Does spring constant of the spring change with the length of the spring? If 10 meter long spring has a spring constant $k= 5 N/meter$,
so does 1000 meter long spring have $k=500 N/meter$?
Please explain!
 A: Start with your $10$m spring that has a spring constant $k$ and compress it by $1$m. The force in the spring is now $k$ newtons. So far so good.
Now take a hundred of your springs and place them end to end to form the $1000$m spring. Compress this spring by $1$m. Since the big spring is made up of one hundred identical smaller springs each of these smaller springs will compress by an identical amount. That means each individual spring is compressed by $0.01$m, and therefore that the force in each spring is $0.01k$.
But the force in the big spring is the same as the force in all the smaller springs that make it up i.e. the force in the big spring is $0.01k$ newtons. And that means the force constant of the big $1000$m spring is one hundred times smaller than the spring constant of the $10$m springs.
This is a general result. Assuming the springs are made from the same material the force constant is inversely proportional to the (relaxed) length of the spring.
A: Young's modulus,Y= stress/strain
For spring
Y=(kx/A)/(x/l)
Where l is length of spring
=> Y=kl/A
Keeping area of cross section constant,
spring constant and length of spring are inversely proportional
A: Spring constant is a function of the geometry and the material of the spring. 
A longer spring of the same thickness, material, winding diameter, but different lengths will have a lower spring constant.  This is because when you stretch or compress an ideal helical coil spring, each piece of the wire is twisting slightly.  A helical spring is essentially a long wire that gets twisted.
The longer the wire, the easier it is to twist it the same amount.  This makes the long spring less stiff, and therefore lowers the spring constant.
