Hooke's Law with Series Springs

In summary, the conversation was about a problem involving the equations F=-kx and k1x1=k2x1. The attempt at a solution resulted in the answer Keq= (k1k2)/(k1+k2), but the person wanted to confirm if their idea was correct. Through further calculations using the equations, the result was simplified to F=-[(k1k2)/(k1+k2)]*x2, leading to the conclusion that Keq = (k1k2)/(k1+k2).
  • #1
maulucci
9
0

Homework Statement



The problem is in the attachment

Homework Equations



F=-kx
k1x1=k2x1

The Attempt at a Solution



I got as my answer Keq= (k1k2)/(k1+k2)

i just wanted to see if i had the right idea or no.
 

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  • #2
Welcome to PF;
i just wanted to see if i had the right idea or no.
... then you need to tell us the idea and not just the final result you got ;)
 
  • #3
-k1x1=-k2x2=F
F=-keq*x
solving for x1
x1=[(k2)/(k1+k2)] +x2
putting into F=-k2x2+k2x1
F=x2 (-k1k2-k2^2+k2^2)/(k1+k2)
simplified
F=-[(k1k2)/(k1+k2)]*x2

then the Keq = (k1k2)/(k1+k2) ?
 

1. What is Hooke's Law with Series Springs?

Hooke's Law with Series Springs is a physical law that describes the relationship between the force applied to a spring and the resulting displacement of the spring. It states that the force applied to a spring is directly proportional to the amount the spring is stretched or compressed.

2. How does Hooke's Law with Series Springs work?

The law works by using a mathematical formula, F = -kx, where F is the force applied to the spring, k is the spring constant, and x is the displacement of the spring. The negative sign indicates that the force and displacement are in opposite directions.

3. What is the spring constant in Hooke's Law with Series Springs?

The spring constant, k, is a measure of the stiffness of a spring and is unique to each spring. It is determined by the material and physical characteristics of the spring, such as its length, thickness, and number of coils.

4. How is Hooke's Law with Series Springs used in real life?

Hooke's Law with Series Springs is used in many real-life applications, such as in the design of suspension systems for cars, in measuring devices like weighing scales, and in the construction of buildings and bridges.

5. What are the limitations of Hooke's Law with Series Springs?

Hooke's Law with Series Springs is only applicable to elastic materials and small deformations. It also assumes that the spring is massless and that the force is applied along the same axis as the displacement. Additionally, the law may not accurately predict the behavior of some materials, such as rubber or foam, which have non-linear relationships between force and displacement.

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