630_Dynamics 11ed Manual

# 630_Dynamics 11ed Manual - s = V 1 1 N m = V 2 1 N m =...

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Engineering Mechanics - Dynamics Chapter 18 Problem 18-55 A chain that has a mass density ρ is draped over the sprocket which has mass m s and radius of gyration k O . If block A of mass m A is released from rest in the position s = s 1 , determine the angular velocity of the sprocket at the instant s = s 2 . When released there is an equal amount of chain on each side. Neglect the portion of the chain that wraps over the sprocket. Given: m s 2kg = s 1 1m = k O 50 mm = s 2 2m = m A 4kg = r 0.1 m = g 9.81 m s 2 = 0.8 kg m = Solution: Guess T 1 1Nm = T 2 1Nm = ω 10 rad
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Unformatted text preview: s = V 1 1 N m = V 2 1 N m = Given T 1 = V 1 m A − gs 1 2 s 1 g s 1 2 ⎛ ⎝ ⎞ ⎠ − = T 2 1 2 m A r ( ) 2 1 2 m s k O 2 2 + 1 2 2 s 1 ( ) r ( ) 2 + = V 2 m A − gs 2 s 2 g s 2 2 ⎛ ⎝ ⎞ ⎠ − 2 s 1 s 2 − ( ) g 2 s 1 s 2 − 2 ⎛ ⎝ ⎞ ⎠ − = T 1 V 1 + T 2 V 2 + = T 1 V 1 T 2 V 2 ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ Find T 1 V 1 , T 2 , V 2 , , ( ) = 39.3 rad s = 628...
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