physics

(a) The distance x can be found by equating the elastic potential energy equal to the work done in compression; U = W. The work done in compression is equal to the force multiplied by the distance, W = Fx. Therefore, the equation to solve is U = Fx. Plugging in the given values, U = 0.570(450)x = 0.51x, and thus x = 0.51/450 = 0.00114 m. (b) The speed of the block at the top of the track can be found using the equation for the conservation of mechanical energy, Ef = Ei. Ef is the final kinetic energy and Ei is the initial kinetic and potential energy. Ei is equal to the work done in compression of the spring, 0.570(450)x = 0.51x, plus the initial kinetic energy, 1/2(0.570)vB2 = 3.75vB2. Ef will be equal to the final kinetic energy, 1/2(0.570)vT2 = 3.75vT2. Plugging in the given values, 0.51x + 3.75vB2 = 3.75vT2. Solving, vT2 = (0.51x/3.75) + vB2. Since x = 0.00114 m, vT2 =