A mass–spring oscillator is constructed by attaching a mass to the end of an ideal…
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A mass–spring oscillator is constructed by attaching a 0.50kg mass to the end of an ideal (massless) vertical spring of spring constant 35Nm−1 that hangs from the ceiling. After being pulled downward 0.15m from its equilibrium position, the mass is released from rest and allowed to move only in the vertical direction. A student draws an energy bar chart for the motion and states:
“Because gravitational potential energy involves the Earth, I will define my system as the Earth and the mass only. The spring is outside the system, so its force does work on the system. Therefore the total mechanical energy of my system is conserved.”
Assume air resistance is negligible.
(a) Critically evaluate the student’s choice of system. Identify any object(s) that must be included to account correctly for all potential energies present, and redraw (verbally describe) the energy bar chart at the release point and at the equilibrium point.
(b) Explain in detail why the student’s conservation claim is invalid for the system they defined. Your explanation should refer to energy transfers that cross the chosen boundary.
(c) Define an alternative system for which mechanical energy is conserved during the motion. Using this system, derive an expression for the maximum speed vmax of the mass in terms of the amplitude A, the spring constant k, and the mass m, with clear reasoning.
(d) Compute the numerical value of vmax for the given data.