Why does the spring constant double when a spring is cut in half?

Question

Why does the spring constant double when a spring is cut in half?

Answer 1

Let us look at a 10 coil spring as an example. Suppose we apply a force to the spring that compresses it 1 inch meaning that each coil is compressed 1/10 of an inch. If we then cut the spring in half, leaving 5 coils, and then compress it 1 inch, then each coil is compressed 2/10 or 1/5 of an inch. The general spring equation is

F = -kx

where F is the applied force, k is the spring constant and x is the distance the spring is compressed. So the force needed to compress a single coil by 2/10 of an inch is twice as large as to compress it 1/10 of an inch. Therefore the spring constant (k) of the 5-coil spring must be twice that of the 10-coil spring, because each individual coil of the 5-coil spring is compressed twice as far as each individual coil of the 10-coil spring for the same overall distance.

So in general the spring constant of a spring is inversely proportional to the number of coils in the spring.

Answer 2

Since f=kx, then k=f/x.

Now if you apply the same force to the half-length spring it only moves half as far. So if x is halved above, then k will double.

Basically there are now half as many coils to take up the force via displacement.

Answer 3

These are no reasons to support the answers. What if the spring is cut in the ratio 2:1 or any other.

The fact is, spring constant k is inversely proportional to length of spring.

Let k1 and k2 are the spring constants of two new springs.

let l1 and l2 be their resp lengths.

Now k1/k2 = l2/l1.

and use the equation for series addition of spring constants:

1/k1 + 1/k2 = 1/k.

k is original spring constant.

Answer 4

Because it will be harder to stretch. Just think about it logically... you'll get it.

Answer 5

Because 2 is twice as much as 1.

Answer 6

Actually, I once asked my teacher what happens to the spring constant if a spring is cut in half and he said that the spring constant doesn't change because it depends on the material used to make the spring. It depends on the properties (molecular structure) of that material. One analogy he used is whether if you are boiling 1 liter of water or 50 liters, the boiling point is always 100 degrees Celsius.