Velocity of snapium given constant and weight

[nlingraham]

Homework Statement

A snapnium-loaded toy launcher shoots a 22 g plastic ball. What is the launch speed if the snaptastic constant is 4.6×10⁴ N/m³, with the units you found in part A, and the piece of snapnium is compressed 14 cm ? Assume the barrel is frictionless.

OTHER INFO:

A materials scientist comes up with a new elastic she calls "snapnium" that obeys the force law F_x=-q(x-x_e)³, where x_e is the equilibrium position of the end of the particular sample and q is the "snaptastic" constant. For simplicity, we'll let x_e=0m . Then F_x=-qx³.

Homework Equations

U(x)= (qx⁴)/4

part A was finding units of q, which were N/m³

The Attempt at a Solution

The answer is 20 m/s, but I have no idea how to do it. Can someone explain to me what the process is to get to this answer?

 

[voko]

Use conservation of total energy.