Find Stretch of Each Spring After Cutting 100-Coil Spring

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When a 100-coil spring is cut into two 50-coil springs, each spring supports half the mass of the object, leading to a different stretch. The initial stretch of the original spring was 0.155 m, and after cutting, the stretch of each new spring is calculated to be 0.0387 m. The discussion highlights the relationship between spring constant, mass, and stretch, emphasizing the need for understanding force balance in the system. A participant initially struggled with the calculations but ultimately arrived at the correct answer. The conversation invites further explanation of the underlying concepts related to spring mechanics.
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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?
 
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Have any thoughts?
 
well, since the mass is carried by two springs, each spring carries half the mass...but that's all i know... =(
 
100:0.115 = 50:x

x = .115/2
 
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?
 
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