ProblemSet 3: Problem 5.Problem:A single piece of cord of lengthfpasses through a ring connected to a sphere of massm.The sphere rotates at constant speed,v, in a horizontal circular path. Noting that the tension in the cordis the same in both portions of the cord, findvas a function off,θ,φand gravitational acceleration,g.Solution:The total length of the chord,f, is the sum of the two segments, and is thus related to the radiusof the circle,ρ,byf=ρsinφ+ρsinθ=⇒fsinθsinφ=ρ(sinθ+sinφ)=⇒ρ=fsinθsinφsinθφNow, summing forces in the vertical direction, the vertical components of the two tension forces balancethe weight of the sphere, so that3F
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