PS3-5 - Problem Set 3: Problem 5. Problem: A single piece...

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Problem Set 3: Problem 5. Problem: A single piece of cord of length f passes through a ring connected to a sphere of mass m . The sphere rotates at constant speed, v , in a horizontal circular path. Noting that the tension in the cord is the same in both portions of the cord, find v as a function of f , θ , φ and gravitational acceleration, g . Solution: The total length of the chord, f , is the sum of the two segments, and is thus related to the radius of the circle, ρ ,by f = ρ sin φ + ρ sin θ = f sin θ sin φ = ρ (sin θ +sin φ )= ρ = f sin θ sin φ sin θ φ Now, summing forces in the vertical direction, the vertical components of the two tension forces balance the weight of the sphere, so that 3 F
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