What would hapen to coefficent of spring if we cut it

[reza]

what would hapen to coefficent of spring if we cut it into 2 equal parts?

 

[lalbatros]

And what will you do with the parts, exactly?
Each of the part will have a double coefficient.
To stretch it to the same length as before, you will need to deform it twice as much.
(deformation= (final length)/(initial length))

 

[reza]

Each of the part will have a double coefficient.

I want to know why it became double

 

[reza]

sorry for my bad English
i mean why it's coefficient become twice i want logic answer
i want to know why K1=2K2 (if k1 is the first spring and k2 is belong to other spring-the second one-)

 

[Doc Al]

You can calculate the spring constant by considering k = F/x, where x is the amount the spring is stretched.

Imagine that you apply a force F to the full spring and it stretches an amount x. Now realize that the full spring is just two half-springs in series. How much does each half-spring stretch? What force does each half-spring exert? (Careful with that last question.)

 

[reza]

the stretch of each one x/2
and the forces are equal (F1=F2)

 

[i.mehrzad]

In can be put mathematically like this. When you cut a spring in two equal halves then the value of spring cinstant doubles.

 

[Doc Al]

the stretch of each one x/2
and the forces are equal (F1=F2)

Exactly. Now calculate the new spring constant:
k' = Force/stretch = F/(x/2) = 2 F/x = 2k

Make sense?

 

[reza]

I understand and thank you so much
but i want to know it's microscopic answer i mean what is the nature of spring constant (a physical answer not a mathematical answer)
can you give me brif answer or guid me a source to found it out
thank you wvery much for your good answer again.