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Analytical Mech Homework Solutions 50

# Analytical Mech Homework Solutions 50 - h b h mv 2 mg mg R...

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cos h b θ = ( ) ( ) 2 2 3 h mv mg mg R mg h b h h b b b b b = = = the particle leaves the side of the sphere when 0 R = 3 3 b h = , i.e., b above the central plane 4.22 2 1 0 2 mv mgh + = h b = − 2 at the bottom of the loop, so 2 1 mv mgb = v = 18 , 2 g + b 2 r mv F mg R b = − = 2 2 3 mv R mg mg mg mg b = + = + = the equation for the energy as a function of s in Example 4.6.2, 4.23 From 1 1 mg v h b 2 2 E ms = + ± s is und 2 2 4 A s , ergoing harmonic motion with: " " 1 k g ω = = = 4 2 m A A g Since 4 sin s A φ = , φ increases by 2 π radians during the time interval: 2 2 g π 2 A T π ω ′ =
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