Application of Oskillation
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Trying to think of a new topic about which to blog I somehow remembered seeing this video and thought it only appropriate after finishing the unit on oskillaiton. Inspired by the Tacoma Bridge collapse (1st video) Shawn Frayne designed a small wind generator that uses an oskillating tensioned belt to generate energy from the wind (2nd video).
http://www.youtube.com/watch?v=IqK2r5bPFTM&feature=related
http://www.youtube.com/watch?v=IqK2r5bPFTM&feature=related
http://www.popularmechanics.com/science/energy/solar-wind/4224763
In 10mph of wind the design produced an output of about 40 milliwatts (true facts) and assuming the system is perfectly efficient, has an amplitude of about 2.5cm, and a belt with mass 4g (these are just assumptions) we may be able to find the frequency of the oskillating belt.
Let's gather some formulas:
We have power and P = W/t
W = ΔKE
When the belt passes through equilibrium Etotal = KE = (1/2)mv^2.
vmax (which occurs at equilibrium) = Aω
ω = 1/T
T = second/cycle
Now if we put them together, focusing on the time t it takes the belt to travel from the amplitude to equilibrium (T/4) we can say that:
P = [(1/2)m(Aω)^2 - 0] / (T/4)
P = 2m(A^2)(1/T)^3
T^3 = (2mA^2)/P
T^3 = 2(0.004kg)(0.025m)^2/(0.040W)
T^3 = 0.000125s^3 (It's always a good sign when your units work)
T = 0.05s
Furthermore, with f = 2π/T we get a frequency of about 126 Hz.
Considering that much of the energy of the belt is lost we can assume that to produce the same milliwatts it oskillates much faster meaning a smaller period and a faster frequency.
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