Restoring force and force constant

Introduction

One might be familiar with the term ‘Force’. Any attraction, friction or repelling movement towards any mass can be termed as a force. Here the topic of restoring force is discussed deeply with all necessary examples. The restoring force is the attraction of the equilibrium point to the mass away from it. The restoring force is also known as Simple Harmonic motion. Generally, it is represented as F=-kx. Robert Hooke first defined this formula. The formula contains a proportionality constant known as the force constant or spring constant. For spring constant, Hooke states that when an object is deformed in a flexible manner, a displacement corresponding to the strain load is proportional.

Restoring force 

As the term refers, restoring force is the attraction of the equilibrium position towards its moving mass to restore the size, shape or position. In simpler words, the restoring force restores the particles to their equilibrium state. This force acts on the particles of mass, which move away from their initial point. E.g., when the pendulum in the clock is switched off, it stops moving and its position is restored at its equilibrium point, i.e., centre. Moreover, restoring force is also termed as Simple Harmonic Motion.

• Simple Harmonic Motion

Firstly, Simple Harmonic Movement is a sort of periodic motion where the particle with restoring force proportional to the displacement of its magnitude acts towards the object’s equilibrium position. 

• Restoring force formula

In the simple harmonic motion formula, restoring force can be denoted as F = -kx, where force is marked as ‘F’ and distance as ‘x’. The ‘k’ is said as a constant of proportionality. This constant is termed as Spring constant. Moreover, the formula has the minus sign and occuring restoring force opposes the displacement of mass and attracts towards the equilibrium position.  

• Restoring force in oscillations

The restoring force is also one main constituent of oscillations. In an oscillating system, a restoring force  constantly pushes towards the equilibrium position. When an object is going towards equilibrium, the restoring force pushes and increases its speed. A simple oscillation can be observed by the particle with restoring force proportional to displacement. 

Force constant 

Force constant is a constant which is used while calculating the restoring force. This force constant is a constant of proportionality and it is termed the Spring constant. Moreover, this constant is generally denoted by ‘k’. This Constant was first represented in Law by Robert Hooke, a British physicist in the 17th century.

• Hooke’s Law 

In a nutshell, Hooke’s Law describes that materials are elastic only when the force and displacement are proportional. This Law is also known by the name ‘Law of elasticity’. Hooke’s Law states that the magnitude of  displacement is proportional to the strain force or load for comparatively modest elastic deformation of an item. The item preserves its shape and size whenever the pressure is released under these conditions. It is also proportional to the applied force that causes minimal displacements of the components, particles or ions from their standard locations. 

Illustrations

• Simple Harmonic Motions

Simple harmonic motions can be observed in day to day activities. For instance, take Bungee Jumping, the bungee cord’s elasticity causes the jumper to oscillate up and down, depicting the Simple Harmonic Motion. 

Similarly, a guitar and other stringed musical instruments also reflect the SHMs. Whenever the string is made displaced and oscillates, its equilibrium point attracts it back, when it returns to its position, its simple harmonic motion.

• Hooke’s Law or Spring constant

If a 15000 Newton force is required to pull a spring 50.0 cm from its equilibrium position, what is the spring constant of the force?

• Firstly, applying general formula of Hooke’s law,

Force = – Spring constant * Distance

Therefore, Spring constant = -ForceDistance 

= -15000 Newton / 0.50 M (50cm = 0.50m)

= -30000 Newton per metres

Though, we can now say that the force 15000 newton away 50 cm from the equilibrium position has the proportionality constant of -30000 newton for restoring force.

Conclusion

We went through all the crucial aspects of restoring force and force constant and looked at some examples. We can now say that the restoring force is the force that attracts any moving mass towards its equilibrium or initial position. Moreover, the formula of restoring force F = -kx has the Constant of proportionality (i.e. ‘k’), often termed Spring constant. The restoring force is also known as simple harmonic motion, which is one of the main constituents of oscillations. We also learned Hooke’s Law, restoring force’s formula and restoring force in oscillations.