The figure below shows a bar of mass m = 0.300 kg that can slide without frictio

Question

The figure below shows a bar of mass m = 0.300 kg that can slide without friction on a pair of rails separated by a distance e = 1.20 m and located on an inclined plane that makes an angle theta = 35.0degree with respect to the ground. The resistance of the resistor is R = 1.80 Ohm and a uniform magnetic field of magnitude B = 0.500 T is directed downward, perpendicular to the ground, over the entire region through which the bar moves. With what constant speed v does the bar slide along the rails? Your response differs from the correct answer by more than 10%. Double check your calculations, m/s

Explanation / Answer

induced emf in the rod = B*v*L*sin(90-theta)

= B*v*L*cos(theta)

induced current, i = induced emf/R

= B*v*L*cos(theta)/R

magnetic force, FB = B*i*L*sin(90)

= B*i*L

when FB*cos(theta) = Fg*sin(theta), the rod moves with constant speed.

B*i*L*cos(theta) = m*g*sin(theta)

B*(B*v*L*cos(theta)/R)*L*cos(theta) = m*g*sin(theta)

v = m*g*sin(theta)*R/(B^2*L^2*cos^2(theta))

= 0.3*9.8*sin(35)*1.8/(0.5^2*1.2^2*cos^2(35))

= 12.6 m/s <<<<<<--------------Answer

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