This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: A hollow spherical ball of mass m and of radius r is rolling back and forth in the bottom of a bowl in the shape of a hemisphere of radius R . You can assume that r R . (a) Write an expression for the total energy E of the ball as function of , the distance of the ball from the bottom of the bowl as measured along the bowl, and v the speed of the ball. (b) What is an approximate expression for E when is very small? (c) By comparing with the total energy E for a mass on a spring, calculate the period of this motion. Check the units of your nal answer. Problem 9 1 By plugging into the diferential equation For a damped mass on a spring, m d 2 x dt 2 =kxb dx dt veriFy the solution: x ( t ) = A ebt/ 2 m cos( t + ) where = k/mb 2 / 4 m 2 . 2...
View
Full
Document
This note was uploaded on 08/04/2011 for the course PHYS 1112 taught by Professor Leclair,a during the Fall '07 term at Cornell University (Engineering School).
 Fall '07
 LECLAIR,A
 Mass

Click to edit the document details