Lesson Notes By Weeks and Term v4 - SHS 3
KINEMATICS
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KINEMATICS
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Subject: Physics
Class: SHS 3
Term: 1st Term
Week: 13
Grade code: 3.1.2.LI.4
Strand code: 1
Sub-strand code: 2
Content standard code: 3.1.2.CS.1
Indicator code: 3.1.2.LI.4
Theme: MECHANICS AND MATTER
Subtheme: KINEMATICS
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This lesson explores the energy transformations that occur in a system undergoing Simple Harmonic Motion (SHM). We see SHM all around us in Ghana – a child on a playground swing at the park, the gentle swaying of a palm tree in the wind, or even the vibrations of a guitar string. Understanding the energy of these systems is crucial because it connects to the fundamental principle of conservation of energy. We will learn how energy is constantly converted between potential and kinetic forms, and how to calculate the total energy of the system. This knowledge is key to understanding everything from how clocks keep time to how a car's suspension system handles our bumpy roads.
Recap: What is SHM? Before we discuss energy, let's remember the two conditions for SHM: The acceleration of the object is directly proportional to its displacement from the equilibrium position. The acceleration is always directed towards the equilibrium position. This is summarised by the equation: F = -kx, where `F` is the restoring force, `k` is the force constant, and `x` is the displacement. Energy in a Mass-Spring System Imagine a block of mass `m` attached to a horizontal spring with a spring constant `k`. When we pull or push the block and release it, it oscillates back and forth. This system has two types of energy: Potential Energy (PE) This is the energy stored in the spring due to its compression or extension. We call it Elastic Potential Energy. Derivation (from the Load-Extension Graph): Recall from Hooke's Law that the force `F` needed to stretch a spring by an extension `x` is `F = kx`. The work done in stretching the spring is stored as potential energy. This work done is equal to the area under the Force-Extension graph.
The area of the triangle is ½ × base × height. Area = ½ × x × F Since F = kx, we substitute it into the equation: Work Done = PE = ½ × x × (kx)
> Potential Energy (PE) in SHM: > PE = ½kx²
Where: `PE` is the potential energy in Joules (J). `k` is the spring constant in Newtons per metre (N/m). `x` is the displacement from the equilibrium position in metres (m).