1. Consider the four block-and-spring(s) systems shown at right. Each block moves on a horizontal, frictionless...

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1. Consider the four block-and-spring(s) systems shown at right. Each block moves on a horizontal, frictionless table. The blocks all have the same mass m, and all of the springs are identical and ideal, with spring constant k. At the instant shown, each block is released from rest a distance A to the right of its equilibrium position (indicated by the dashed line). In case B, assume that each spring is at its equilibrium length when the block is at its equilibrium position. a. Rank the cases according to magnitude of the net force on the block at the instant shown, from largest to smallest. (Hint: In case C, how far was the point connecting the two springs displaced when the block was displaced a distance A?) Explain. Case A www Case B Case C A wym A m lllllluuu m Case D www.w wwwwww A m b. Use your answers above to rank the cases according to the time it takes the block to return to its equilibrium position. Explain. c. The total potential energy of a system of multiple springs is defined to be the sum of the potential energies stored in each of the springs. Rank the cases according to total potential energy at the instant shown. (Hint: In each case, consider how much each individual spring is extended.) Explain. 1. Consider the four block-and-spring(s) systems shown at right. Each block moves on a horizontal, frictionless table. The blocks all have the same mass m, and all of the springs are identical and ideal, with spring constant k. At the instant shown, each block is released from rest a distance A to the right of its equilibrium position (indicated by the dashed line). In case B, assume that each spring is at its equilibrium length when the block is at its equilibrium position. a. Rank the cases according to magnitude of the net force on the block at the instant shown, from largest to smallest. (Hint: In case C, how far was the point connecting the two springs displaced when the block was displaced a distance A?) Explain. Case A www Case B Case C A wym A m lllllluuu m Case D www.w wwwwww A m b. Use your answers above to rank the cases according to the time it takes the block to return to its equilibrium position. Explain. c. The total potential energy of a system of multiple springs is defined to be the sum of the potential energies stored in each of the springs. Rank the cases according to total potential energy at the instant shown. (Hint: In each case, consider how much each individual spring is extended.) Explain.

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