# Elasticity

## Overview

Welcome to the course material on Elasticity in Physics. This topic delves into the fascinating world of materials and their response to external forces. Understanding elasticity is crucial as it helps us comprehend how materials deform and return to their original shape when forces are applied and removed.

One of the key aspects covered in this topic is the force-extension curve, which provides valuable insights into a material's behavior under stress. This curve typically illustrates the relationship between applied force and resulting extension, showcasing important points such as the elastic limit, yield point, and breaking point. These critical points help us determine the maximum stress a material can endure before permanent deformation occurs.

Hooke's Law is another fundamental concept within elasticity that states the extension of a material is directly proportional to the applied force, as long as the elastic limit is not surpassed. This law is pivotal in understanding how materials behave within their linear elastic range and is often expressed as F = kx, where F is the force applied, x is the extension, and k is the material's stiffness constant.

Furthermore, Young's Modulus is a crucial parameter for materials, representing their stiffness and ability to withstand deformation. It quantifies the ratio of stress to strain in a material and is a key characteristic used to compare the elasticity of different substances.

Practical measurements of force are often carried out using a spring balance, a device specifically designed for measuring forces through the extension of a spring. By utilizing the principles of elasticity, spring balances provide accurate force measurements, making them indispensable tools in physics laboratories.

When studying springs and elastic strings, it is essential to calculate the work done per unit volume in these elements. Work done in such structures plays a significant role in understanding energy transfer and deformation processes, providing valuable insights into the behavior of elastic materials.

In conclusion, the topic of Elasticity offers a profound understanding of how materials respond to external forces, highlighting key concepts such as force-extension curves, Hooke's Law, Young's Modulus, and practical force measurement techniques using spring balances. By mastering these concepts, we can explore the intricate world of material science and its implications in various fields of physics and engineering.

## Objectives

1. Use Spring Balance to Measure Force
2. Interpret Force-Extension Curves
3. Interpret Hooke’s Law and Young’s Modulus of a Material
4. Determine the Work Done in Spring and Elastic Strings

## Lesson Note

Elasticity is a fundamental concept in physics that describes the ability of a material to return to its original shape and size after the removal of a force that causes deformation. Materials that exhibit high elasticity can stretch or compress significantly and then return to their original shape without permanent deformation. This ability is crucial in a wide range of applications, from everyday objects like rubber bands to sophisticated engineering materials like those used in building bridges.

## Lesson Evaluation

Congratulations on completing the lesson on Elasticity. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.

You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.

Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.

1. What is the term used to describe the point beyond which a material will not return to its original shape once the deforming force is removed? A. Elastic limit B. Yield point C. Breaking point D. Young's modulus Answer: C. Breaking point
2. Which law states that the extension of a material is directly proportional to the applied force within the elastic limit? A. Hooke's law B. Newton's law C. Boyle's law D. Ohm's law Answer: A. Hooke's law
3. Which device is commonly used to measure force by utilizing the extension or compression of a spring? A. Barometer B. Hydrometer C. Spring balance D. Thermometer Answer: C. Spring balance
4. What is the physical quantity that measures the amount of energy transferred to a material when work is done on it per unit volume? A. Pressure B. Density C. Young's modulus D. Strain energy density Answer: D. Strain energy density
5. Which physical quantity describes the ratio of stress to strain in a material and indicates its stiffness? A. Elastic limit B. Hooke's constant C. Young's modulus D. Strain energy Answer: C. Young's modulus

## Past Questions

Wondering what past questions for this topic looks like? Here are a number of questions about Elasticity from previous years

Question 1

(a)(i) State Hooke's law. (ii) A spring has a length of 0.20 m when a mass of 0.30 kg hangs on it, and a length of 0.75 nm when a mass of 1.95 kg hangs on it. Calculate the: (i) force constant of the spring; (ii) length of the spring when it is unloaded. [g = 10m/s$$^2$$]

(b)(i) What is diffusion? (ii) State two factors that affect the rate of diffusion of a substance. (iii) State the exact relationship between the rate of diffusion of a gas and its density.
(c) A satellite of mass, m orbits the earth of mass. M with a velocity, v at a distance R from the centre of the earth. Derive the relationship between the period T, of orbit and R.

Question 1

A piano wire 50 cm long has a total mass of 10 g and its stretched with a tension of 800 N. Find the frequency of the wire when it sounds its third overtone note.

Question 1

The work done in extending a spring by 40 mm is 1.52J. Calculate the elastic constant of the spring.

Practice a number of Elasticity past questions