Determine the new spring constant of the springs

In summary, the spring constant is a measure of the stiffness of a spring and depends on the length, cross-sectional area, and young's modulus of the material. When a spring with spring constant k and length L is cut into two identical parts, the new spring constant for each part would be 2k. However, this formula only applies to a straight wire, and for a regular helical spring, the shear modulus of the material is more important in determining the spring constant.
  • #1
leena19
186
0

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?
 
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  • #2
Yes, k depends on the length of the spring.

The formula for k:

[tex]k =\frac{E A}{L}[/tex]

E = young modulus
A=cross-sectional area
L = length
 
  • #3
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.
 
  • #4
Hi songoku,

songoku said:
Yes, k depends on the length of the spring.

The formula for k:

[tex]k =\frac{E A}{L}[/tex]

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.)
 
  • #5
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
 
  • #6
songoku said:
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.)
 
  • #7
Oh i see

thx a lot alphysicist ^^
 

1. How do you determine the new spring constant of the springs?

The new spring constant can be determined by calculating the ratio of the applied force to the resulting extension or compression of the spring. This can be done by conducting experiments with different weights and measuring the corresponding change in length of the spring.

2. What factors can affect the new spring constant?

The new spring constant can be affected by the material and shape of the spring, the temperature, and the amount of force applied. Changes in these factors can lead to variations in the spring constant.

3. Can the new spring constant be calculated mathematically?

Yes, the new spring constant can be calculated using Hooke's Law, which states that the force applied to a spring is directly proportional to the spring's change in length. The equation for Hooke's Law is F = -kx, where F is the applied force, k is the spring constant, and x is the change in length.

4. How can the new spring constant be used in practical applications?

The new spring constant is useful in various engineering and scientific fields. It is used in the design and construction of structures and machines that rely on springs, such as shock absorbers, car suspensions, and door hinges. It is also used in experiments and studies that involve springs, such as in physics and material science research.

5. Is the new spring constant affected by the number of springs used?

Yes, the new spring constant can be affected by the number of springs used and how they are arranged. When multiple springs are connected in series, the overall spring constant is equal to the sum of the individual spring constants. When the springs are connected in parallel, the overall spring constant is equal to the reciprocal of the sum of the reciprocals of the individual spring constants.

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