Proof of the stiffness of the horizontal component of a spring

In summary, the problem involves finding the equivalent stiffness of a horizontal spring separated by a certain angle from the original spring with force F=k*z. The horizontal equivalent is expected to have a force F(x)=k(x)*x, and after substituting equations F=k*z, F = F(x)*cos(theta), and x=z*cos(theta) into the equation F(x)=k(x)*x, the resulting equation is k = k(x)*cos^2(theta). However, the correct answer is k(x)=k*cos^2(theta), indicating that the horizontal equivalent stiffness is smaller than k. A schematic would be helpful in clarifying the problem.
  • #1
jonathan308
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Homework Statement



Suppose a spring with forces F=k*z. Find the equivalent stiffness of a horizontal spring, where the spring and its horizontal equivalent is separated by theta degrees. The horizontal equivalent presumably will have a force F(x)=k(x)*x

Homework Equations



F = F(x)*cos(theta)
x = z*cos(theta)

The Attempt at a Solution



I have try to substitute F=k*z, F = F(x)*cos(theta) and x=z*cos(theta) into the equation F(x)=k(x)*x, but i only end up with a equation k = k(x)*cos^2(theta). The answer should be k(x)=k*cos^2(theta) and it only makes sense if the horizontal equivalent of stiffness is smaller than k. Please help and point out where I have made a mistake. thanks :)
 
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  • #2
Welcome!
Could you show any schematic?
 

Related to Proof of the stiffness of the horizontal component of a spring

What is proof of the stiffness of the horizontal component of a spring?

Proof of the stiffness of the horizontal component of a spring refers to the process of confirming the stiffness or spring constant of a spring in the horizontal direction. This is an important factor in understanding the behavior and properties of a spring.

Why is proof of stiffness important in studying springs?

Proof of stiffness is important in studying springs because it helps determine the amount of force required to compress or stretch a spring in the horizontal direction. This information is crucial in designing and using springs for various purposes, such as in mechanical systems and devices.

How is proof of stiffness measured?

Proof of stiffness is typically measured by applying a known force to a spring and measuring the resulting displacement in the horizontal direction. This data is then used to calculate the spring constant, which is a measure of the stiffness of the spring.

What factors can affect the stiffness of the horizontal component of a spring?

The stiffness of the horizontal component of a spring can be affected by various factors, such as the material and thickness of the spring, the number of coils, and the temperature. These factors can alter the spring constant and therefore impact the stiffness of the spring.

Are there any practical applications of understanding the stiffness of the horizontal component of a spring?

Yes, understanding the stiffness of the horizontal component of a spring has many practical applications. It is essential in designing and optimizing mechanical systems, such as suspension systems in vehicles, and in creating accurate models for predicting the behavior of springs in various situations.

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