Spring Constant Formula

Spring Constant Formula

SHM, or simple harmonic motion, is an intriguing kind of motion. It is frequently applied to objects moving in oscillatory motion. Springs frequently contain SHM. Springs have “spring constants” built into them that specify how stiff they are. A well-known law called Hooke’s law gives an explanation of the SHM and a formula for the applied force using the spring constant.

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Hooke’s Law

The force necessary to compress or extend a spring is inversely proportional to the length stretched, according to Hooke’s law. Newton’s Third Law of Motion states that a spring will return with a restoring force after being pulled. Hooke’s Law, which connects spring force to constant spring force, is followed by this restoring force.

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Spring Constant (K)

The force required for each unit of spring extension is now the definition of the spring constant. Calculating the amount of force necessary to deform the spring is simple when you know the spring constant.

From Hooke’s law,

F = -KX

K = -F/ X ⇢ (1)

Equation (1) is a formula for the spring constant, and it is measured in N/m (Newton per meter).

Spring Constant Dimensional Formula

F = -KX

Therefore, K = -F/ X

Dimension of F = [MLT-2]

Dimension of X = [L]

Therefore, dimension of K = [MLT−2]/[L] = [MT−2].

Potential Energy of a Spring (P.E.)

The term “spring potential energy” describes the energy held within a compressible or stretchable object. Elastic potential energy is another name for it. It is determined by multiplying the force by the distance.

Limitations of Hooke’s law

A restriction of Hooke’s Law is that it is only applicable within the elastic limit of any material, which implies that for a material to obey Hooke’s Law, it must be completely elastic. In essence, Hooke’s law fails past the elastic limit.

Disadvantages of Applying Hooke’s Law

The shortcomings of Hooke’s law are as follows:

  • Only the elastic region is applicable to Hooke’s Law; after that, it breaks down.
  • Only solid bodies subjected to modest forces and deformations produce accurate results according to Hooke’s Law.
  • In general, Hooke’s Law does not apply.

Applications of Hooke’s Law

  • Hooke’s Law is most frequently used in the springtime because of the elasticity of springs.
  • They are employed not just in engineering, but also in the study of medicine.
  • It is utilised in the skin, lungs, spring beds, diving boards, and suspension systems in automobiles.
  • The manometer, spring scale, and clock balance wheel all operate on this basic tenet.
  • It also serves as the foundation for acoustics, molecular mechanics, and seismology.

Sample Problems

  1. What is the Spring Constant defined as?

Ans. According to Hooke’s Law, when a spring is stretched, the force applied is proportional to the lengthening from the equilibrium length. The formula k = -F/x, where k is the spring constant, can be used to determine the spring constant. F stands for force, and x for the variation in spring length.

2. How Does the Spring Constant Change with Length?

Ans. Consider a 6 cm spring with a k-value for the spring constant. What happens if the spring is split into two pieces of the same size? The new spring constant for one of these shorter springs will be 2k. Assuming a specific spring material and thickness, a spring’s spring constant is typically inversely proportional to the spring’s length.

Consider the spring in the previous example is cut exactly in half to produce two shorter springs that are each 3 cm long. A spring constant that is twice as large as the original will be used for the smaller springs. This occurs as a result of the fact that it is inversely proportional to the spring length and constant.

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