A conducting rod (of mass m = 0.4 kg and length l =15 m)) slides down two conduc

Question

A conducting rod (of mass m = 0.4 kg and length l =15 m)) slides down two conducting rails, starting from rest at t = 0. The rails are connected by a resistor R = 2.0 ? so that a complete circuit is made (ignore any other resistances in the circuit, and don't worry about friction). There's a uniform vertical magnetic field B = 1.2 T, and the whole contraption is sitting at an angle ? from horizontal. The poorly-scanned figure below shows how it's set up.

Find the emf induced in the rod as a function of its velocity down the rails.

Write Newton's law of motion for the rod; show that the rod will approach a terminal velocity, and figure out what that speed is.

Explanation / Answer

m*g = 50 * 9.8 = 490 N. = Wt. of crate = Normal force (Fn). a. Fs = u*Fn + u*F*sin30 Fs = 0.75*490 + 0.375F = 367.5 + 0.375F F*cosA-Fs = m*a F*cos30-(367.5+0.375F) = m*0 = 0 0.866F-367.5-0.375F = 0 0.866F-0.375F = 367.5 0.491F = 367.5 F = 748.5 N b. Fs = 0.75*490 - 0.75*F*...

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