Spring Energy Problem Conservative forces

[GenericHbomb]

Homework Statement

A spring is attached to a ceiling, and has a relaxed length of 25cm. When a mass m=.80kg is attached to the spring it stretches to an equilibrium length of L₀=34cm.
a.)Find the Spring Constant of the Spring?

b.)I lift the mass until the spring returns to its relaxed length, and then release it. When the mass returns to the equilibrium length, what is its speed?

c.)After I release the mass and it falls, what is the length of the spring when the mass reaches its lowest point?

Homework Equations

K=mg/x

E₁ + Wnc = E₂

The Attempt at a Solution

A.) k=mg/x
k= [.80(9.8)]/.09
k=87 N/m

b.) E1= E2
0=.5mv² + .5kx² +mgh
0=.5(.8)v² + .5(87)(.09²) + .8(9.8)(-.09)
v=.9397 m/s

c.) I am not really sure where to go on C. I tried setting E1=E2 up as follows but my final answer was smaller than the equilibrium length so it can't be right.
E1=E2
.5mv² + .5kx² +mgh=.5mv² + .5kx² +mgh
.5(.8)(.9397²)+.80(9.8)(34)= .5(87)x²

 

[cupid.callin]

c.) I am not really sure where to go on C. I tried setting E1=E2 up as follows but my final answer was smaller than the equilibrium length so it can't be right.
E1=E2
.5mv² + .5kx² +mgh=.5mv² + .5kx² +mgh
.5(.8)(.9397²)+.80(9.8)(34)= .5(87)x²

Let us not take the E1 and E2 you have chosen
let E1 is the E1 in (b) ie when mass is in your hands

and let E2 be condition when mass is at lowest point

now try the question again

 

[GenericHbomb]

So if I set E1 to be when the spring is at the relaxed length then E1=0
E2 is lowest point so velocity would be zero since it stopped moving
E1=E2
0= .5mv² + .5kx² +mgh
0=.5(.80)(0)+ .5(87)(x)²+ (.8)(9.8)(h)
I know I need to solve for x because that is spring length but I am not sure what to put for h.
If I assume h to be 0 then my final answer would be 0.

 

[cupid.callin]

x is the extension in string ...

h is height decreased

what can be relation b/w them
try by making a diagram

 

[GenericHbomb]

So I made a diagram and thank you for reminding that x is extension not length.
We are starting from x=0 and ending at x=?
Since h can be whatever I want I made h=0 where x=0
Therefore x=-h
So
0=.5(.80)(0)+.5(87)(x²)-.8(9.8)(x)
x=0, .18023
Length at lowest point = x + length at E1
Length= .25 + .18023
Length= .43 meters?