Blog caffeinateddd

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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So as I was chugging along on the Rotational Motion WebAssign I was startled to notice a seemingly coincidental relationship between my givens and my answer. But after, procrastinating longer than is healthy, trying it with other numbers, the relationship was consistent.

This pertains to question 2 on the WebAssign. I found that, for a record on a turntable with an initial rpm that slows with a constant angular acceleration until rest in time t in minutes, the number of revolutions the record makes before stopping x = (rpm)(t)/2.

So if, when the turntable is shut off, the record is rotating at 100 rpm and comes to a stop in 24 seconds or 0.4 minutes, the record will make (100)(0.4)/2 = 20 revolutions before coming to rest. You can take a step further to find the angular displacement θ by multiplying by 2π . From this we get θ = (rpm)(t)(π)

I am wondering whether there is a clear derivation and reason for this. After linking it to θ, I think I know why it works and makes sense sorta. It's finding an average. Really it should be Δrpm. It's still a little fuzzy to me.

Can you clear it up?

http://www.youtube.com/watch?v=iUzr-4W3imw