Understanding the Effective Spring Constant When Cutting a Spring in Half

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In summary, the effective spring constant of a spring doubles when it is cut in half because each half of the spring exerts the same force but is only stretched half as much, resulting in a spring constant that is twice the original. This is a basic explanation and the actual constant is dependent on factors such as material, cross-sectional area, and number of turns per unit length.
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DLinkage
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I should probably know this being a college grad w/ 4 years of mechanics, but can anyone give me a clear explanation why the effective spring constant of a spring doubles when you cut the spring in half? I understand physically smaller springs are stiffer but is there a proof someone can give? thanks
 
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Consider this: Stretch the spring a distance X. The tension is the same throughout the spring. Now consider the spring as consisting of two springs (each half as big) hooked together. They exert the same force, but each is only stretched X/2. So the spring constant of each must be twice the original. Make sense?
 
  • #3
So is this to say that if I manufacture springs originally with a length of 1 meter and spring constant k, then if i cut the thing into n equal lengths, the spring constant of each length will be nk?

Obviously I would assume this is only a very basic high level description of a spring and the actual constant is a function ofthe material, cross sectional area, and numbers of turns per unit lenght?
 

What is a simple spring?

A simple spring is a mechanical device that is made up of a coiled or spiral piece of metal, usually steel, that can be compressed or extended to store and release energy. It is commonly used in various applications such as toys, clocks, and shock absorbers.

How does a simple spring work?

A simple spring works by utilizing Hooke's law, which states that the force exerted by a spring is directly proportional to the distance it is stretched or compressed. When a force is applied to a spring, it deforms and stores potential energy. When the force is removed, the spring returns to its original shape and releases the stored energy.

What are the factors that affect the behavior of a simple spring?

The behavior of a simple spring is affected by several factors, including the material it is made of, the diameter and length of the spring, and the number of coils. The stiffness or spring constant of a spring also plays a role in determining its behavior. Additionally, external factors such as temperature and applied force can also affect the behavior of a simple spring.

What are some real-world applications of simple springs?

Simple springs have a wide range of applications in various industries. They are commonly used in mechanical devices such as watches, toys, and shock absorbers. They are also used in machinery and equipment for industries such as automotive, aerospace, and construction. Additionally, simple springs are used in medical devices, such as prosthetics and surgical instruments, and in household items like door handles and furniture.

How can the behavior of a simple spring be changed?

The behavior of a simple spring can be changed by altering its physical properties, such as its material, diameter, and length. Adjusting the number of coils or the applied force can also affect its behavior. In some cases, adding or removing weight from the spring can also change its behavior. Additionally, the addition of other components, such as dampers or shock absorbers, can also alter the behavior of a simple spring.

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