PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
Two identical springs, each of force constant k, are used separately on a smooth horizontal table. Spring–block system A has a block of mass m and amplitude 0.10m, while system B has a block of mass 2m and amplitude 0.05m. Answer the following:
(i) Obtain an expression for the total mechanical energy of each system in terms of k and m.
(ii) For each system, write the expression for kinetic energy as a function of instantaneous displacement x.
(iii) On the same set of qualitative axes, sketch the graphs of kinetic energy versus displacement for systems A and B. Clearly indicate their maximum kinetic energies and the displacements where these occur.
(iv) Using the graphs or otherwise, determine the displacement(s) (if any) at which both systems possess the same kinetic energy. Show the necessary algebraic steps.