Spring Constant

According to Hooke’s law, the force required to compress or extend a spring is proportional to the distance .The elasticity of the spring will return to its original state when the external force, no matter how large, is removed. The amount of mechanical energy stored and used by the spring at that time is related to power and displacement — when the spring is pulled hard, it slows down.

The restoring force, F, of the extended spring is proportional to its length. This expandable behavioral relationship is known as Hooke’s law and is defined by

F = -kx

 Where k is a called spring constant, 

Spring Strength = – (Spring Constant) × (Migration)

A negative sign indicates that the reaction force is moving in the opposite direction.

F: restoring force

K: Spring constant in N.m-1.

X: distance from its equilibrium.

What is the spring constant? 

Spring constant is a spring measure that measures the amount of force affecting the spring and the movement caused by it. In other words, it describes how strong the spring is and how long it will stretch or press.

The spring constant can be determined based on four parameters:

• Wire diameter: the width of the wire that covers the spring
• Coil diameter: the width of each coil to measure the density of the coil
• Free length: spring length at rest
• Number of active coils: the number of coils that are free to increase and decrease
• Spring Element: The elements that make up the spring also play a role in determining the stability of spring, as well as other visible structures of spring.

Spring constant is now defined as the energy required for each spring expansion unit. Knowing regularly in the spring allows you to easily calculate how much energy is needed to disable the spring.

From Hooke’s law,

F = -KX

K = -F / X ⇢ (1)

The unit of force constant  is N / m (Newton meter).

Spring Constant Dimensional Formula

As is well known,

F = -KX

Therefore, K = -F / X

Dimensional formula of force is [MLT-2]

Dimensional formula of distance [L]

Therefore, the dimensional formula of K = [MLT-2] / [L] = [MT-2].

Solving problems related to Spring Constant

When solving any physics problem, point to the question, the information provided, and the math that you need to use. Let’s apply this approach to the ongoing spring crisis.

You hang a spring in the ring area and use 20N power upside down. If spring is a 0.1m shift, what is the spring constant for this spring?

Let’s apply the strategy we just discussed to this issue:

What do you want? Spring constant.

What information is provided? 10N power, as you pull down the spring, and displacement of 0.1m.

Which equation should you use? F = -kx.

You know the ongoing equation of spring, but you need to redesign it to resolve the continuous spring:

F = -kx

k = -F / x

Now, connect the values ​​and resolve:

k = – (- 10N) * 0.1m

k = 1N / m. 

Another solved example

—What is the spring constant of a spring that needs a force of 5 N to be compressed from 50 cm to 45 cm?

Ans:

        The spring changes from a length of 50 cm to 45 cm, hence it compresses

 50 cm – 45 cm = 5 cm Δx = 5 cm = 0.05 m

Now you know how to solve questions related to spring constant. 

Conclusion

We can conclude by saying that the spring constant is a value used for the calculation of certain functions based on Hooke’s law. There are various criteria to be followed which now you have understood, so this will help you in your further studies.