University Physics with Modern Physics with Mastering Physics (11th Edition)

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10.100: a) The distance from the center of the ball to the midpoint of the line joining the points where the ball is in contact with the rails is ( 29 , 2 2 2 d R - . 4 so 2 2 cm d R ω v - = when , 0 = d this reduces to , R v cm ϖ = the same as rolling on a flat surface. When , 2 R d = the rolling radius approaches zero, and . any for 0 ϖ cm v b) 2 2 2 1 2 1 ϖ + = I mv K c) ( 29 ( 29 ( 29 . 4 1 2 5 10 4 5 2 2 1 2 2 2 cm 2 2 2 cm 2 2 cm - + = - + = R d mv d R v mR mv Setting this equal to mgh and solving for cm v gives the desired result. c) The denominator in the square root in the expression for
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Unformatted text preview: cm v is larger than for the case cm so , v d = is smaller. For a given speed, than the large is = d case, so a larger fraction of the kinetic energy is rotational, and the translational kinetic energy, and hence cm v , is smaller. d) Setting the expression in part (b) equal to 0.95 of that of the = d case and solving for the ratio 1.05. gives = R d R d Setting the ratio equal to 0.995 gives . 37 . = R d...
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