Put the ideas to work.

A technician compares two spring bumpers for a horizontal trolley. Spring A has a straight force-extension loading graph through the origin. Spring B has a curved loading graph but returns fully to its original length when unloaded. Both are used within a range where no permanent deformation occurs. Assume there are no internal energy losses within either spring on loading or unloading. A pupil makes two claims: “Elastic always means force is proportional to extension, so 0.5kx² gives the stored energy for both springs” and “The trolley accelerates at a constant rate until it leaves either spring.” Evaluate both claims. Explain how the force-extension graph gives the work done loading each spring, how this relates to energy transferred on release, and the effect of a constant resistive force on the trolley's motion. Assume the spring masses are negligible. [6]