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 ? = 1.20 m and located on an inclined plane that makes an angle ? = 33.0

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 ? = 1.20 m and located on an inclined plane that makes an angle ? = 33.0A degree with respect to the ground. The resistance of the resistor is R = 3.30 ? 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? m/s

Explanation / Answer

Here , let the bar slides with a speed v m/s

then induced EMF = B*v*l*sin(90-theta)

and induced curent = BVL*cos(theta)/R

now, magnetic force acting is Fm =BIL

Fm = (BVL*cos(theta)/R)*BL

Fm = B^2*v*L^2*cos(theta)/R

now, for constant velocity

Fm*cos(theta) = mg* sin(theta)

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

0.5^2 * v * 1.2^2 * (cos(33))^2/3.3 = 0.3 * 9.8 *sin(33)

v = 20.9 m/s

the constant speed of bar is 20.9 m/s

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