Test Question (Potential Energy): Need help finding answer

[gokugreene]

I can't figure out what I did wrong on this test question.

A 4kg block is dropped from a height of 0.8m above a spring, k=120N/m. Find the maximum compression of the spring.

I have the PE at the top is equal to KE at the bottom.
PEtop=31.4J
KEbottom=31.4J

The potential energy in the spring when compressed should equal the KE at the bottom. Based upon that I should be able to find the maximum distance the spring will compress.

KEbottom=Wspring
31.4J=.5*120*x^2
Rearranging x=sqrt(2*31.4/120) and I get x=-0.723m

What am I doing wrong here? Can someone point it out.

Thanks, peace

 

[SpaceTiger]

Remember that the spring is compressing in the vertical direction, so there is more gravitational potential energy to take into account:

Initial gravitational potential energy = Final spring potential energy

$$mg(x_0+x_{spring})=\frac{1}{2}kx_{spring}^2$$

 

[gokugreene]

Your equation will give me the exact same answer I got.
mg(0.8 + 0) =.5kx^2

 

[SpaceTiger]

Your equation will give me the exact same answer I got.
mg(0.8 + 0) =.5kx^2

No, in my response, x_spring is the same as x in your response. On the left side, you set the second term to 0, when it should be mgx. It's a quadratic equation.