Solve Physics Essay on Wave Power Plants with IB Course

[Techlogic]

Hello PF, I'm new here but I found you while googling around :> The forum seems great and has large activity, the only thing I miss is a chat function :p Anyways, I came here for some help regarding my physics essay, I'm in my second IB year (if you're familiar with this course) and need some help with the extended essay.This question is about wave power plants

Homework Statement

You have a coil of N turns spinning with the function x(t)=A cos⁡〖2π/T t〗
Where A = 0,01 and T = (2π×0,01)/(-2π/6 1,6 sin⁡〖2π/6〗 t)
yes, the period is messy :d If you question it, I retrieved it from this information:

Spoiler

The waves will travels with the water as their medium, and there will be a deformation in pressure which will cause the buoy to oscillate.
The waves in the water depend on the geographical position and the weather conditions, and therefore the idea will be tested on waves with different properties, and then compared to each other. This will be done in order to investigate how the electricity conducted will change as the waves change, as well as for which waves the idea will be optimal.
For the first case waves found on the west coast of Sweden will be used. These waves have an average wave height of 1,6m and an average period of 6,0 seconds, and we can define our phase shift to be 0. which gives them the function:
X(t)=1,6 cos⁡〖2π/6〗 t
Or, for velocity of the wave:
V(t)=-2π/6 1,6 sin⁡〖2π/6〗 t
We know that the wave will move between +A and –A, which gives us ∆A=3,2m and it will make this change in half a period, 3 seconds. The generator will then spin with a function of ∆A/r 〖δt〗^(-1), where r is the radius of the axis. Since we want the generator to spin as fast as possible, and it will spin faster as r approaches 0, we want r to be as small as possible. However, there will be a limit where the friction won’t be enough to make the generator rotate, therefore a value of r will be chosen where there’s enough friction for the generator to rotate, and r is small enough to cause a high revelations per second. The value chosen for r is 1cm, which will be enough for the generator to spin as well as small enough for the speed to be high.
The function showing the displacement of the generator is
X(t)=A cos⁡〖2π/T t〗

Homework Equations

Flux=BAcos(θ)
ℇ=-N dflux/dt
Lenz' law

The Attempt at a Solution

BAcos(90cos 2π/(2πx0,01/(2π/6 1,6sin 2π/6 t)))=flux

I use values 0,34T for B and 0,1m for A

flux =0,034cos(90cos 2π/(2πx0,01/(2π/6 1,6sin 2π/6 t)))

Problem is, I don't know how to use this information in order to find the relevant information about the current. My guess is that i should take the function for flux and shift it upwards with the amplitude and integrate it. And from there find the maximum emf and the "average" emf (squareroot(y(x)^2). But that'll give a DC current, which I don't have. So i should not shift it upwards and instead just integrate the function as it is? I'm lost :(

P.S Linus, if you got an account here, and I bet you do, It's on its way :d

 

[member 553083]

The main equation you need to consider here is Lenz's law, which states that the induced emf (electromotive force) in a coil is equal to the negative of the rate of change of magnetic flux. The magnetic flux is given by the equation: Flux = BAcos(θ)Where B is the magnetic field strength and θ is the angle between the field and the coil. Using the information you have provided, you can calculate the flux at any given time t. Once you have the flux, you can then use Lenz's law to calculate the induced emf. The equation for the induced emf is: ℇ = -N dflux/dtWhere N is the number of turns in the coil and dflux/dt is the rate of change of magnetic flux.Once you have calculated the induced emf, you can then use this to calculate the current in the coil. This is done by rearranging the equation ℇ = IZ (where I is the current and Z is the impedance of the coil).I hope this helps. Good luck with your essay!