Review Conceptual Example 3 and the drawing as an aid in solving this problem. A

Question

Review Conceptual Example 3 and the drawing as an aid in solving this problem. A conducting rod slides down between two frictionless vertical copper tracks at a constant speed of 5.8 m/s perpendicular to a 0.67-T magnetic field. The resistance of the rod and tracks is negligible. The rod maintains electrical contact with the tracks at all times and has a length of 1.1 m. A 0.96- resistor is attached between the tops of the tracks. (a) What is the mass of the rod? (b) Find the change in the gravitational potential energy that occurs in a time of 0.21 s. (c) Find the electrical energy dissipated in the resistor in 0.21 s.

Explanation / Answer

induced emf e = lvB

induced current i = e/R = 1.1* 5.8*0.67/(0.96) = 4.45 A

F=mg = iLB

m = 4.45* 1.1*0.67/9.8 = 0.334 kgs

b. h = 0.5 gt^2 = 0.5*9.8*0.21^2 = 0.216 m

GPE = mgh = 0.334*9.8* 0.216 =0.7088 J

c. eletrical energy = i^2 Rt = 4.45^2 * 0.96 *0.21 = 4 J

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