Hooke's Law Elevator Spring Question

[MMVS]

Homework Statement

Elevator initially at rest.
Equilibrium length L₀=40.0cm
60-kg person stands on spring
L₁= 32.0cm

The elevator than speeds upwards at 2.50 m/s²
What is the new length (L₂)

Homework Equations

F_net=ma
F_sp=-kdeltaX
F_G=mg

The Attempt at a Solution

Taking down as positive y hat direction
Before:
F_net=F_sp+F_G
0=-k(0.32-0.40)+(60.0)(9.81)
K=-7358
After:
F_net=F_sp+F_G
ma=-kdeltaX+mg
m(-2.5)=-(-7358)(L₂-0.40)+60(9.81)
L₂=[{60(-2.5)-60(9.81)}/-(-7358)]+0.40
=0.30m from equilibrium

I am confused since i don't know how this makes sense according to the coordinate system. (I know the answer is right as my prof posted the answer, not the work, just answer)
At rest change in x = -0.08
When accelerating change in x= -0.10
But since my coordinate system is set up so Y-hat is positive is the downward direction doesn't this mean my spring is being displaces upward?
This doesn't make sense to me , can someone please explain very clearly?

 

[JeremyG]

Fnet=Fsp+FG
0=-k(0.32-0.40)+(60.0)(9.81)
K=-7358

Take a look at your signs again. Are they consistent with the defined direction?

 

[MMVS]

Take a look at your signs again. Are they consistent with the defined direction?

I kinda see what you are getting at

 

[SteamKing]

Homework Statement

Elevator initially at rest.
Equilibrium length L₀=40.0cm
60-kg person stands on spring
L₁= 32.0cm

The elevator than speeds upwards at 2.50 m/s²
What is the new length (L₂)

Homework Equations

F_net=ma
F_sp=-kdeltaX
F_G=mg

The Attempt at a Solution

Taking down as positive y hat direction
Before:
F_net=F_sp+F_G
0=-k(0.32-0.40)+(60.0)(9.81)
K=-7358
After:
F_net=F_sp+F_G
ma=-kdeltaX+mg
m(-2.5)=-(-7358)(L₂-0.40)+60(9.81)
L₂=[{60(-2.5)-60(9.81)}/-(-7358)]+0.40
=0.30m from equilibrium

I am confused since i don't know how this makes sense according to the coordinate system. (I know the answer is right as my prof posted the answer, not the work, just answer)
At rest change in x = -0.08
When accelerating change in x= -0.10
But since my coordinate system is set up so Y-hat is positive is the downward direction doesn't this mean my spring is being displaces upward?
This doesn't make sense to me , can someone please explain very clearly?

If you're standing in an elevator when it starts to go up, do you feel heavier or lighter when the car starts to move? Is the spring therefore going to get longer or shorter as a result?

You seem to have sprinkled a generous helping of negative signs throughout your calculations without systematically considering coordinate systems.