Question

Help please. I don't know how to setup the equation to this question
an ideal spring is suspended from the ceiling. a mass m=4kg is attached to the spring stretching it a distance of 20cm.
a) find the spring constant k of the spring
b) how much work must be done to stretch the spring an additional 25cm

Answer 1

the mass is in equilibrium, so the net force acting on it must be zero.
the two forces applied on the mass are, weight (\(W=mg\)) and spring force \(F_s=k.\Delta x\), so we can write:
\[\sum F = F_s-W=0\]
and solve that to get the spring constant \(k\). I called the spring stretch \(\Delta x\) here.