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a) f = mg sin theta - B^2 l^2/R sin^2 theta m d v/dt = mg sin theta - B^2 l^2v/R sin^2 theta 0.48 dv/dt = 4.8 sin angsph 2 - 2 times 2 times 0.375^2/52 sin^2 42v 0.48 dv/dt = 5.2 - 4.8 times 10^-3v 100 dv/dt = 32 times 10^3/48 -v 100 dv/666.67 v dt -100 ln 666-67v/666.67 - dt 666.67 (i.e^-t/100) = v b) equivalent fine constant = 100s^-1 \s\n c) for maximum speed dy/dt = 0 mg sin theta = B^2l^2 sin^2 theta/R U = mgr/B^2 l^2 sin theta V = 666.67 m/s d) force necessary to more vod with constant speed = B^2 l^2 sin^2 theta/R = 4 times theta .375)^2 times 666.67 times sin^2 4^2/5^2 = 8.61q e) electrical power dissipated = i^2R = (Blu sin theta)^2 R = 2152.6 j
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