I am having a bit of trouble with some physics calculations here.
The experiment we did was rather simple, dropping rare earth magnets down tubes of different unknown metals and seeing how the eddy currents generated by the magnetic fields provided a force that opposed gravity decreasing the amount of time it took to fall through the tube.
Now I need to figure out the resistance of the metals to figure out what the metal is...and I got everything I need to match the resistivity to the metal, but I cannot find the resistivity of the metal itself. I mean I have some formulas but I am always missing something.
I have basically any raw data you can imagine, like the tube inner and outer diameters, the voltage generated in the metal as the magnet falls through it, the time it takes to fall.....but I am just having trouble getting the resistance of the metal....probably from my lack of sleep.
I will take any help I can get, and if it helps, here are some formulas that I have been working with
F=[(B^2)(l^2)v]/R, where B = magnetic field, l = circumference of tube, v = velocity of magnet, and R = resistance of pipe.
That will give the force created by the eddy current. Your regular downwards force is F = mgh, where M = Mass, G = Gravity (9.81) and h = height.
So F = [(B^2)(I^2)v]/R - (mgh).
So the smaller the Resistance, the faster the magnet will fall. The resistance will increase with the magnet's strength, so if you know the downwards force (Or re-arrange for Velocity), then put them in quickest to slowest and slot them into your magnet types.
If you have to be more specific, you say you have the emf (voltage) created in the pipe as the magnet falls. The resistance will then be R = V/I.
...I think. I've only done A level and most of this is guess work.
^ Slight correction to the above, gravitational force is just mg, no h.
I'm guessing you timed how long it took for the magnets to fall. If it took time 't' for the magnet to fall a known distance 'x' (you probably measured this or it was given), you can figure out the acceleration of the magnet:
x = (1/2)*a*t^2 --> a = 2x / (t^2)
Looking at the equation that Seth gave you, you know that the net force (left side of the equation) is equal to m*a, where m = mass of your magnet, so
' Wrote:'r' is the unit vector (Which only appears in the vector form of the equation). The 'scalar' form of the equation is: F = mg
This is the proper form of the gravitational force.
Note that bold items are actually vectors, carrying both magnitude and direction.
In this case we are talking about objects on earth. So |r| (scalar distance between the object and earth's center of mass), m1 (mass of earth) and G (Gravitational constant) can be lumped into a function of r. This function is the gravitational acceleration.
Approximate r to the radius or earth, and you'll find the acceleration due to gravity is about 9.81m/s. (Earth is a slightly squished sphere so latitude affects the gravitation acceleration, but that won't matter in introductory courses.)
So the force due to gravity on the surface of earth will be F= mg.
The gravitational potential energy is U=mgh, where h is height.
Anyway, sorry I can't help you kikatsu. I've always hated magnetism.