

may or may not have needles fixed to the ends) is

lying on two easily breakable objects, e.g. on twoglasses, on two raw eggs or hanging in two paper

loops, such that the ends of the stick are supported

(see figure 2, after [5]).

Hitting the rod in the middle very hard leads

to breaking of the rod. Subsequently, the two

half rods fall down without damaging the supports,

which is quite astonishing to any audience, in

particular if using, for example, raw eggs as

support. The outcome is often explained such

that after breaking, either part of the rod is only

supported on one side. Due to the pull of gravity it

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Figure 2. Historic illustration of the breaking stick experiment (after [5]).

starts to rotate around its centre of gravity, thereby

lifting it off the support. Since the movement is

very fast, one is not able to observe it with the

naked eye. However, using a high-speed camera

easily allows us to study the process in slow

motion (figure 3), revealing the physics behind it,

which needs further explanation [6].

The rod breaks completely within 2 ms.

The fast hit transfers momentum according to

mv = F t , which leads to a centre of mass

velocity of each half rod. In addition, the force

induces a change of angular momentum L due

to the induced torque according to L =

M t ,where L = J ω. With known moment of

inertia J of the rod, one finds that the velocities

of the ends of the half rods should be 4 vCM(downward) at the end where the hand had hit

and −2vCM (i.e. upward) at the end where the rod

was supported. In addition, the induced change

of angular momentum leads to a constant angular

velocity ω = dφ/dt , i.e. the angle of rotation φ of

each half rod should change linearly with time.

This theoretically expected behaviour was

analysed using the images from figure 3 (a video

of a karate hit on a rod breaking it into two

pieces is available at stacks.iop.org/physed/46/ 472/mmedia). They were recorded at 1000 fps

and 1/1000 s integration time. From the known

dimensions (length of rod: 80 cm, height of

glasses: 18.9 cm), one can estimate the hand

velocity while hitting to be around 11.8 ±

0.5 m s−1, which is also the downward velocity

of the half rods at this position right after the hit.

The upward velocities (mean value of both ends)

were found to be about 5.4 ± 0.5 m s−1, which

is reasonably close to the expected 5.9 m s−1.

Another way of testing the theory is to plot the

-1 2 6

10 18

Figure 3. Snapshots of a breaking wooden rod (numbers correspond to time in ms). φ denotes the angle of rotationof the pieces.




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a n g l e

o f r o t a t i o n i

n (

° )

Figure 4. Angle of rotation φ of the half rod afterbreaking of a long rod as a function of time (for

details, see the text).

200

160

120

80

40

0

0 10 20 30

time (ms)

40 50 60 70

angle of rotation of the half rod after the hit.

Figure 4 depicts the result for the first 70 ms,

during which one rod rotates by 180◦, i.e. half a

turn. As expected, the angular velocity is constant.

A hint for better performance is to make sure

that the rod is not (too) elastic; we usually use

some kind of laminated wood (wood pieces glued

together to form boards of about 15 mm thickness).

It must also be possible to break it with sudden

hits. First, test the breaking by hitting it with a

stable rod. The wood should not produce splinters

while breaking. For the in-class demonstration it

is more attractive to use the hand and show the

audience a ‘karate’ hit.

At first glance it may seem advantageous

to increase the initial velocity, e.g. by using a

stable rod to extend the length of the arm. This

can easily increase the velocity by a factor of

two. Unfortunately, the outcome also depends

on the stability of the rod. Figure 5 shows

what may happen if you hit too hard (video

of a karate hit on a rod breaking it into fourpieces, available at stacks.iop.org/physed/46/472/

mmedia); the excitation upon initial breaking

results in waves, which can lead to local stress in

adjacent regions and thus to fragmentation of the

rod into more than two pieces (compare the section

on spaghetti below). In this case, the motion of

the pieces is not very well defined. Uncontrolled

motion can lead to failure of this experiment if the

support is hit by part of the rod and falls to the

ground.

Deformation of bouncing balls

In sports and play, many students use balls and

the motivating physics of thrown, bouncing and

spinning balls has been extensively studied ex-

perimentally as well as theoretically (e.g. [7–11]).

However, even the bounce of balls falling from a

height of 1 m poses problems when using regular

video cameras. The problem becomes worse when

studying balls which are thrown by hand or hit by

a racket. The respective velocities are too large

and high speed imaging is needed for quantitative

analysis. Figure 6 depicts a series of snapshots,

recorded at 5000 fps and integration time of

(1/20 000) s (a video of a collision of a tennis ballwith the floor is available at stacks.iop.org/physed/

46/472/mmedia). An (old) tennis ball, previously

hit by a racket, is moving vertically towards the

surface of a table, where it bounces back. The

short integration times nicely allow us to record

sharp images of the ball. From the known diameter

of the ball, which serves as a length reference, and

the given time stamps in the images, velocities can

be calculated.

Figure 5. Snapshots of the (uncontrolled) breaking of a rod upon impact with a solid rod at velocity >20 m s−1.


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-3.4 0 1.6

4 10.8

Figure 6. A vertical tennis serve on a table. The ball (mass = 58.2 g) needs about 3 ms to travel the distance of its64 mm diameter in the downward movement 5.9 ms after the bounce. Total contact time with the table was 4 ms.The numbers give time in ms with regard to first contact.

In figure 6, the velocity before the bounce was

about 21.3 m s−1 corresponding to a kinetic energy

of 13.2 J. Tennis professionals reach about three

times this speed. After the bounce the velocity was

10.8 m s−1 and the kinetic energy was 3.4 J. The

missing 9.8 J were transferred to thermal energywhich leads to a warming up of the ball as well

as of the floor. The contact spot on the floor

easily shows temperature rises by several kelvin

for time scales of a minute or so (see [12, 13]).

The total contact time with the floor was 4 ms

with the time of maximum compression of the

ball taking place 1.6 ms after the start of contact.

Tennis balls are elastic, therefore the undisturbed

spherical shape (here diameter 64 mm) changes to

a deformed shape during contact with the floor.

At maximum compression, the horizontal size

increased to 72 mm while at the same time, the

vertical size from the floor to the top of ball was

only 41 mm.

A very similar experiment was also

recorded with the cheaper Casio EX F1 camera.

Figure 7 shows one snapshot (a video of the

collision of a tennis ball with the floor (Ca-

sio) is available at stacks.iop.org/physed/46/472/

mmedia). It demonstrates that in principle it is

easily possible to also record and analyse such

phenomena with the Casio camera. However, the

difference in image size is also apparent. As a

Figure 7. Tennis ball recorded with the Casio ExilimF1 camera at 1200 fps and 1/1250 s integration time attime of maximum compression.

consequence, the Casio only observes a vertical

distance from the top of the image to the table of

about 10 cm. For the 20 m s−1 speed, it takes

the ball about 4–5 images before it reaches the

surface. The contact takes another four images

and the rise maybe eight images; overall the event

can be observed on 16–20 images. If a total of

a few seconds is recorded, one needs to pick out

these few images from several thousand images,

which can be quite tedious. For the NAC recording

(about 120 images of the event for a total of 10 000

images) the event was easy to find due to manual

or automated triggering [2]. The Casio does not

allow external triggering. Therefore one should try

to make it easier to find events. For the tennis ball

we just put some small pieces of paper (confetti)

on the table. The bouncing of the ball leads to

air movements which lead to movement of some

of the paper pieces. Therefore, a quick scan of the




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Figure 10. Snapshots from bounce experiments with a basketball at points of maximum deformation. Left: if thrown hard, the ball (598.7 g) needs about 23.8 ms to travel the distance of its 239 mm diameter in the downwardmovement 34.2 ms after the bounce. Right: after falling from a height of 1.3 m.

Strange trajectories of superballs

The strange dynamics of superballs has been

studied for quite a while (e.g. [9–11, 15]). These

balls were invented in 1965 and are made from a

synthetic rubber polymer material. It is not only

their vertical bouncing with very high coefficients

of restitution but mostly the change of spin of the

balls upon each reflection that makes them unique.

Figure 11(a) illustrates this effect. A ball is thrown

at an angle onto the floor with very little or no

spin. It gains clockwise spin and enters a tablefrom below. Due to its spin, it bounces off in

a direction which does not follow at all the law

of reflection (similar to a billiard ball with spin).

Furthermore it reverses its spin direction. After it

hits the floor for the second time, it again travels

with very little spin in a direction which is nearly

parallel to the incident one. Therefore such a ball

can be regarded as performing a retroreflection.

High-speed imaging can nicely visualize the initial

gain of spin and its reversal. Figure 11 depicts

the trajectories and includes one snapshot with

the superimposed ball location as recorded (the

video of ‘Superball: collisions in a horizontal

channel’ is available at stacks.iop.org/physed/46/

472/mmedia).

In the experiment, two parallel plates (sur-

faces of tables) were at a distance of 32 cm. The

5 cm ball (mass 69.5 g) entered (pink circles) with

a speed of about 12.6m s−1 andlittle rotation (ω ≈

84 s−1 counterclockwise). After the first bounce

from the bottom plate (blue circles) the transla-

tional speed decreased to around 8 m s−1 whereas

at the same time the angular frequency drastically

increased to around 465 s−1 (clockwise). After the

second bounce from the top plate (green circles),

the speed further decreased to 6.2 m s−1 while the

angular frequency changed sign and decreased to

around 300 s−1 (counterclockwise). Finally, after

the third bounce from the bottom (red circles), the

translational speed increased to 6.9 m s−1 while

the angular frequency decreased to only 58 s−1

(counterclockwise). Average contact times with

the surfaces were around 2 ms each.

The process of how the rotation starts toincrease upon bouncing off from a surface

becomes clear in slow motion: at the beginning

of a bounce, only deformation occurs. Then

the ball starts to roll (not slide) on the surface

thus gaining spin before leaving. During each

bounce in figure 11, the ball lost at least 20%

of its initial kinetic energy, Still, the huge shift

from rotational to translational energy caused

an increase of translational speed after the third

bounce. For more details of the theoretical

treatment, see [9, 10, 15].

Obviously, retroreflection should not only

work for horizontal plane reflections, but for those

from vertical walls as well. Figure 12 depicts

two possible ball trajectories that superballs may

take when thrown hard at an angle into a vertical

channel made from two parallel tables. Obviously

it should be possible to throw a ball downward and

it will be reflected back upward and even exit the

channel after three of four bounces. Similar to

the case of horizontal surfaces, each bounce will

change translational speed as well as rotational

frequency.




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Figure 11. (a) Scheme for the reflections of a superball between two horizontal surfaces (after [10]).(b) The toy ball used in the experiments. Black lineswere painted on the surface to study rotations of the

ball during flight. (c) A snapshot image of the ball atfirst contact with the bottom plate at time 6 ms after

entering the scene. Various locations of the ball(numbers indicate time in ms) outlining thetrajectories are superimposed. Pink: before firstcollision; blue: between 1st and 2nd collision; green:between 2nd and 3rd collision; red: after 3rdcollision.

(a)

(b)

(c)

The result of an experiment with three

bounces is shown in figure 13 as one snapshot

(at 190 ms) with superimposed circles at the

Figure 12. Schematic trajectories of the super ballthrown into a vertical channel made, for example,from two tables. It should be possible for the ball tore-emerge from the channel after, for example, three

or four bounces within the channel.

Figure 13. Three-bounce trajectory of a superball

within two vertical walls (separation about 35 cm, balldiameter 5 cm). The ball entered at an angle of 28◦

with speed of 8.9 m s−1. The colour sequence is as infigure 11.

positions of the ball at times in ms, indicated by the

numbers (the video of ‘Superball: three collisions

in a vertical channel’ is available at stacks.iop.org/

physed/46/472/mmedia).

Initially the speed (pink) was v1 ≈ 8.9 m s−1

with little rotation (ω1 < 17 s−1). After the first

bounce (blue circles) the speed decreased to v2 ≈

7.1 m s−1

with increased angular frequency (ω2 ≈

200 s−1). Speed and angular frequencies after the

second and third bounce were v3 ≈ 5.4 m s−1,

ω3 ≈ 180 s−1 and v4 ≈ 4.9 m s

−1 with ω4 < ω1.

The three contact times with the walls amounted

to less than 1.75 ms each.

The outcome of this experiment does sensi-

tively depend on the initial velocity and the angle

of the throw. If the ball velocity is too small,

the pull of gravity will inevitably dominate and

the ball will never make it up again. In this case

it may have multiple bounces inside the channel




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Figure 14. Four-bounce trajectory of a superball withintwo vertical walls (separation about 35 cm, balldiameter 5 cm). The ball entered at an angle of 43 ◦ with14.6 m s−1. The colour sequence is as in figure 11.

which will lengthen the fall time. For sufficient

ball velocity the angle will decide how many

bounces are needed for the ball to exit the channel

again. Small angles like


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Figure 16. The fragments of broken spaghetti show transverse vibrations. The right fragment oscillates at afrequency of 250 Hz.

images are shown in figure 15, recorded at

4000 fps (integration time 1/4000 s). The

spaghetti did break into three parts. A hint of

the dynamics is depicted in figure 16 in three

snapshots, demonstrating the bending oscillation

of the large right fragment (a video of the breaking

of bent spaghetti into three pieces is available

at stacks.iop.org/physed/46/472/mmedia). Within

2 ms it completes half an oscillation, leading to

a frequency of the bending oscillation of about

250 Hz.

In order to find out whether the breaking

occurs simultaneously or one after the other,

experiments were also carried out at 10000

and 20 000 fps. Figure 17 shows an example

where spaghetti breaks into four parts (a video

of the breaking of bent spaghetti into four

pieces is available at stacks.iop.org/physed/46/

472/mmedia).

Very careful analysis, also at 20 000 fps

revealed that the breaking happens more at less

simultaneously within about 0.2 ms, however, the

limited spatial resolution did not allow any more

precise statements.

The quantitative explanation of why spaghetti

does not break into two halves was given in

2005 [16]. In simple terms, spaghetti—if strongly

bent—breaks as soon as a curvature limit (defined

by material constants) is reached. The sudden

relaxation of the new free ends leads to a burst of

flexural waves travelling along the spaghetti rods.

These flexural waves then locally increase the still

present curvature of the rod such that the stability

limit for curvature is exceeded. As a result, there


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Figure 17. Example of breaking spaghetti into four pieces.

Figure 18. Example of breaking spaghetti into two pieces with a karate hit of the finger.

are additional spots where the spaghetti breaks.

The time delay can be very small and in the

original work with a 1000 fps camera, the time

delay between the breaking events could not be

detected. For example, if the speed of sound of the waves in spaghetti were, say, 1000 m s−1, then

breaking in a distance of 1 cm could occur even

within 10−5 s.

However, it is also possible to successfully

break spaghetti into two pieces only, by doing a

karate-like experiment as with the wooden rods.

Figure 18 shows a few snapshots of a single

piece of spaghetti which is hit by the little finger

(diameter 15 mm, v ≈ 11 m s−1) (a video of karate

breaking spaghetti into two pieces is available at

stacks.iop.org/physed/46/472/mmedia). Breaking

occurs within 0.5 ms and within 0.25 ms, the end

of the spaghetti on the table lifts off. One can

also readily observe bending oscillations of the

fragments.

If, as in the case of the wooden rod, the

initial velocity is increased (here 14 m s−1) while

simultaneously decreasing the size of the hitting

object (top part of a screwdriver, lateral size

less than 3 mm), the spaghetti again breaks

into more parts (figure 19) (a video of karate

breaking spaghetti into four pieces is available

at stacks.iop.org/physed/46/472/mmedia). In this

case, the applied force is so strong, that a much

larger deformation happens in the middle. Since


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Figure 19. Example of breaking spaghetti into four pieces with a stronger karate hit by a smaller screwdriver.

the time for breaking (≈0.5 ms) is much smaller

than the time the spaghetti needs for bending due

to its elastic properties, the decision as to whether

there will be only two or more pieces depends on

the local curvature. This is much larger while

hitting faster with the much smaller tip of the

screwdriver (as can be seen comparing figures 18

and 19).

Outlook

The experiments discussed represent only a verysmall selection in the field of mechanics where

high-speed cameras can be used. Many more

examples were tested and some can be found as

videos on the internet. Potential and successfully

tested candidates in the field of mechanics of solids

include experiments with inertia, e.g. quickly

kicking out a coin from the middle of a tower

of dice without touching the dice and destroying

the tower, or the well-known magician’s trick of

removing a table cloth from a table with dishes

and glasses by very quickly pulling the table cloth.

It is also possible to directly demonstrate thedifference in free fall velocities of a metal sphere

compared to the top of a rod initially inclined

at an angle. One may study spinning tops and

also ‘tippe tops’ which turn upside down during

operation as well as the so-called rattlebacks

(also called Celtic stones or wobble stones) which

have a preferred direction for spinning. If spun

in the opposite direction, they become unstable,

rattle and reverse the spin. The bouncing ball

experiments can be pursued further by studying

bouncing of two or three balls on top of each

other. Also trajectories of spinning balls, e.g. of

table tennis balls, may be studied, demonstrating

the Magnus effect. It is also very entertaining to

record a ruler falling between two fingers. High-

speed images can distinguish the pure reaction

time from the finger closing time, the sum of

which is usually measured with this experiment

in the classroom. In ballistics, one can directly

study the speed of bullets, e.g. from air guns.

These bullets may later on be used for experiments

demonstrating the incompressibility of liquids by,for example, shooting into raw eggs in contrast to

empty egg shells. In acoustics, one may study

the vibrations of tuning forks or vibrating strings

from a guitar. We will present more examples from

other fields of physics soon.

Received 25 February 2011, in final form 17 March 2011

doi:10.1088/0031-9120/46/4/018

References

[1] Chiaverina Ch and Vollmer M 2006 Learning

physics from experiments Informal Learningand Public Understanding of Physics, Selected

Contributions of the Third Int. Girep Seminar

2005 ed G Planinsic and A Mohoric (Slovenia:University of Ljubljana)

[2] Vollmer M and Möllmann K-P 2011 Highspeed—slow motion: technology of modernhigh speed cameras Phys. Educ. 46 191–202

[3] Heck A and Uylings P 2010 In a hurry to work with high-speed video at school? Phys. Teach.48 176–81

[4] Aguirregabiria J M, Hernández A andRivas M 2007 Falling elastic bars and springs

Am. J. Phys. 75 583–7


http://dx.doi.org/10.1088/0031-9120/46/4/018http://dx.doi.org/10.1088/0031-9120/46/2/007http://dx.doi.org/10.1088/0031-9120/46/2/007http://dx.doi.org/10.1119/1.3317451http://dx.doi.org/10.1119/1.3317451http://dx.doi.org/10.1119/1.2733680http://dx.doi.org/10.1119/1.2733680http://dx.doi.org/10.1119/1.2733680http://dx.doi.org/10.1119/1.3317451http://dx.doi.org/10.1088/0031-9120/46/2/007http://dx.doi.org/10.1088/0031-9120/46/4/018


15/15


[5] Tissandier G 1880 Les R´ ecr´ eations Scientifiquesou l’ Enseignement par les jeux (Paris:Masson)

Tissandier G 1881 Popular Scientific Recreationsin Natural Philosophy (London: Ward Lock)

[6] Mamola K C and Pollock J T 1993 The breakingbroomstick demonstration Phys. Teach.31 230–3

[7] Brody H 1984 That’s how the ball bounces Phys.Teach. 22 494–7

[8] Brody H 1990 The tennis ball bounce test Phys.Teach. 28 407–9

[9] Cross R 2002 Grip-slip behavior of a bouncingball Am. J. Phys. 70 1093–02

[10] Hefner B T 2004 The kinematics of a superballbouncing between two vertical surfaces Am. J.Phys. 72 875–83

[11] Cross R 2010 Enhancing the bounce of a ballPhys. Teach. 48 450–2

[12] Möllmann K-P and Vollmer M 2007 Infraredthermal imaging as a tool in university physicseducation Eur. J. Phys. 28 S37–50

[13] Vollmer M and Möllmann K-P 2010 Infrared Thermal Imaging: Fundamentals, Research

and Applications (New York: Wiley)

[14] Brody H 1979 Physics of the tennis racket I Am. J. Phys. 47 482–7

Brody H 1981 Physics of the tennis racket II Am.

J. Phys. 49 816–9[15] Garwin R L 1969 Kinematics of an ultraelastic

rough ball Am. J. Phys. 37 88–92[16] Audoly B and Neukirch S 2005 Fragmentation of

rods by cascading cracks: why spaghetti doesnot break in half Phys. Rev. Lett. 95 095505

Michael Vollmer is a professor of experimental physics at the University of Applied Sciences in Brandenburg,Germany. His research interests includeatmospheric optics, spectroscopy,infrared thermal imaging and didactics of physics. He is also involved in in-serviceteacher training in Germany.

Klaus-Peter M öllmann is a professor of experimental physics at the University of Applied Sciences in Brandenburg,Germany. He works on MEMStechnology, infrared thermal imaging andspectroscopy. He is also involved inin-service teacher training in Germany.

http://dx.doi.org/10.1119/1.2343734http://dx.doi.org/10.1119/1.2343734http://dx.doi.org/10.1119/1.2341635http://dx.doi.org/10.1119/1.2341635http://dx.doi.org/10.1119/1.2343088http://dx.doi.org/10.1119/1.2343088http://dx.doi.org/10.1119/1.1507792http://dx.doi.org/10.1119/1.1507792http://dx.doi.org/10.1119/1.1701843http://dx.doi.org/10.1119/1.1701843http://dx.doi.org/10.1119/1.3488187http://dx.doi.org/10.1119/1.3488187http://dx.doi.org/10.1088/0143-0807/28/3/S04http://dx.doi.org/10.1088/0143-0807/28/3/S04http://dx.doi.org/10.1119/1.11787http://dx.doi.org/10.1119/1.11787http://dx.doi.org/10.1119/1.12399http://dx.doi.org/10.1119/1.12399http://dx.doi.org/10.1119/1.1975420http://dx.doi.org/10.1119/1.1975420http://dx.doi.org/10.1103/PhysRevLett.95.095505http://dx.doi.org/10.1103/PhysRevLett.95.095505http://dx.doi.org/10.1103/PhysRevLett.95.095505http://dx.doi.org/10.1119/1.1975420http://dx.doi.org/10.1119/1.12399http://dx.doi.org/10.1119/1.11787http://dx.doi.org/10.1088/0143-0807/28/3/S04http://dx.doi.org/10.1119/1.3488187http://dx.doi.org/10.1119/1.1701843http://dx.doi.org/10.1119/1.1507792http://dx.doi.org/10.1119/1.2343088http://dx.doi.org/10.1119/1.2341635http://dx.doi.org/10.1119/1.2343734

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