Consider a circular-motion problem in which tension not only must provide the proper radial acceleration but also must balance gravity. As we shall see, it can do both. A tetherball is attached to a swivel in the ceiling by a light cord of length L, as measured from the ceiling to the center of the tetherball. When the ball is hit by a paddle, it swings in a horizontal circle with constant speed vv, and the cord makes a constant angle β with the vertical direction. The ball goes through one revolution in time T. Assuming that T, mass mm, and length L of the rope are known, derive algebraic expressions for the tension FT in the cord and the angle β. a)What is the period T of the ball’s motion if L=2.0m and the cord makes an angle of β=40∘with the vertical?
Consider a circular-motion problem in which tension not only must provide the proper radial acceleration but also must balance gravity. As we shall see, it can do both. A tetherball is attached to a swivel in the ceiling by a light cord of length L, as measured from the ceiling to the center of the tetherball. When the ball is hit by a paddle, it swings in a horizontal circle with constant speed vv, and the cord makes a constant angle β with the vertical direction. The ball goes through one revolution in time T. Assuming that T, mass mm, and length L of the rope are known, derive algebraic expressions for the tension FT in the cord and the angle β.
a)What is the period T of the ball’s motion if L=2.0m and the cord makes an angle of β=40∘with the vertical?
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