8.47, 8.51, 8.62, 8.70

# 8.47, 8.51, 8.62, 8.70 - PHYS2626 Introductory Classical...

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PHYS2626 Introductory Classical Mechanics Suggested Solutions for Assignment 3 November 2008 1. Problem 8.51 Let f be the friction between the plank and the coin, A and a be the accelerations of the plank and coin respectively, and α be the angular acceleration of the coin. F - f = MA, (1) f = Ma, (2) fR = 1 2 MR 2 α = 1 2 MR ( A - a ) f = 1 2 M ( A - a ) . (3) F = M ( A + a ) . (4) 1 2 M ( A - a ) = Ma = A = 3 a. (5) Hence, a = F 4 M , (6) A = 3 F 4 M . (7) Let t be the time for the coin to reach the left end of the plank. 1 2 ( A - a ) t 2 = L 1 2 (2 a ) t 2 = L 1 2 at 2 = L 2 . (8) Therefore the distance traveled by the coin is L/ 2. 1

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2. Problem 8.47 We have assumed that T sin θ < mg , so that the spool stays on the ground. Let F be the friction on the ground and a be the acceleration of the spool. T cos θ - F = ma, (9) FR - Tr = I a R . (10) Then ( T cos θ - ma ) R - Tr = I a R T ( R cos θ - r ) R = ( I + mR 2 ) a a = TR ( R cos θ - r ) I + mR 2 . (11) cos
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8.47, 8.51, 8.62, 8.70 - PHYS2626 Introductory Classical...

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