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midterm 1 prac

midterm 1 prac - SE 101B/MAE 130B Dynamics Mock Mid-term...

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SE 101B/MAE 130B Dynamics Mock Mid-term Examination WI08 SOLUTIONS PROBLEM 1 . A 3 lbf ball is given an initial velocity v A of 8 ft/s at an angle of 45 O from the horizontal at position A, where the two attached springs are unstretched with free lengths of 12 in. The ball follows the dashed path in space and at some point in the future crosses point B, which is 5 in directly beneath point A. Calculate the velocity v B of the ball at B. Each spring has a stiffness of 10 lbf/in. SOLUTION : This problem should be solved by energy methods, since all forces acting are conservative. Thus, energy is conserved. This also means that the path that the ball takes through space doesn’t matter: the only important information is contained at the endpoints! If we take the lower point (B) to be a gravitational potential energy reference, the ball only has potential and kinetic energy at A (springs are unstretched at A), and this is translated into elastic potential and kinetic energy at B. By using right triangle geometry, the springs stretch to 13 in at B (12 2 + 5 2 = 13 2 ). So, we have T 1 + V g ,1 + V e ,1 = T 2 + V

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