The figure below shows a bar of mass m = 0.275 kg that can slide without frictio

Question

The figure below shows a bar of mass m = 0.275 kg that can slide without friction on a pair of rails separated by a distance f 1 20 m and located on an incined plane that makes an ngle 31.0° with respect to the ground. The resistance of the resistor is R·2.70 n, and a uniform magnetic field of magnitude B 0.500 T is directed downward pen endalar 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 10.43

Explanation / Answer

since its a constant speed Fg = Fb
gravitational force equals magnetic force

Fg = mg sin31

EMF = d/dt = d/dt (Blx*cos31) = B cos31* lv
I = Blv cos31/R

Fb = BIL cos315 = B^2*l^2*v*(cos31)^2/R
Fb = Fg

B^2 l^2 v cos31/R = mg sin31
v = (R mg sin31)/(B^2*l^2*(cos31)^2)
v = (2.7*0.275*9.8 * sin31)/(0.25*1.44*(cos31)^2) = 14.2 m/s

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