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Unformatted text preview: U 1 2 = T 2 T 1 so that m 2 gx 1 2 kx 2 = 1 2 m 1 v 2 Therefore, we find v 2 = 2 m 2 g m 1 x k m 1 x 2 Now, when v achieves its maximum value, so does v 2 . Thus, we can determine the maximum value of v by working with v 2 . dv 2 dx = 2 m 2 g m 1 2 k m 1 x and d 2 v 2 dx 2 < So, v 2 and v reach their maximum values when dv 2 /dx = 0 , wherefore x = m 2 g k Hence, there follows v 2 max = 2 m 2 g m 1 m 2 g k k m 1 p m 2 g k Q 2 = 2 m 2 2 g 2 m 1 k m 2 2 g 2 m 1 k = m 2 2 g 2 m 1 k Thus, the maximum velocity is v max = m 2 g m 1 k (b) Using the given values of m 1 g = 0 . 5 lb, m 2 g = 0 . 75 lb and k = 9 lb/ft, we have v max = m 2 g m 1 gk/g = . 75 lb (0 . 5 lb)(9 lb / ft) / (32 . 174 ft / sec 2 ) = 2 . ft sec...
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This note was uploaded on 10/12/2009 for the course AME 301 at USC.
 '06
 Shiflett

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