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a) Ep = ½kx² = ½ * 19.2N/m * (0.04m)² = 0.01536 J Ek = 0.01536 J = ½mv² = ½ * 0.47kg * v² v = 0.256 m/s b) Ek = E - Ep = 0.01536J - ½ * 19.2N/m * (0.015m)² = 0.0132 J = ½ * 0.47kg * v² v = 0.237 m/s c) see b. 0.237d) At one-half the maximum speed, the kinetic energy is 1/4 the total energy; therefore the potential energy is 3/4 of the total energy. 0.01536J * 0.75 = ½ * 19.2N/m * x² x = 0.0346 m = 3.46 cm
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