A block of mass 0.50kg rests on a vertical spring that is fixed to the floor. The spring has force constant 250Nm−1. The block is pushed downward, compressing the spring, and then released from rest. Ignore all friction and treat the spring as ideal.
parts:[{"content":"(a) Derive an equation that relates the initial compression x of the spring to the maximum vertical height h above the spring’s natural (uncompressed) length that the block subsequently reaches."},{"content":"(b) The experiment is performed and the block is observed to rise to a maximum height of 1.8m above the spring’s natural length. Calculate the initial compression x."},{"content":"(c) Determine the speed of the block as it passes the spring’s natural length while moving upward."},{"content":"(d) Sketch a graph (qualitatively, with clearly labeled axes) of the potential energy of the system as a function of the block’s vertical position, marking the points corresponding to the release point, the natural length, and the highest point."}]