Find Stretch of Each Spring After Cutting 100-Coil Spring

[huskydc]

An object is attached to the lower end of a 100-coil spring that is hanging from the ceiling. The string stretches by 0.155 m. The spring is then cut into two identical springs of 50 coils each. As the drawing shows, each spring is attached between the ceiling and the object. By how much does each spring stretch?

 

[Knavish]

Have any thoughts?

 

[huskydc]

well, since the mass is carried by two springs, each spring carries half the mass...but that's all i know... =(

 

[plucker_08]

100:0.115 = 50:x

x = .115/2

 

[huskydc]

sorry plucker, but that's not the right answer. again, i drew another FBD,
for one spring: F(spring) = mg

k = mg/x(1)

for 2 springs: 2F(spring) =mg
2 k x(2) =mg

but with only x(1) known, and no mass, how should i approach this?


...ok, after some tries..
i somehow found the right answer as .0387. but does anyone want to explain the concepts behind it?