Fisika Kelas 11 Teknik - Besaran Vektor #1 - Resultan 2 Vektor

Introduction

This tutorial is designed to help you understand the concept of resultant vectors, specifically focusing on the addition of two vectors. Understanding how to calculate resultant vectors is essential in physics, particularly in mechanics, and can simplify many complex problems. This guide will break down the process into clear, actionable steps that you can follow along with.

Step 1: Understanding Vectors

• Definition of a Vector: A vector is a quantity that has both magnitude (size) and direction. Examples include displacement, velocity, and force.
• Components of a Vector: Vectors can be broken down into their horizontal and vertical components, which can be represented as:
  • Vector A = (Ax, Ay)
  • Vector B = (Bx, By)

Step 2: Visualizing Vectors

• Graphical Representation: Draw vectors on a coordinate system:
  • Start from the origin (0,0) to represent the initial point.
  • Use arrows to indicate direction and length to represent magnitude.
• Tip: Use a ruler for accuracy and a protractor to ensure angles are correct.

Step 3: Calculating the Resultant Vector

• Resultant Vector Formula: The resultant vector (R) can be found by adding the components of the vectors:
  • R_x = A_x + B_x
  • R_y = A_y + B_y
• Example Calculation:
  • If Vector A has components (3, 4) and Vector B has components (1, 2):
    • R_x = 3 + 1 = 4
    • R_y = 4 + 2 = 6
    • Resultant vector R = (4, 6)

Step 4: Finding the Magnitude of the Resultant Vector

• Magnitude Formula: To find the magnitude of the resultant vector, use the Pythagorean theorem:
  • Magnitude |R| = √(R_x² + R_y²)
• Example:
  • For R = (4, 6):
    • |R| = √(4² + 6²) = √(16 + 36) = √52 ≈ 7.21

Step 5: Determining the Direction of the Resultant Vector

• Direction Formula: The direction (angle θ) can be calculated using the tangent function:
  • θ = tan⁻¹(R_y / R_x)
• Example Calculation:
  • For R = (4, 6):
    • θ = tan⁻¹(6 / 4) ≈ 56.31 degrees

Conclusion

In this tutorial, we covered the fundamental concepts of vectors, how to visualize them, calculate the resultant vector, and determine both its magnitude and direction. Understanding these principles will enhance your grasp of physics and enable you to tackle more complex problems involving vectors. As a next step, practice with different vector pairs to solidify your understanding.