# Hooke’s Law

### Introduction to Hooke’s Law

• Hooke’s Law is a principle in physics that states the force (F) needed to extend or compress a spring by some distance (x) is proportional to that distance.

• This law applies to ideal springs and other elastic objects. As per this law, such objects will return to their original shape once the force applied to them is removed.

### Formula of Hooke’s Law

• The mathematical representation of Hooke’s Law is F = -kx, where:
• F is the force applied,
• x is the displacement of the spring from its equilibrium position,
• k is the spring constant,
• The negative sign indicates that the force exerted by the spring is in the opposite direction to its displacement.
• The spring constant (k) measures the stiffness of a spring. Its value depends on the material from which the spring is made and the tightness of the coil. It is measured in N/m (newtons per metre).

### Limits of Hooke’s Law

• Hooke’s Law is not limitless. There is a point known as the elastic limit, beyond which the law is no longer valid as the material will no longer return to its original shape when the stress is removed.

• If the elastic limit is surpassed, the material is said to be in the plastic stage and will permanently deform.

### Applications of Hooke’s Law

• Hooke’s Law plays a central role in elastic potential energy calculations. The potential energy (E) stored in an elastic spring is given by the equation E = 0.5kx².

• It finds wide applications in diverse fields such as mechanical engineering, material science, and even in understanding biological systems and structures.

### Understanding Hooke’s Law

• Familiarise with the key variables in the equation and how they interact. Increasing the displacement of the spring (x) will increase the force required (F), assuming the spring constant (k) remains the same.

• Be aware that not all materials obey Hooke’s Law. For such materials, their stress-strain graph won’t be a straight line passing through the origin.

• In exam questions, you may have to rearrange the equation to solve for one of the variables when given the values for the others.

• Understand the difference between the elastic and plastic phases of a material - it is crucial for predicting how a material will behave under stress.

Mastering Hooke’s Law and its applications builds a critical foundation for exploring more complex areas of mechanics. It helps shape your understanding of how objects behave under different forces and conditions, which is the essence of mechanical behaviour.