A lightweight coil spring is suspended vertically from a rigid support
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics
Problem
A lightweight coil spring is suspended vertically from a rigid support. The unstretched length of the spring is L0. A metal object of mass m is gently hung from the lower end of the spring and the system is allowed to come to rest at a new equilibrium length L1. Air resistance is negligible.
(a) Draw a clearly labeled free-body diagram for the metal object once the system has reached equilibrium.
(b) Derive an algebraic expression for the extension ΔL=L1−L0 of the spring in terms of m, the spring constant k, and any relevant physical constants.
(c) Without substituting any numbers, describe how the extension ΔL would change under each of the following independent modifications:
(i) The mass m is doubled.
(ii) The spring is replaced by another spring whose spring constant is twice as large.
Provide a brief justification for each case.