Physics Help Forum spring constant

 Periodic and Circular Motion Periodic and Circular Motion Physics Help Forum

 Feb 6th 2015, 07:06 AM #1 Junior Member   Join Date: Jan 2015 Posts: 15 spring constant If a spring (which spring constant is k) is divided into m:n ratio, where 'm' is greater than 'n', what will be the value of spring constant for new springs?
 Feb 8th 2015, 05:34 AM #2 Physics Team     Join Date: Jun 2010 Location: Morristown, NJ USA Posts: 2,333 Hint: if the original length of the spring is L, and a cut length is M, then the spring constant for the shortened spring is k(L/M). Here you don't know L explicitly, but you do know it equals M+N. Give it a try and post back with what you are able to determine. Last edited by ChipB; Feb 9th 2015 at 04:39 AM.
 Feb 8th 2015, 04:17 PM #3 Senior Member   Join Date: Jun 2010 Location: NC Posts: 412 Intriguing Question I despise "intuition" but if the spring is very long with constant k, won't the pieces "m" and "n" have constants, k? Does this have to do with how the constant is measured? TSH for PHF
 Feb 9th 2015, 04:48 AM #4 Physics Team     Join Date: Jun 2010 Location: Morristown, NJ USA Posts: 2,333 Hi Thermo. Yes, it has to do with how 'k' is determined. The spring constant is equal to force applied divided by the change in length of the spring, where that change has units of distance. Suppose you have a long spring and put a marker at the midpoint, then apply a force at the end. The end will deflect by an amount F/k, but what happens at the midpoint? It deflects only half as much, so effectively the spring constant of one half of the spring is equal to 2k. Perhaps you are thinking in terms of percentage change of length of the two halves, rather than the absolute change in length? If so, then you would be correct - if the full spring compresses 10% under a certain load, then each half also compresses 10%. In engineering we use the relationship Stress = E times Strain, which is based on this idea. It says that for a given material the force per unit area applied (stress) equals E (which is Young's modulus, and is a characteristic of the stiffness of the material) times change in length per unit length (strain). Using this approach allows the use of a constant value for E regardless of the length of the material. Last edited by ChipB; Feb 10th 2015 at 09:59 AM.