Elastic and Inelastic Deformation

Objects can undergo either elastic or inelastic deformation when subjected to forces.

Definition: Elastic deformation occurs when an object returns to its original shape after the applied force is removed.

Definition: Inelastic deformation occurs when an object does not fully return to its original shape after the applied force is removed.

Examples of elastic objects:

• Springs
• Elastic bands

Examples of inelastic objects:

• Plastic
• Clay

Highlight: The elastic and inelastic deformation in physics concept is crucial for understanding material properties and behavior under stress.

Work Done on a Spring

When a spring is stretched or compressed, work is done, and energy is transferred to its elastic potential energy store. The work done on a spring can be calculated using the equation:

Formula: Ee = ½ × k × x²

Where:

• Ee is the elastic potential energy
• k is the spring constant
• x is the extension

Highlight: This formula only applies to objects that haven't exceeded their limit of proportionality.

Hooke's Law and Extension

Hooke's law is a fundamental principle in physics that describes the relationship between force and extension in elastic objects.

Definition: Hooke's law states that the extension of an elastic object is directly proportional to the force applied, up to the limit of proportionality.

The limit of proportionality is the point beyond which an elastic object may extend but won't return to its original shape when the force is removed. This value varies by material.

Force-Extension Graphs

Force-extension graphs visually represent Hooke's law. These graphs typically show:

1. A linear region where force and extension are directly proportional
2. A non-linear region beyond the limit of proportionality (marked as point P)

Example: In a force-extension graph for a spring, the initial straight line represents the elastic region, while the curved portion indicates the plastic region.

Calculating Spring Constant

The spring constant (k) can be determined from force-extension graphs by finding the gradient:

Formula: k = gradient = ΔF / Δe

Where:

• ΔF is the change in force
• Δe is the change in extension

Highlight: A steeper gradient indicates a larger spring constant, meaning the spring is stiffer.

Changing Shape and Deformation

When multiple forces act on an object, it may undergo deformation through stretching, compressing, or bending. This process transfers energy to the object's elastic potential energy store.

Definition: Deformation refers to a change in an object's shape due to applied forces.

The three main types of deformation are:

1. Stretching: Forces acting in opposite directions away from the object
2. Compressing: Forces acting in opposite directions towards the object
3. Bending: Forces distorting the object's shape

Highlight: Deformation only occurs when two or more forces are applied. A single force would simply cause the object to move.