126 - ∆ = ∆ = ∆ − ∆ − = ∆Φ − i.e g v g v g...

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2.126Given: The pulley system shown starts from rest. W A = 12-lb, W C = 8-lb, and W D = 10-lb. Block C is stopped once the system has traveled 3 ft . Find: The total distance traveled before the system comes to a rest. Solution: The motion of the system takes place during two distinct stages: (1) when it falls x 1 = 3 ft and the speed increases to v 1 , and (2) when it falls some distance x 2 further and decreases in speed to 0. Since we are given x 1 , we need only to find x 2 . To do this, it would help to have v 1 , since then we could use conservation of energy. i.e., during stage 2: () ( ) ) ( ) 2 / 1 ( 2 v m m KE h g m h g m D A D A
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Unformatted text preview: ∆ + = ∆ = ∆ − ∆ − = ∆Φ − , i.e. g v g v g v m m m m x D A D A 2 11 / 2 22 ) 2 / 1 ( / ) 2 / 1 ( 2 1 2 1 2 1 2 = = − + = ∆ Using the same method for the first interval yields ( ) ( ) ) ( ) 2 / 1 ( ) ( 2 v m m m KE h g m m h g m D C A D C A ∆ + + = ∆ = ∆ + − ∆ − = ∆Φ − , i.e. g v g v g v m m m m m m x D C A D C A 2 5 / 6 30 ) 2 / 1 ( / ) 2 / 1 ( 2 1 2 1 2 1 1 = = + + − + + = ∆ , so 5 / 2 1 2 1 x g v ∆ = , and ft x g x g x 6 . 6 5 11 2 5 / 2 11 1 1 2 = ∆ = ∆ × = ∆ , so Total distance traveled = 3 + 6.6 ft = 9.6 ft...
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