Lesson Notes By Weeks and Term v4 - SHS 2
MATTER
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MATTER
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Subject: Physics
Class: SHS 2
Term: 1st Term
Week: 7
Grade code: 2.1.2.LI.3
Strand code: 1
Sub-strand code: 2
Content standard code: 2.1.2.CS.1
Indicator code: 2.1.2.LI.3
Theme: MECHANICS AND MATTER
Subtheme: MATTER
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This lesson explores the concept of energy stored in elastic materials when they are stretched or compressed. We see this principle in action all around us in Ghana: from the simple rubber band used to tie our *waakye* leaves, to the shock absorbers in a *tro-tro* navigating a bumpy road, to the traditional bow and arrow used for hunting. When we deform an elastic material, we do work on it, and this work is stored as potential energy. Understanding how to calculate this energy is fundamental to engineering, design, and many everyday technologies.
A. Recap: Elasticity and Hooke's Law Before we can talk about the energy stored, let's remember the basics of stretching a material. Elasticity: The ability of a material to return to its original shape and size after a deforming force is removed. Hooke's Law: Within the elastic limit, the force (F) applied to an elastic material is directly proportional to the extension (e) it produces. Mathematically: F ∝ e This gives us the famous equation: F = ke Where: F is the applied force (or load), measured in Newtons (N). e is the extension (the change in length), measured in metres (m). k is the spring constant (or force constant), a measure of the material's stiffness, measured in Newtons per metre (N/m). B. The Load-Extension Graph When we plot the load (Force, F) on the vertical (y-axis) against the extension (e) on the horizontal (x-axis) for a material obeying Hooke's Law, we get a straight line passing through the origin. The Gradient: The gradient (slope) of this graph is Rise/Run = ΔF/Δe, which is equal to the spring constant, k. The Area Under the Graph: This is the most important concept for today's lesson. C. Work Done and Energy Stored To stretch a spring or a rubber band, you must pull on it. This means you are applying a force over a distance. In Physics, applying a force over a distance is called doing work. Work Done (W) = Force (F) × Distance (d)
However, when stretching a spring, the force is not constant. It starts at 0 N and increases to a final force F as you stretch it. Therefore, we must use the average force. Average Force = (Initial Force + Final Force) / 2 Average Force = (0 + F) / 2 = ½ F
The distance over which this average force is applied is the extension, e. So, Work Done in stretching = Average Force × extension W = (½ F) × e = ½ Fe
This work done on the spring is not lost. It is stored within the material as Elastic Potential Energy (Eₚ). D. Deducing Energy Stored from the Graph Now, let's look at the area under our load-extension graph again. The area is a triangle. Area of a triangle = ½ × base × height From the graph, the base is the extension, e. The height is the final load, F. Therefore, Area = ½ × e × F = ½ Fe