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.

Using Hooke's Law

Hooke's Law is expressed by the equation:

Formula: F = k × e

Where:

• F is the force (in Newtons, N)
• k is the spring constant (in Newtons per meter, N/m)
• e is the extension (in meters, m)

Vocabulary: Extension is calculated by subtracting the original length from the final length of the object.

Solving Hooke's Law Problems

To solve problems using Hooke's Law:

1. List known quantities
2. Write down and rearrange the relevant equation
3. Calculate extension (final length - original length)
4. Convert units if necessary
5. Substitute values into the equation

Highlight: Pay attention to units when solving Hooke's Law problems. The standard units are meters for length and Newtons per meter for spring constant.

Example: When calculating the spring constant using force extension graphs, ensure that you convert centimeters to meters by dividing by 100.

This comprehensive guide provides a solid foundation for understanding Hooke's law force extension relationship and related concepts in physics, suitable for GCSE and KS3 level students.