Physics
Physics
Problem
A light vertical spring of force constant is fixed at its upper end to a rigid support. A block of mass is attached to its lower end and allowed to hang freely so that the system comes to rest at its equilibrium position where the spring is extended by from its natural length. Answer the following questions related to the energy changes in this arrangement: a. (i) Define gravitational potential energy and elastic potential energy for this system, clearly stating the reference levels you choose. b. (ii) The block is now very slowly lowered further by a distance and then brought back slowly to the equilibrium position. Explain qualitatively how the gravitational potential energy, elastic potential energy and the total mechanical energy of the system vary during this process. c. (iii) Starting from the equilibrium position, the block is pulled down an additional small distance and released from rest so that it executes vertical oscillations. Describe, with reasons, at which positions during one complete oscillation (a) elastic potential energy is maximum, (b) gravitational potential energy is maximum, (c) kinetic energy is maximum.Intuitive explanation
The key insight is recognizing that at equilibrium, the spring force balances gravity—so —and that this relationship lets you connect mechanical energy changes to the spring's stored energy. When the block moves from equilibrium, both gravitational and elastic potential energy shift, but their sum with kinetic energy remains constant. Understanding how to measure potential energy from the equilibrium position (rather than from the natural length) often simplifies the math and reveals the underlying harmonic motion.
Intuitive explanation
The key insight is recognizing that at equilibrium, the spring force balances gravity—so —and that this relationship lets you connect mechanical energy changes to the spring's stored energy. When the block moves from equilibrium, both gravitational and elastic potential energy shift, but their sum with kinetic energy remains constant. Understanding how to measure potential energy from the equilibrium position (rather than from the natural length) often simplifies the math and reveals the underlying harmonic motion.