2. ELASTIC SPACE Reporter: Domagoj Pluec IYPT 2013 TEAM OF
CROATIA
Slide 2
Problem The dynamics and apparent interactions of massive balls
rolling on a stretched horizontal membrane are often used to
illustrate gravitation. Investigate the system further. Is it
possible to define and measure the apparent gravitational constant
in such a world? 2 Elastic spaceCroatian teamDomagoj Pluscec
Slide 3
3
Slide 4
Summary Hypothesis Theory Fabric shape Test ball Keplers laws
Apparatus and methods Results Fabric shape Gravitational constant
Orbit Energy and angular momentum Conclusion 4 Elastic
spaceCroatian teamDomagoj Pluscec
Slide 5
Hypothesis It was assumed that the shape of the curve behaves
like a gravitational potential and that the form should be
inversely proportional to z 5 Elastic spaceCroatian teamDomagoj
Pluscec
Slide 6
Fabric shape and force on the ball G N -deformation depends on:
1.The coefficient of elasticity 2.The mass of the ball 3.The
position of the ball on the fabric Shape cant be calculated
analyticaly because of big deformations it was determined
experimentaly 6 Elastic spaceCroatian teamDomagoj Pluscec
Slide 7
Test ball circular orbit z() z N FiFi G Elastic
membraneUniverse Force Speed Test ball small mass negligibile
deformation 7 Elastic spaceCroatian teamDomagoj Pluscec Looking
from balls inertial system:
Slide 8
Test ball energy 8 Elastic spaceCroatian teamDomagoj Pluscec
Approximation friction is constant Friction that does work on the
ball is occuring when ball deformates the fabric when traveling on
it (assumption is relatively small) Kinetic energy: Potential
energy:
Slide 9
Test ball angular momentum Elastic spaceCroatian teamDomagoj
Pluscec z L angular momentum angular velocity
Apparatus Balls that we used 11 Elastic spaceCroatian
teamDomagoj Pluscec
Slide 12
Method fabric shape 1)Massive ball was placed in the middle of
the wheel 2)Camera was perpendicular to the lowest point of elastic
membrane 3)Coordinates of the fabric ends were determined by
computer program ImageJ 12 Elastic spaceCroatian teamDomagoj
Pluscec
Slide 13
Example of shapes photography 13 Elastic spaceCroatian
teamDomagoj Pluscec
Slide 14
Method motion of the balls 14 Elastic spaceCroatian teamDomagoj
Pluscec Massive ball center of the wheel Small ball ejected from
the channel with initial speed Camera was perpendicular to the
plane of the wheel Coordinates of the balls were obtained by video
analysis (120-240)fps
Slide 15
Fabric shape Ball: m 1 =109g; r 1 =1.5 cm 15 Elastic
spaceCroatian teamDomagoj Pluscec
22 Elastic spaceCroatian teamDomagoj Pluscec Ball distance from
center vs time
Slide 23
Second Keplers law 23 Elastic spaceCroatian teamDomagoj Pluscec
dA
Slide 24
Energy 24 Elastic spaceCroatian teamDomagoj Pluscec E(t)
numerically calculated from a video
Slide 25
Angular momentum Elastic spaceCroatian teamDomagoj Pluscec 25
L(t) numerically calculated from video
Slide 26
Conclusion We have determined the potential of the system by
experimentaly determing shape of our membrane Potential in our
system isnt proportional to Keplers potential We have calculated
constant of our system which is not analogous to the gravitational
constant because we couldnt determine dependence of deformation to
the mass We have a non-central force (friction) in system Second
Keplers law isnt valid in our case 26 Elastic spaceCroatian
teamDomagoj Pluscec
Slide 27
Conclusion comparison between universe and elastic membrane
UniverseElastic membrane Potential Force Circular orbit speed
Period of an orbit Angular momentum Energy Elastic spaceCroatian
teamDomagoj Pluscec
Slide 28
THANK YOU IYPT 2013 TEAM OF CROATIA
Slide 29
Period of an orbit Elastic space Croatia team Domagoj
Pluscec