Overview
This lecture explains how to add more than two vectors using the polygon method, illustrated with a sample problem involving four force vectors.
Methods of Vector Addition
- Vectors can be added using the parallelogram method, polygon method, or component method.
- The polygon method is used when adding three or more vectors tip-to-tail.
Sample Problem Setup
- Four forces act on a particle:
- Force 1: 10 N, 45° north of east
- Force 2: 5 N, 10° south of east
- Force 3: 6 N, east
- Force 4: 6 N, 20° south of west
- Scale used: 0.5 cm represents 1 N on the drawing.
Steps in Polygon Method
- Draw Cartesian plane to guide vector directions.
- Draw each vector tip-to-tail using given magnitude, direction, and correct scale.
- After drawing all vectors sequentially, the closing vector from start to end represents the resultant.
- Measure the resultant vector's magnitude and direction with respect to the east axis.
- In the example, the resultant vector measures 13 N at 18° north of east.
Analyzing the Resultant Vector
- The resultant force indicates the net effect of all individual forces on the particle.
- The particle will move in the direction of the resultant: 13 N, 18° north of east.
Key Terms & Definitions
- Vector Addition — The process of combining multiple vectors to get a single vector (the resultant).
- Polygon Method — A graphical method for adding vectors by connecting them tip-to-tail.
- Resultant Vector — The single vector that has the same effect as all the original vectors combined.
Action Items / Next Steps
- Practice drawing vector addition using the polygon method with different example problems.
- Prepare for the next lesson on vector addition using the component method.