Unformatted text preview: of the plateau? When the hollow ball hits the game board, the vertical displacement of the ball is –h 2 . The flight time of the hollow ball is -h = -(1/2)gt 2 ⇒ t = √ (2h 2 /g) = 0.0782 s During this time interval, the horizontal displacement is d. The velocity of the ball at the edge is d = v t v = d/t = 2.56 m/s b) What is the speed of the ball at point P? While the ball rolls on the surface, the mechanical energy of the ball is conserved. The ball rolls without slipping. Hence the velocity of the center of mass of the ball and its angular velocity are related as v = r ω . The speed ot the ball at point P is E i = E f (1/2)mv 2 + (1/2)I ω 2 = (1/2)mv 2 + (1/2)I ω 2 + mgh 1 (1/2)mv 2 + (1/2)(2/3)mr 2 (v/r) 2 = (1/2)mv 2 + (1/2)(2/3)mr 2 (v/r) 2 + mgh 1 v = √ (v 2 + 6gh 1 /5) = 2.67 m/s...
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- Spring '08
- Angular Momentum, Rigid Body, Physical quantities, ball, Tomoyuki Nakayama