problem10_p100

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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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 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
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Ask a homework question - tutors are online