Overview
This lecture explains how to use vector diagrams to calculate the resultant force when two forces act on an object at an angle, including step-by-step drawing methods and a sample exam-style problem.
Resultant Forces Recap
- Resultant force is a single force that has the same effect as multiple forces acting together.
- Previous examples considered only parallel forces.
Forces at an Angle
- When two forces act at an angle, a vector diagram helps determine their resultant.
- Example: A 10 N force and an 8 N force at a 30° angle.
Drawing Vector Diagrams
- Choose a scale for your diagram (e.g., 1 cm = 1 N).
- Draw the first force as an arrow from a point (e.g., 10 cm for 10 N).
- Use a protractor to measure the given angle from the first force.
- Draw the second force from the same point at the specified angle (e.g., 8 cm for 8 N).
- Complete the parallelogram by copying and aligning the vectors at their heads.
- Draw the diagonal from the origin point to the opposite corner: this is the resultant force.
- Measure the resultant’s length; convert back to Newtons using your scale.
Example Solution
- For the 10 N and 8 N forces at a 30° angle, the resultant measures 17.5 cm, so resultant force = 17.5 N.
- Exam answers may accept a small range due to measurement variations.
Practice Question Walkthrough
- Given: 280 N and 320 N forces at a 20° angle.
- Scale used: 1 cm = 40 N.
- Draw two vectors (7 cm and 8 cm) at 20°, complete parallelogram, draw diagonal.
- Resultant measured as 14.8 cm, so resultant force = 592 N.
Key Terms & Definitions
- Resultant Force — A single force with the same effect as multiple forces acting together.
- Vector Diagram — A scale drawing showing the direction and magnitude of forces acting at angles.
- Parallelogram Method — Technique of forming a parallelogram to find the resultant of two vectors.
Action Items / Next Steps
- Practice drawing vector diagrams with different scales and angles.
- Review examples in your workbook or assigned materials.
- Prepare for vector diagram questions on exams.