Elasticity is the property of a material to return to its original shape and size after the removal of an applied force. It allows materials to undergo temporary deformation without permanent change. Elastic behavior is crucial in applications such as springs rubber bands and other flexible materials in engineering.
Class 11 Physics Chapter 8 investigates the mechanical properties of solids focusing on stress strain and elasticity. It explains how materials deform under various forces and their ability to return to their original shape. Essential topics include Hooke’s law different types of stress and strain and the significance of elasticity in real-world applications.
With knowledge of elasticity, one can follow the following procedure to estimate the maximum height of a mountain on Earth.
1. Understanding Elasticity: The term elasticity has a very clear definition: Elasticity is defined as the capability of a material to deform when a stress is applied and recover its original form after the removal of the applied stress. The crust of Earth acts elastically for some stress ranges.
2. Estimating Stress: The maximum height of a mountain is influenced by the stress exerted by the weight of the mountain itself. This stress can be estimated using the formula:
σ = F / A
where σ is the stress, F is the force (weight of the mountain), and A is the area over which the force is distributed.
3. Material Property: The yield strength of the rock material constituting the mountain is to be considered. If the stress caused by the mountain’s weight exceeds the yield strength, the deformation of the rock is permanent; therefore, the mountain’s height cannot increase beyond that limit.
4. Finding Maximum Height: The maximum height can be found using the formula for stress, strain, and Young’s modulus E (a measure of stiffness). The formula can be written as:
σ = E * ε
where ε is the strain. This can be rearranged as:
ε = σ / E
The change in height (strain) can be approximated by:
Δh = ε * h
where h is the original height before deformation.
5. Setting Up the Calculation: Substituting the values for stress based on the mountain’s mass and area, along with the elastic properties of the rock, you can estimate the maximum height before reaching the elastic limit.
6. Comparative Analysis: Compare the calculated maximum height with known mountain heights, such as Mount Everest, to validate the estimation. Erosion, tectonic activity, and geological history also play a role in actual mountain heights.
In conclusion, through the knowledge of elasticity, a mountain’s height can be approximated by simply calculating the amount of stress which the mountain imposes, the type of material the rocks are made up of, and the strain as a result of this stress.
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