Statics and Dynamics Quiz
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DYNAMICS
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A smooth bead of mass mm is threaded on a frictionless vertical circular loop of radius RR. The bead starts from rest at the bottom of the loop. A compressed spring at the bottom of the loop (oriented tangentially) gives the bead an initial kinetic energy E0E_0 by releasing its stored energy entirely into the bead before the bead leaves the spring.
What is the minimum value of E0E_0 required for the bead to maintain contact with the loop at the very top? Note that for a bead on a wire (as opposed to a ball on a track), the wire can exert both inward and outward normal forces on the bead.
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