Gravitational and elastic energy

[pdrjuarez]

Homework Statement

A spring with spring constant k is hanging from the ceiling, at equilibrium point. The length of the spring in equilibrium is h₂. Then you hang a mass less string from the end of the spring, holding a mass m. The length of the string and the mass together equal y.
The height of the floor to the ceiling is h₁

Using elastic and gravitational energy equations, what is the necessary length of the spring and the mass combined (y), so that when you hang the mass, it just touches the floor? (in other words, solve for y?)

Homework Equations

E_e=kx²/2

E_g=mgh

 

[rl.bhat]

If x is the extension in the spring, then
h1 = h2 + x + y.
Substitute the value of x, in the relevant equations and solve for y.