Lesson Notes By Weeks and Term v4 - SHS 3
BASIC PHYSICS
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BASIC PHYSICS
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Subject: Physics
Class: SHS 3
Term: 1st Term
Week: 4
Grade code: 3.1.1.LI.2
Strand code: 1
Sub-strand code: 1
Content standard code: 3.1.1.CS.2
Indicator code: 3.1.1.LI.2
Theme: MECHANICS AND MATTER
Subtheme: BASIC PHYSICS
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We have all observed that when we throw a stone upwards, it comes back down. A ripe mango detaches from its branch and falls to the ground, not into the sky. This ever-present pull towards the Earth is called gravity. But what is it really? Is it just a property of the Earth, or is it something more universal? In this lesson, we will explore the fundamental nature of gravity. We will connect two very important ideas: the force that gives us our weight here in Accra or Tamale (Weight = mg) and the universal force that keeps the Moon orbiting the Earth and the Earth orbiting the Sun (Newton's Law of Universal Gravitation).
This lesson bridges two concepts you have encountered before. Let's review them carefully before we connect them. Concept 1: Weight and Acceleration Due to Gravity (g) From Newton's Second Law of Motion, Force = mass × acceleration (F = ma). When an object is in free fall near the Earth's surface, the force acting on it is its weight (W), and its acceleration is the acceleration due to gravity (g). Therefore, we can write the formula for weight as: `W = m × g` Definition: Acceleration due to gravity (g) is the acceleration experienced by an object in free fall due to the gravitational pull of a large body, like the Earth. Its value is approximately 9.8 m/s² near the Earth's surface. This value is a *local* constant. It changes slightly with altitude and location on Earth (e.g., it's slightly different at the top of Mt. Afadja compared to sea level at Tema). Concept 2: Newton's Law of Universal Gravitation (G) Sir Isaac Newton proposed that gravity is not just an Earthly phenomenon. Every object with mass in the universe attracts every other object with mass. This is a *universal* law. The law states: *The force of gravitational attraction between two point masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.* The formula is: `F_g = (G * M * m) / r²` Where: `F_g` is the gravitational force. G is the Universal Gravitational Constant. It is a fundamental constant of nature and has the same value everywhere in the universe. G ≈ 6.67 × 10⁻¹¹ Nm²/kg². It's a very small number, which is why we don't feel the gravitational pull from everyday objects like our desks or our friends. `M` is the mass of the larger body (e.g., Mass of Earth, `M_E`). `m` is the mass of the smaller body (e.g., your mass). `r` is the distance between the centres of the two masses. The Derivation: Connecting g and G
Now, let's perform the main task of our lesson. We will deduce the relationship by considering an object of mass `m` on the surface of the Earth.
Thinking Process (Enquiry): What is the force pulling this object towards the Earth's centre? We can describe this force in two ways. *Method 1:* We call it the object's weight. From Concept 1, this force is `W = mg`. *Method 2:* We can use the universal law. The force is the gravitational attraction between the Earth (mass `M_E`) and the object (mass `m`). From Concept 2, this force is `F_g = (G * M_E * m) / R_E²`.
Key Insight: These two expressions describe the *exact same force*! The weight of an object on the Earth's surface *is* the gravitational force exerted by the Earth on it. Therefore, we can set them equal to each other.