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: 5
Grade code: 2.1.1.LI.2
Strand code: 1
Sub-strand code: 2
Content standard code: 2.1.1.CS.3
Indicator code: 2.1.1.LI.2
Theme: MECHANICS AND MATTER
Subtheme: MATTER
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This lesson introduces the fundamental concept of vectors and how to combine them to find a 'resultant' vector. In our daily lives in Ghana, we constantly deal with quantities that have both size (magnitude) and direction. Think about giving directions to a friend to find your house: "Walk 100 metres towards the market, then turn right and walk 50 metres." Each part of that instruction is a vector. Understanding how to combine these movements helps us in fields like navigation (a fisherman on the Volta Lake), engineering (building our roads and bridges), and even sports (predicting the path of a football).
2.1. Scalars and Vectors In Physics, we classify physical quantities into two main groups: Scalars: These are quantities that have magnitude (size) only. They are fully described by a number and a unit. *Ghanaian Examples:* The mass of a bag of gari (e.g., 5 kg). The price of a ball of kenkey (e.g., GHS 3.00). The time it takes for a tro-tro to travel from Kaneshie to Circle (e.g., 20 minutes). The temperature in Bolgatanga (e.g., 35°C). Vectors: These are quantities that have both magnitude and direction. To describe them fully, you need a number, a unit, and a direction. *Ghanaian Examples:* The velocity of a car travelling on the Accra-Tema motorway (e.g., 80 km/h East). The force a student uses to push a desk (e.g., 25 N forward). The displacement of a student walking from the classroom to the science lab (e.g., 150 m due North). The acceleration due to gravity (9.8 m/s² downwards).
We represent a vector graphically with an arrow. The length of the arrow represents the magnitude. The arrowhead points in the direction of the vector. 2.2. The Resultant Vector Often, an object is acted upon by more than one vector at the same time. For example, two people might be pushing a heavy cart. The Resultant Vector is the single vector that has the same effect as all the individual vectors acting together. It is the sum or combination of two or more vectors.
We will learn two methods to find the resultant of two vectors, A and B. Method 1: Graphical Method (Triangle Law of Vector Addition) This method uses a ruler and a protractor to draw the vectors to scale. It is also known as the "head-to-tail" method.
Steps: Choose a suitable scale: Convert the magnitude of the vectors into a manageable length (e.g., 1 cm = 10 N, or 1 cm = 5 m). Draw the first vector: Using your ruler and protractor, draw the first vector (A) to scale and in the correct direction. Draw the second vector: From the head (tip) of the first vector, draw the second vector (B) to scale and in its correct direction. Draw the Resultant: The resultant vector (R) is the line drawn from the tail (start) of the first vector to the head (tip) of the final vector. Measure the Resultant: Use your ruler to measure the length of the resultant vector R. Convert this length back to the original units using your scale to find its magnitude. Use your protractor to measure the angle the resultant vector R makes with a reference direction (e.g., the horizontal or North). This is its direction.