379_Dynamics 11ed Manual

379_Dynamics 11ed Manual - Engineering Mechanics - Dynamics...

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Engineering Mechanics - Dynamics Chapter 15 Problem 15-109 A small particle having a mass m is placed inside the semicircular tube. The particle is placed at the position shown and released. Apply the principle of angular momentum about point O ( Σ M 0 = H 0 ), and show that the motion of the particle is governed by the differential equation θ '' + ( g / R ) sin = 0. Solution: Σ M 0 t H 0 d d = R mg sin () t mvR d d = g sin t v d d = 2 t s d d 2 = But, sR = Thus, g sin R '' = or, '' g R sin + 0 = Problem 15-110 A toboggan and rider, having a total mass M , enter horizontally
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