Overview
The lecture explains how to solve a vector addition problem using the polygon method, specifically with two forces acting on a particle.
Problem Setup
- Two forces act on a particle: Force A (3 N, north) and Force B (4 N, 30° north of east).
- The goal is to find the resultant force using the polygon (head-to-tail) method.
Step-by-Step Solution Using Polygon Method
- Assign a scale: 1 cm on the ruler represents 1 newton of force.
- Draw vector A as a 3 cm line pointing straight north on a Cartesian plane.
- For vector B (4 N, 30° north of east), measure 30° from east using a protractor at the tip of vector A.
- Draw a 4 cm line from the tip of vector A at the 30° angle to represent vector B.
- The resultant vector (R) is drawn from the starting point of vector A to the tip of vector B.
- Measure the length of the resultant vector; it is 6 cm, so the magnitude is 6 N.
- Measure the angle of the resultant vector from the east; it is 55°.
- Final resultant: 6 N, 55° north of east.
Key Concepts in Vector Addition
- Polygon method (head-to-tail): The next vector starts from the tip of the previous vector.
- Closure of the diagram represents the resultant vector.
- Resultant direction is measured from a reference axis (usually east).
- For two or more vectors: resultant = vector 1 + vector 2 [+ vector 3 + ...].
Key Terms & Definitions
- Vector — a quantity with both magnitude and direction.
- Resultant Vector — a single vector representing the sum of two or more vectors.
- Polygon (Head-to-Tail) Method — a technique where vectors are drawn one after another from tip to tail to find their sum.
Action Items / Next Steps
- Practice vector addition using the polygon method with problems involving more than two vectors.