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Spring of mass 'm' hung from ceiling.total elongation? 
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#1
Nov3013, 08:42 AM

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spring of mass 'm' hung from ceiling.what is the total elongation?
assume total spring constant 'k',length 'l' and of uniform density when in natural state. also where is the center of mass? can we express density at a point as a function of distance from the ceiling? 


#2
Nov3013, 04:00 PM

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Well you can use calculus if that's your strength. Or you can reason it out.....If the spring is slowly lowered to its equilibrium position, and the mass was concentrated all at the lower end, its elongation would be mg/k, using Hooke's Law. If the mass was all concentrated at the upper end, the spring would not elongate at all! But the center of mass of the spring is not at the top or bottom , its in the middle. So, the elongation is not mg/k , nor 0, but rather, it is ?????



#3
Nov3013, 05:39 PM

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But sometimes, you get lucky and the wrong logic still gives the right answer 


#4
Nov3013, 05:45 PM

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Spring of mass 'm' hung from ceiling.total elongation?
But sometimes, you get lucky and hit the right answer by an invalid argument 


#5
Nov3013, 08:30 PM

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#6
Nov3013, 10:33 PM

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I did the calculus and got the elongation as 'mg/2k'.I think I am wrong because I am not so good at calculus.
the case is much more like rope of young's modulus 'Y' hung from ceiling.slinky is the closest reference.elongation in slinky is 'mg/2k' according to wikipedia 


#7
Nov3013, 10:59 PM

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You can call it whatever sort of reasoning you want, but if you made that argument in a report that I had to sign off at work, I wouldn't sign it. 


#8
Nov3013, 11:06 PM

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For the rope, the equivalent "spring stiffness" k = EA/L where A is the cross section area. For a spring, it is harder to give a formula for k in terns of the diameter of the wire, diameter of the coils, number of coils per unit length, material properties of the wire, etc, so you just use the value of k. I think your answer is right. 


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