What Is the Force Constant of a Spring and Does It Change with Mass?

[Ogakor]

Homework Statement

A force of 720 N stretches a certain spring a distance of 15 cm. What is its force constant? If a 60-kg mass is hung on it, how far will it stretch?

Solving for Force Constant
given:
F (Restoring Force) = 720 N
ΔL (spring's elongation) = 15 cm x (1 m / 100 cm) = 0.15 m
k (Force constant) = ?

k = F / ΔL
k = 720 N / 0.15 m
k = 4,800 N/m

Solving for spring's elongation if mass is 60kg
given:
m = 60 kg
g = 9.8 m/s²
F = ?
ΔL = ?
ΔL = F / k
since F = mg,
ΔL = mg / k
Im not really sure what k is because the mass change. If I'll use the k from the first question, this will be the outcome.
ΔL = (60kg)(9.8m/s²) / 4800 N/m

ΔL = 0.1225 m

My problem is ithat, I am not sure what k (Force constant) is (in the 2nd problem). I've solved it with the first problem but since the mass change, maybe force constant is not the same as the first question. And if k is not the same, there will be two unknowns.
What do you think? Am I going to use the k in the first question or am I going to use another solution? What solution should I use?
On the other hand, I think force is constant because of the name. Not really sure, I am a noob at physics.

 

[rock.freak667]

The force constant for a spring is well...constant. So you did it correctly.

 

[Ogakor]

The force constant for a spring is well...constant. So you did it correctly.

thanks rock.freak