Vector_of_Force_Expanded............pptx

Vector force

1. Vector of Force Concept, Background, Examples, and Applications

2. Introduction to Vector of Force • Force is a vector quantity with both magnitude and direction. • Resultant force determines an object's motion. • Applications include engineering, sports, and transportation.

3. Why Study Vector Forces? • Predicting Motion: Determine acceleration, deceleration, or direction change. • Practical Applications: Essential in designing structures, vehicles, and machines. • Problem Solving: Simplifies complex force systems.

4. Basic Definitions • Force: A push or pull on an object. • Vector: A quantity with both magnitude and direction. • Resultant Force: Combined effect of all forces acting on an object.

5. Vector Representation • Represented by arrows: - Length = Magnitude - Direction = Direction of force • Notation: F = (Fx, Fy)

6. Components of Force • Horizontal (x) and Vertical (y) Components • Calculated using trigonometry: - Fx = F cos(θ) - Fy = F sin(θ)

7. Example 1: Finding Components A force of 50 N acts at 30° above the horizontal. • Calculate the x and y components. • Fx = 50 cos(30°) • Fy = 50 sin(30°)

8. Solution to Example 1 • Fx = 50 cos(30°) = 43.3 N • Fy = 50 sin(30°) = 25.0 N • Components: (43.3, 25.0)

9. Resultant Force • The combined effect of all forces acting on an object. • Found using vector addition: - Rx = Σ Fx - Ry = Σ Fy

10. Example 2: Calculating Resultant Two forces act on an object: • 30 N to the right • 40 N at 60° above the horizontal • Find the resultant force and direction.

11. Solution to Example 2 • Resolve forces into components: - Fx1 = 30 N, Fy1 = 0 - Fx2 = 40 cos(60°), Fy2 = 40 sin(60°) • Add components: - Rx = 30 + 20 = 50 N - Ry = 0 + 34.64 = 34.64 N

12. Magnitude and Direction • Resultant Magnitude: - R = √(Rx² + Ry²) = 60.83 N • Direction: - θ = tan⁻¹(Ry / Rx) = 34.99° above horizontal