About spring constant and Hooke's law

In summary, the conversation discusses Hooke's law and the relationship between restoring force and displacement of a spring. It also explores the concept of adding a second force to a spring and how it affects the spring constant and displacement. Ultimately, it is concluded that the spring constant will remain constant for a spring of given dimensions and the displacement will double when a second identical force is applied.
  • #1
KFC
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Hi all,
I am reading an online material on elastic force and Hooke's law on spring. The definition of the Hooke's law reads that the restoring force is linear proportional to the displacement of the spring with constant k. The restoring force is defined as the force bringing the object back to the equilibrium position and k characterize the system's (spring's) nature. So if we have a spring with equilibrium position sitting in the origin of the coordinate so the restoring force F satisfies
$$F = -k x$$
Now, if there is a way to add a second force ($F'$) which is exactly the same as $F$ (same direction and magnitude), since $F'$ is along $F$ all the time, so $F'$ always pointing toward the equilibrium position too. In this sense, should I conclude that
$$F+F' = 2F = -k' x$$
if so, can we say that by adding an additional force $F'$, the spring constant k changed to k'=k/2 ? But I think the spring constant should be given by the spring only, so how does the paradox come from?
 
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  • #2
The spring constant k will be constant for a spring of given dimensions.

If you have a force F applied on the spring such that F = kx and you apply a second identical force then the extension 'x' will just double as well.
 
  • #3
rock.freak667 said:
The spring constant k will be constant for a spring of given dimensions.

If you have a force F applied on the spring such that F = kx and you apply a second identical force then the extension 'x' will just double as well.

Thanks rock. You are right, I totally forget that the displacement should be changed too if I double the force.
 

What is the spring constant?

The spring constant, also known as the force constant, is a measure of the stiffness of a spring. It is represented by the letter "k" and is typically measured in units of newtons per meter (N/m).

What is Hooke's law?

Hooke's law is a principle in physics that states the force exerted by a spring is directly proportional to the distance it is stretched or compressed from its equilibrium position. This relationship is represented by the equation F = -kx, where F is the force, k is the spring constant, and x is the displacement from equilibrium.

How is the spring constant determined?

The spring constant can be determined by measuring the force and displacement of a spring and using the formula F = kx. Alternatively, it can be calculated by dividing the force applied by the displacement produced. The resulting value will be the spring constant.

Is the spring constant the same for all springs?

No, the spring constant can vary depending on the material, shape, and size of the spring. It is a property that is unique to each spring and is affected by factors such as the number of coils, the diameter of the wire, and the type of material used.

What is the significance of the spring constant?

The spring constant is a crucial factor in understanding the behavior of springs and elastic objects. It helps determine how much force is required to stretch or compress a spring, and how much the spring will stretch or compress for a given amount of force. It is also used in various applications, such as designing suspension systems, creating mechanical devices, and measuring forces in experiments.

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