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qz8sol_7193f10 - displacement of the ball is –h 2 The...

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TA: Tomoyuki Nakayama Monday, October 25, 2010 PHY 2048: Physic 1, Discussion Section7193 Quiz 8 (Homework Set #9) Name: UFID: Formula sheets are not allowed. Calculators are allowed. Do not store equations in your calculator. You need to show all of your work for full credit. ________________________________________________________________________________ In the figure below, a thin spherical shell is shot from point P . It rolls smoothly along a horizontal path, up along a ramp, and onto a plateau. Then it leaves the plateau horizontally to land on a game board, at horizontal distance d = 20.0 cm from the right edge of the plateau. The vertical heights are h 1 = 25.0 cm and h 2 = 10.0 cm. a) What is the velocity of the spherical shell at the edge of the plateau? When the shell hits the game board, the vertical
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Unformatted text preview: displacement of the ball is –h 2 . The flight time of the projectile motion is -h = -(1/2)gt 2 ⇒ t = √ (2h 2 /g) = 0.143 s During this time interval, the horizontal displacement is d. The velocity of the shell at the edge is d = v t v = d/t = 1.40 m/s b) With what speed is the spherical shell shot at point P ? While the shell rolls on the surface, the mechanical energy of the shell is conserved. For a smooth rolling, the velocity of the center of mass of a rolling object and its angular velocity are related as v = r ω . The speed ot the shell 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) = 2.21 m/s...
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