Question #43284

A uniform rigid rod of mass $M = 0.6 \text{ kg}$ and length $L = 1.0 \text{ m}$ is freely pivoted at its upper end. A small soft iron core of mass $m = 0.2 \text{ kg}$ and volume $V = 5 \times 10^{-4} \text{ m}^3$ is attached to the lower end. The pendulum is released from rest in the horizontal position ($\theta = 90^\circ$). At the lowest point of its swing, the iron core passes through a narrow region of localized magnetic field. During this brief passage, the external magnetic field exerts a total retarding angular impulse of $J = 0.4 \text{ kg m}^2/\text{s}$ on the pendulum about the pivot. The soft iron core undergoes exactly one complete hysteresis cycle during the passage. The area of the hysteresis loop for the soft iron material is $A_h = 2000 \text{ J/m}^3$. Assuming the rod is non-magnetic and non-conducting, what is the energy dissipated as heat due to eddy currents in the iron core? (Take $g = 10 \text{ m/s}^2$)