Further Mathematics - Senior Secondary 3 - Statics

Statics

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TERM: 2ND TERM

WEEK: 1

Class: Senior Secondary School 3
Age: 17 years
Duration: 40 minutes of 4 periods
Subject: Physics
Topic: Statics
Focus: Forces in Equilibrium, Resultant of Parallel Forces, Moment of a Force, Polygon of Forces, Resolution of Forces and Friction.

SPECIFIC OBJECTIVES:
By the end of the lesson, students should be able to:

  1. Define force and understand its effect on a rigid body.
  2. Identify the conditions of equilibrium for forces acting on a body.
  3. Calculate the resultant of parallel forces acting in the same and opposite directions.
  4. Calculate the moment of a force (with 2 and 3 forces acting as a point).
  5. Construct and apply the polygon of forces.
  6. Resolve forces and understand the concept of friction.

INSTRUCTIONAL TECHNIQUES:

  • Question and Answer
  • Demonstration
  • Discussion
  • Guided practice
  • Real-life examples

INSTRUCTIONAL MATERIALS:

  • Whiteboard and markers
  • Charts illustrating components of forces
  • Flashcards of forces and their resolutions
  • Rigid bodies for practical demonstration
  • Worksheets for moment of forces practice

 

PERIOD 1 & 2: Forces in Equilibrium and Resultant of Parallel Forces
PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Introduces the concept of force and equilibrium, explaining that forces are in equilibrium when their vector sum equals zero. Discusses real-life applications of equilibrium.

Students listen attentively and ask clarifying questions.

Step 2 - Forces in Equilibrium

Explains the conditions for equilibrium: ΣFx = 0 (horizontal) and ΣFy = 0 (vertical). Introduces examples of forces acting on a body (e.g., a stationary ladder leaning against a wall).

Students participate in the discussion, ask questions about practical examples of equilibrium.

Step 3 - Resultant of Parallel Forces

Demonstrates the concept of resultant forces for parallel forces acting in the same direction and in opposite directions on a rigid body.

Students observe the example and note the calculations for resultant forces.

Step 4 - Guided Practice

Provides several problems for students to calculate the resultant of parallel forces. Emphasizes forces acting in the same and opposite directions.

Students solve the practice problems individually or in pairs.

NOTE ON BOARD:

  • Forces in Equilibrium: ΣFx = 0, ΣFy = 0
  • Resultant of parallel forces in the same direction: Add the forces.
  • Resultant of parallel forces in opposite directions: Subtract the forces.

EVALUATION (5 exercises):

  1. What is meant by forces in equilibrium?
  2. How do you calculate the resultant of parallel forces acting in the same direction?
  3. How do you calculate the resultant of parallel forces acting in opposite directions?
  4. Give an example of a situation where forces are in equilibrium.
  5. Define the moment of a force.

CLASSWORK (5 questions):

  1. Calculate the resultant of two parallel forces of 5N and 8N acting in the same direction.
  2. Calculate the resultant of two parallel forces of 10N and 6N acting in opposite directions.
  3. If a 6N force acts on a body at an angle of 45°, what is the horizontal component of the force?
  4. Calculate the net force when 3 forces of 2N, 5N, and 6N are acting in the same direction.
  5. A 10N force and a 4N force act in opposite directions. What is the resultant force?

ASSIGNMENT (5 tasks):

  1. Research the conditions of equilibrium in a structure.
  2. Calculate the resultant force when 12N and 7N forces act in opposite directions.
  3. Describe the effect of friction on the equilibrium of a body.
  4. Draw and label a diagram showing forces in equilibrium.
  5. Explain the concept of torque in terms of the moment of a force.

 

PERIOD 3 & 4: Moment of a Force and Resolution of Forces
PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Moment of a Force

Introduces the concept of the moment of a force as the turning effect of a force about a point. Demonstrates how to calculate the moment: Moment = Force × Distance.

Students observe the teacher’s example and take notes on calculating moments.

Step 2 - Moment of 2 and 3 Forces Acting as a Point

Explains the calculation of moments for two and three forces acting on a body. Uses real-life examples such as a seesaw or door.

Students listen to examples and participate in the calculation of moments.

Step 3 - Resolution of Forces

Explains how to resolve a force into its horizontal and vertical components using sine and cosine functions. Provides examples.

Students solve problems involving force resolution, and discuss how components influence motion.

Step 4 - Friction

Introduces the concept of friction as a force that resists motion. Demonstrates how friction can be accounted for in force resolution.

Students participate in the discussion and identify scenarios involving friction.

NOTE ON BOARD:

  • Moment of a force = Force × Distance
  • Resolving forces:
    • Horizontal component: Fx = F cos(θ)
    • Vertical component: Fy = F sin(θ)

EVALUATION (5 exercises):

  1. Calculate the moment of a 10N force acting at a distance of 3 meters from a point.
  2. Resolve a 10N force acting at an angle of 30° into horizontal and vertical components.
  3. What is the moment of a 15N force acting at a distance of 2 meters?
  4. Calculate the moment when two forces of 10N and 5N act at distances of 4 meters and 2 meters, respectively.
  5. Explain the role of friction in force resolution.

CLASSWORK (5 questions):

  1. Calculate the resultant force when two forces of 6N and 8N act at a point.
  2. If a force of 10N is applied at an angle of 45°, resolve the force into its horizontal and vertical components.
  3. Calculate the moment of a force of 20N acting at a distance of 5 meters from the pivot.
  4. What is the moment when two forces of 15N and 25N act at distances of 3 meters and 4 meters?
  5. A force of 6N acts at an angle of 60°. What is the horizontal component?

ASSIGNMENT (5 tasks):

  1. Research a real-life example of a moment of a force.
  2. Solve a practical problem involving friction and force resolution.
  3. Calculate the moment of a 30N force acting 2 meters from the pivot.
  4. Resolve a 20N force acting at 45° into horizontal and vertical components.
  5. Describe how friction affects the equilibrium of a body in motion.