Solving resultant vectors graphically involves drawing the vectors to scale and measuring the resulting vector.
The graphical method for finding the resultant vector (the sum of two or more vectors) is a visual way to understand vector addition. It's based on the principle of connecting vectors head-to-tail. While less precise than analytical methods, it offers a clear picture of the vector sum.
Here's how you do it:
Steps to Find the Resultant Vector Graphically
The process involves two main steps, as described in the provided reference:
-
Step 1: Draw the first vector, then join the initial point of each subsequent vector with the terminal point of the previous vector.
- Begin by selecting a suitable scale (e.g., 1 cm represents 10 Newtons or 10 meters).
- Draw the first vector starting from an origin point. Ensure its length corresponds to its magnitude based on your chosen scale, and draw it in the correct direction.
- For the second vector, start its initial point (tail) from the terminal point (head) of the first vector. Draw it to scale and in its correct direction.
- Continue this process for all subsequent vectors, always connecting the tail of the new vector to the head of the previous one. You are essentially creating a chain of vectors.
-
Step 2: Find the resultant vector, or the vector sum, by drawing a vector from the initial point of the first vector to the terminal point of the last vector we added.
- Once all vectors are drawn head-to-tail, draw a new vector that starts exactly where your first vector began (the initial origin point) and ends precisely where your last vector finished (the terminal point of the final vector drawn).
- This newly drawn vector is the resultant vector. Its length represents the magnitude of the resultant (using your scale), and its direction (angle relative to a reference axis like the positive x-axis) is its direction.
Practical Tips for Accuracy
- Use a ruler to measure vector lengths precisely according to your chosen scale.
- Use a protractor to draw vectors at their correct angles.
- Use graph paper for better alignment and measurement.
- Choose a scale that allows the vectors to fit comfortably on your drawing surface while being large enough for accurate measurement.
Example
Imagine you have two vectors:
- Vector A: 3 units East
- Vector B: 4 units North
- Step 1:
- Draw Vector A, 3 units long, pointing East.
- From the head of Vector A, draw Vector B, 4 units long, pointing North.
- Step 2:
- Draw the resultant vector from the starting point of Vector A to the ending point of Vector B. You will see this forms the hypotenuse of a right triangle.
- Measure the length of this resultant vector with your ruler (it should be approximately 5 units) and measure its angle with your protractor (it should be approximately 53.1 degrees North of East).
The graphical method is intuitive and helpful for visualization, especially for two or three vectors. However, its accuracy is limited by the precision of your drawing tools and measurements.
