Conical Pendulum Speed · PhysicsBowl 2024 #37

Physics · mechanics

Problem

A small sphere of mass m is attached to one end of a light string of length L with the other end of the string attached to a fixed point. The ball is moving at a constant speed v in a horizontal circle of radius r such that the string makes an angle θ with the vertical. Given that the tension in the string is T, what is the correct expression for the object's speed v? a. v=TLsin⁡θmv = \sqrt{\frac{TL\sin\theta}{m}} b. v=gsin⁡θLv = \sqrt{\frac{g\sin\theta}{L}} c. v=TLmgv = \sqrt{\frac{TL}{mg}} d. v=mgTLv = \sqrt{\frac{mg}{TL}} e. v=2TLmgv = \sqrt{\frac{2TL}{mg}}

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