physics--springs and potential elastic energy?

Question

A 3.2-kg block is hanging from the end of vertical spring that is attached to the ceiling. The elastic potential energy of this spring/mass is 1.8 J. What is the elastic potential energy of the system when the 3.2-kg block is replaced by a 5.0-kg block?

Answer 1

The elastic potential energy I will assume is the energy stored in the spring
.5*k*x^2=1.8 J
where x is the elongation from equilibrium and k is the spring constant
We also can use the loss in PE from equilibrium of the hanging mass as
x*3.2*g=1.8J
so x=0.05734

using that we can solve for k

k=1095 N/m

switch to the 5 k block and
.5*1095*x^2=5*9.81*x
solve for x
x=0.090 m


plugging into the energy equation
4.4 J

j