Finding effective spring constants

In summary, the effective spring constant for two springs in series with different spring constants k1 and k2 is given by ka = (k1k2)/(k1+k2), assuming negligible mass. For two springs hanging in parallel with the same unstretched length but different spring constants k1 and k2, the effective spring constant is ka = k1 + k2. For three springs connected in series with spring constants k1, k2, and k3, the effective spring constant is ka = (k1k2k3)/(k1k2 + k1k3 + k2k3). This is similar to how resistors are added in parallel.
  • #1
shepherd882
12
0

Homework Statement


a) Consider 2 springs, connected in series. If they have different spring constants k1 and k2 then what is the effective spring constant for the double spring system? Give a convincing argument for your formula. You may assume that the mass of the springs is negligible.

b) Now suppose that 2 springs are hanging in parallel. (Assume that they are connected to the same point on a stand and on a hanging weight, so that they both stretch by the same amount.) They both have the same unstretched length but different spring constants k1 and k2. What is the effective spring constant for this double spring system? Again, give a convincing argument.
Fig 4.15:

c) Now suppose that 3 springs are connected in series, with spring constants k1, k2 and k3. What is the effective spring constant in this case?

d) Compare your formula for springs in series and parallel to the formulas for electrical resistances in series and parallel.

THANK YOU

Homework Equations


F = ks
ka <-- effective spring constant
k <-- spring constant

The Attempt at a Solution


a) equation 1 - F=k1s1 = k2s2
equation 2 - F = ka( s1 + s2)
combined equation: ka = (k1k2)/(k1+k2)

not sure what to do for part b and c and kinda have an idea for part d
 
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  • #2
Hints:

b) each spring produces a different force (if the spring constants are different). Do you know how to add two forces to make one equivalent force?

c) extend your answer for a)

d) How do you add resistors in parallel? Compare with your equation for springs in series.
 
  • #3
for part b) would it be like this:

equation 1: Fnet = k1s + k2s
equation 2: F = kas
combined equation: ka = k1 + k2

Thank you for your help!

CWatters said:
Hints:

b) each spring produces a different force (if the spring constants are different). Do you know how to add two forces to make one equivalent force?

c) extend your answer for a)

d) How do you add resistors in parallel? Compare with your equation for springs in series.
 

Related to Finding effective spring constants

1. What is a spring constant and why is it important in scientific research?

A spring constant is a measure of the stiffness of a spring, or how much force is required to stretch or compress the spring by a certain distance. It is important in scientific research because it allows us to accurately predict the behavior of springs in various systems, such as in mechanical engineering or physics experiments.

2. How do you calculate the spring constant of a given spring?

The spring constant can be calculated by dividing the force applied to the spring by the resulting displacement. This can be represented by the equation F = kx, where F is the force, k is the spring constant, and x is the displacement.

3. What factors can affect the spring constant of a spring?

The spring constant can be affected by the material of the spring, the diameter and length of the spring, and the number of coils in the spring. Temperature can also have an impact on the spring constant, as well as the type of force applied to the spring (e.g. tension, compression).

4. How can the spring constant be adjusted or modified?

The spring constant can be adjusted by changing the material, diameter, length, or number of coils in the spring. Additionally, the spring constant can be modified by altering the environment in which the spring is used, such as changing the temperature or the type of force applied.

5. What are some real-world applications of understanding and finding effective spring constants?

Understanding and finding effective spring constants is important in many fields, including engineering, physics, and biomechanics. It can be useful in designing and building structures, such as bridges or buildings, and in developing new technologies, such as shock absorbers and suspension systems. Additionally, knowledge of spring constants can aid in understanding the behavior of natural systems, such as in studying the movement of animals or the mechanics of plant growth.

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