IYPT 2010 Austria, I. R. Iran Reporter: Reza M. Namin 1

IYPT 2010 Austria, I. R. Iran The problem A helical spring is rotated about one of its ends around a vertical axis. Investigate the expansion of the spring with and without an additional mass attached to it’s free end. 2

IYPT 2010 Austria, I. R. Iran Main approach Theory –Background –Theory base –Developing the equations –Numerical solution Experiment –Setup –Parameters, results and comparison Conclusion 3

IYPT 2010 Austria, I. R. Iran Theory - Background Act of a spring due to tensile force: –Hook's law: F = k ∆L F: Force parallel to the spring k: Spring constant ∆L: Change of length –A spring divided to n parts: F = n k ∆L μ = k L remains constant Circular motion –a = r ω 2 a: Acceleration r: Distance from the rotating axis ω: Angular velocity 4

IYPT 2010 Austria, I. R. Iran Theory - Base Effective parameters: –ω: Angular velocity –λ : Spring liner density = m / l –M: Additional mass –μ : Spring module = k l –l, l 1, l 2 : Spring geometrical properties 5 M l1l1 l l2l2

IYPT 2010 Austria, I. R. Iran Theory - Base Looking for the stable condition in the rotating coordinate system –Accelerated system → figurative force Acting forces: –Gravity –Spring tensile force –Centrifugal force 6

IYPT 2010 Austria, I. R. Iran Theory – Developing the equations Approximation in mass attached conditions: –Considering the spring to be weightless: 7 l M ω x y FsFs FcFc Mg

IYPT 2010 Austria, I. R. Iran Theory – Developing the equations Exact theoretical description: –Problem: The tension is not even all over the spring… –Solution: Considering the spring to be consisted of several small springs. 8 M

IYPT 2010 Austria, I. R. Iran Theory – Numerical solution Numerical method –Finite-volume approximation: Converting the continuous medium into a discrete medium –Transient (dynamic unsteady) method –Programming developed with QB. 9 M w T i-1 T i+1 fcfc

IYPT 2010 Austria, I. R. Iran Theory – Numerical solution Mesh independency check 10 n: Number of mesh points As n increases, the result will approach to the correct answer

IYPT 2010 Austria, I. R. Iran Theory – Numerical solution Tension in different points of the spring with different additional mass amounts: 11

IYPT 2010 Austria, I. R. Iran Experiment Finding spring properties –Direct measurement: Mass & lengths –Suspending weights with the spring to measure k and μ Changing the angular velocity, measuring the expansion –Change of the angular velocity with different voltages –Measuring the angular velocity with Tachometer –Measuring the length of the rotating spring using a high exposure time photo 12

IYPT 2010 Austria, I. R. Iran Experiment setup The motor, connection to the spring and the sensor sticker 13

IYPT 2010 Austria, I. R. Iran Experiment setup The rotating spring and tachometer 14

IYPT 2010 Austria, I. R. Iran Experiment setup Hold and base 15

IYPT 2010 Austria, I. R. Iran Experiment setup All we had on the table 16

IYPT 2010 Austria, I. R. Iran Experiments Suspending weights with the spring Finding k and using that to find μ 17 →K = N/m →μ = K l = N

IYPT 2010 Austria, I. R. Iran Experiments Expansion increases with increasing angular velocity 18

IYPT 2010 Austria, I. R. Iran Experiments Measurement of length in different angular velocities Comparison with the numerical theory 19

IYPT 2010 Austria, I. R. Iran Experiments Comparing the shape of the rotating spring in theory and experiment 20 λ =0.103 kg/m μ =0.369 N l = 16.3 cm l 1 =1 cm ω = 120 RPM

IYPT 2010 Austria, I. R. Iran Experiments Investigation of the l-ω plot within different initial lengths 21

IYPT 2010 Austria, I. R. Iran Experiments Comparison between the physical experiments, numerical results and theoretical approximation within different additional masses 22

IYPT 2010 Austria, I. R. Iran Conclusion According to the comparison between the theories and experiments we can conclude: –In case of weightless spring approximation: 23

IYPT 2010 Austria, I. R. Iran Conclusion In general, the numerical method may be used to achieve precise description and evaluation. Some of the results of the numerical method are as follows: 24

IYPT 2010 Austria, I. R. Iran Conclusion Numerical solution results Change of the spring hardness 25

IYPT 2010 Austria, I. R. Iran Conclusion Numerical solution results Change of spring density μ =0.3 N l = 10 cm l 1 =1 cm μ =0.3 N l = 10 cm l 1 =1 cm

IYPT 2010 Austria, I. R. Iran Conclusion Numerical solution result Change of initial length λ =0.2 kg/m μ =0.3 N l 1 =1 cm λ =0.2 kg/m μ =0.3 N l 1 =1 cm

IYPT 2010 Austria, I. R. Iran Conclusion Numerical solution results Change in additional mass

IYPT 2010 Austria, I. R. IranIYPT 2010 Austria, National team of I. R. Iran