Question

working with answers will be great

3. (60pts) A rectangular, conducting, wire loop of sides L and W, total mass m, and total resistance R initially lies in the horizontal ry-plane, with corners at (x, y, z) = (0,0,0), (0,W.0), (L,0,0), and (L, W.0). There is a uniform, upward magnetic field B = Bk in the space within and around the loop. The side of the loop that extends from (0,0,0) to (L,0,0) is held in place on the x-axis; the rest of the loop is free to pivot around this axis. When the loop is released, it begins to rotate due to the gravitational torque. Use the CLOCKWISE direction as positive. Assume that L = 2W, and take the moment of inertia of this rectangular wire around the x-axis to be l = mW (a) Find the net torque (magnitude and direction), symbolically, that acts on the loop when it has rotated through an angle o from its original orientation and is rotating downward at an angular speed w= do (b) Find the angular acceleration as of the loop at the instant described in part (a). do i. First find a algebraically (symbolically) ii. Numerically, assume that at t = 0, the wire starts from rest, meaning angle o = 0 and w=0, calculate o in rad/s? iii. At the instant t = 0.01 s, calculate first w in rad/s and then o in rad using the uniform acceleration kinematic equations w = at two and o = at +wot+ 0 using the values of a, wo and do those found from previous step. Based on these new values of o and w, recalculate the new value of a iv. Repeat the previous step for t = 0.02 s using the values of from step iii for o and w as the new values for oo and wo. Do NOT forget to recalculate the new a v. repeat this process by increasing time by 0.01 s cach time until 25 We need to retain all data so that o eo . Plot the function o = o(t). Using MS Excel, or similar, find the Trendline using a Polynomial function for (0) = 0o+at+ a2t2 + a3. Up to 3 sig figs, what are ao, Q1, a2 and az? (c) Compared to the case with zero magnetic field, does it take the loop a longer or shorter time to rotate through 90°? Using the previous analysis either symbolically or numerically, explain your answer. (d) Is mechanical energy conserved as the loop rotates downward? Explain.