Constructing and Studying a Levitating Frictionless Bearing Ruth Toner Senior Project Speech

Superconductors: The Basics -First discovered 1911 by Heike Kamerlingh Onnes. -Above critical temperature, superconductor behaves like normal material, with high resistivity - Below T c, has zero resistance - If current is established in loop of superconducting material, will continue indefinitely. - Other conditions: superconductor only works when current density and magnetic field are below critical values Jc and Hc. Background:

Type I Superconductors -- The Meissner Effect -Zero resistivity of superconductor means that material can act as “perfect dimagnet” -When superconductor is exposed to magnetic flux, field induces current on surface -Induced current creates opposing magnetic field which leads to force of repulsion between magnet and superconductor -In case of Type I superconductor, magnetic field is completely expelled from superconductor - force strong enough to cause levitation

Type II Superconductors – Flux Pinning - Type II Superconductor: contains small impurities which allows some magnetic flux to pass through filaments in the material -flux lines become “pinned” in place: any attempt to move the superconductor up or down will create a restoring force -combination of Meissner Effect repulsive force and flux pinning restorative force causes levitation -Advantages: -Higher critical temperatures - horizontal position of superconductor also fixed

Materials YBCO Superconductor: Critical Temperature 90°K (-183°C) NdFeB magnet: Surface strength = 1.6 Tesla (32000x the earth’s magnetic field

Creating the Mount [CAD drawing] Materials – base: aluminum handle: G10 AutoCAD Drawing:

A Levitating Frictionless Bearing: Photos Before: The magnet rests on supports on top of the superconductor, not levitating. During cooling: The mount is lowered into liquid nitrogen and allowed to cool to 77°K, under YBCO’s critical temperature. The YBCO becomes superconductive.

A Levitating Frictionless Bearing: Photos The mount is removed from the liquid nitrogen, and the supports are knocked out. The magnet floats in midair, and can only be moved by applying strong pressure.

Studying the Bearing – Part #1: Finding the Spring Constant and Resonant Frequency -The restoring force F applied by objects like the bearing can be described by Hooke’s law: F=-kx, where k is some constant -The frequency of vibration f is described by -Increments of weight were placed on the magnet at three different initial heights, and the resulting displacement was measured; these data points were graphed, and the regression line slope was used to calculate constant k, and then frequency f: At 4 mm: k= f=16.88 s -1 At 9 mm: k= f=13.22 s -1 At 16 mm: k=.8057 f=11.44 s -1

Studying the Bearing – Part #2: Finding the Spin Down Time Constant - Because the bearing doesn’t make surface contact with anything, it is presumed nearly frictionless -Some drag forces do exist, however (e.g., air drag), so that the rotational frequency f behaves according to, where τ is the time constant for rotational decay, the time it takes for f to decrease by 63%. -The time constant was calculated by monitoring the number of rotations in a 10 second period every minute; a regression time was plotted to achieve a value for τ. This was tested at four separate heights. Example: rotational frequency decay at mm Initial elevation (mm) Time constant (seconds)