Help with spring stiffness calculation (k)

[imd25]

Hi

I was given the following problem in my coursework:

Homework Statement

"A spring is initially compressed by 50mm when a steel ball of mass 2kg is released from just being in contact with the uncompressed spring. Determine the spring stiffness (k) of the spring."

Homework Equations

F = mg
Restorative force F = -kx

The Attempt at a Solution

I gave the answer below, but the teacher has marked it as wrong. Can anyone shed any light on where I may have made a mistake? I thought it was just a simple application of Hooke's Law.

F = mg
F = 2 x -9.81
F = -19.62 N

F = -kx
19.62 = -k(-0.05)
19.62 = 0.05k
k = 19.62/0.05
k = 392.4

Thanks, any insight gratefully received.

 

[Bystander]

Units?

 

[imd25]

Thanks for your reply Bystander,

I did actually include the units (N/m) in my coursework - sorry, I omitted them in my original post by accident.

 

[billy_joule]

I think the inclusion of "initially" implies the compression given is the lowest point the weight reaches rather than the equilibrium position that your solution assumes.
Try applying conservation of energy to solve.