Determine the new spring constant of the springs

[leena19]

Homework Statement

When a spring (with spring constant k)and length L is cut into 2 identical parts,determine the new spring constant of the springs

Homework Equations

F=-kx

The Attempt at a Solution

I only know the spring constant is a measure of the stiffness of a spring and (I think?)the spring constant is a constant for a particular spring,but I don't know how cutting a spring into half could vary the spring constant?
Does k depend on the length of the spring?

 

[songoku]

Yes, k depends on the length of the spring.

The formula for k:

$$k =\frac{E A}{L}$$

E = young modulus
A=cross-sectional area
L = length

 

[leena19]

Thanks songoku.
I didn't know k depended on A,E and L.
so the spring constant would now be 2k for the each new spring.

 

[alphysicist]

Hi songoku,

Yes, k depends on the length of the spring.

The formula for k:

$$k =\frac{E A}{L}$$

E = young modulus
A=cross-sectional area
L = length

This gives the right answer for this problem, but it would only apply if your "spring" is a straight wire.

For a regular helical spring being pulled, the spring constant would depend on the shear modulus of the material, since the spring works mainly by twisting the wire that it's made of. (And the shear modulus deterimines the torsion constant.)

 

[songoku]

Hi alphysicist

wow, that's a new information for me
but i don't understand this part "your "spring" is a straight wire".

I think all spring is regular helical spring?

thx

 

[alphysicist]

Hi alphysicist

wow, that's a new information for me
but i don't understand this part "your "spring" is a straight wire".

I think all spring is regular helical spring?

thx

Young's modulus describes a wire (for example) in which the material stretches (or compresses) due to a force pulling or pushing it.

So an example of a case in which your equation would apply: a long straight wire is hanging straight down. A weight is then attached to the end, and the wire stretches some distance. In that case, your equation can be used to give a spring constant for that wire.

However, in a regular helical spring, when the spring stretches, the wire itself is not stretching (to any appreciable amount). Instead, the wire (that makes up the spring) is twisting as the spring stretches. So it is not Young's modulus that is important in a helical spring.

(There are many different kinds of springs--for example, the leaf spring in a car comes to mind.)

 

[songoku]

Oh i see

thx a lot alphysicist ^^