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Homework Statement
(The picture is not from my textbook)
A Faraday Dynamo is used as a brake. The brushes are connected with an external resistance [itex]R_\Omega[/itex]. The circular disk has mass m, and angular velocity [itex]\omega_0[/itex] when t = 0.
a) How long does it take until the kinetic energy of the disk is halved?
Homework Equations
[itex]emf =\frac{B R^2 \omega}{2}[/itex]
[itex]dW=P dt[/itex]
[itex]P=\frac{(emf)^2}{R_\Omega}[/itex]
The Attempt at a Solution
I have no idea how to figure this problem out.
I've tried integrating dW from [itex]\frac{1}{2}m \omega^2_0 R^2[/itex] to [itex]\frac{1}{4}m \omega^2_0 R^2[/itex] setting that equal to the integral from t=0 to t of P dt (where I substitute P for the emf)
Looking at the answer, [itex]t=\frac{m R_\Omega ln(2)}{B^2 R^2}[/itex], I figured I need to integrate over [itex]\frac{1}{x}[/itex], in order to get the ln(2), but I've got no clue how to find that x. Any help much appriciated.