396_Dynamics 11ed Manual

396_Dynamics 11ed Manual - y 3 h 3 y 2 = Problem 15-133 The...

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Engineering Mechanics - Dynamics Chapter 15 * Problem 15-132 The rope has a mass m' per unit length. If the end length y = h is draped off the edge of the table, and released, determine the velocity of its end A for any position y , as the rope uncoils and begins to fall. Solution: F s m t v d d v Di t m i d d + = At a time t , mm ' y = and t m i d d m' t y d d = m' v = . Here, v Di v = , t v d d g = . m' g y m' y t v d d vm 'v () + = gy y t v d d v 2 + = Since v t y d d = , then d t d y v = gy vy y v d d v 2 + = Multiply both sides by 2 y d y 2 gy 2 d y 2 vy 2 d v 2 yv 2 d y + = y 2 gy 2 d v 2 y 2 1 d = 2 3 gy 3 C + v 2 y 2 = C 2 3 gh 3 = v 0 = at yh = 2 3 gh 3 C + 0 = 2 3 gy 3 2 3 gh 3 v 2 y 2 = v 2 3 g
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Unformatted text preview: y 3 h 3 y 2 = Problem 15-133 The car has a mass m and is used to tow the smooth chain having a total length l and a mass per unit of length m'. If the chain is originally piled up, determine the tractive force F that must be supplied by the rear wheels of the car, necessary to maintain a constant speed v while the chain is being drawn out. 394...
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