Physic Labs

Problem 1

A mass mm is released from rest at height hh above the uncompressed top of a vertical spring of stiffness kk. Neglect resistance and take constant gg. Find the maximum compression xx. Assume the string, pulley, electrical source, or optical apparatus is ideal as stated, and neglect any effect not specified. State a clear sign convention, identify the physical Keep one model and sign convention throughout. Reuse each intermediate result with the same convention, then check that the answer has the required physical dimensions. (a) Set up the physical relation. (b) Find an intermediate quantity. (c) Obtain the answer and check its conditions and units.
kx2−2mgx−2mgh=0kx^2-2mgx-2mgh=0
problems.proof.analysis

This is a quadratic in compression; the other root is negative and cannot describe a physical compression. This is consistent with the stated model and the chosen sign convention.