A child is sitting on a swing in a modern fun park that is operated electronically. As shown in the figure below, the swing seat hangs off the support at points $\mathrm{A}$ and $\mathrm{B}$, and is immersed in a uniform magnetic field of $0.50 \mathrm{~T}$ directed up the page. To start the swing moving, a current is passed into the swing in the direction of AXYB.
(a) Which part(s) is/are responsible for the swing moving-AX, $\mathrm{XY}$, or $\mathrm{BY}-$ justify your answer.
(b) In which direction will the swing move initially?
(c) Calculate the magnetic force that is developed to move the swing, if side (the seat) $\mathrm{XY}$ is $4.0 \mathrm{~m}$ long and the current passing through it is $50 \mathrm{~A}$.
Extension
(d) If sides $A X$ and $B Y$ have a negligible mass, and side $X Y$ plus the child weighs $45 \mathrm{~kg}$ altogether, calculate the angle the swing will move through initially. The magnetic field is then turned off to allow the swing to pursue a simple pendulum motion.
(e) If the sides $\mathrm{AX}$ and $\mathrm{BY}$ are $3 \mathrm{~m}$ long, how many cycles will the swing make in a 1 minute interval? (Assume there is no friction.)