Overview
This lecture explains how to use scale drawings to find the resultant force of vectors, how to determine vector equilibrium, and how to resolve vectors into components.
Using Scale Drawings to Find Resultant Force
- Forces can be represented as arrows on a grid, with each arrow’s length proportional to the force (e.g., 1 cm = 1 N).
- Place force vectors tip-to-tail to find the resultant force.
- Draw a straight line from the starting point to the end point to represent the resultant force.
- Measure the resultant line’s length with a ruler and convert it to newtons using the scale.
- Example: 4 N north and 3 N east create a resultant of 5 N at 37° from north.
Determining Equilibrium with Vectors
- An object is in equilibrium if all acting force vectors, arranged tip-to-tail, form a closed shape (e.g., triangle).
- If the vectors join up perfectly, there is zero resultant force.
- The order of arranging vectors tip-to-tail does not affect the result.
Resolving Vectors Into Components
- Resolving a vector means breaking it into horizontal and vertical components.
- Use a scale drawing with the given force at the appropriate angle.
- Draw horizontal and vertical lines from the tip of the vector to form a right triangle.
- Measure the lengths of these lines and convert them to newtons using the scale.
- Example: A 50 N force at an angle becomes 40 N horizontally and 30 N vertically when resolved.
Key Terms & Definitions
- Resultant Force — The single force that has the same effect as all the original forces combined.
- Equilibrium — A state where all forces on an object balance, resulting in zero resultant force.
- Resolving a Vector — Splitting a force into its horizontal and vertical components.
- Scale Drawing — A diagram where distances represent magnitudes of forces according to a consistent scale.
Action Items / Next Steps
- Practice drawing and measuring vector diagrams to calculate resultant forces.
- Try resolving various vectors into their components using scale drawings.