Overview
This lecture covers how to use vector diagrams to resolve a single force into two perpendicular components, specifically horizontal (x-direction) and vertical (y-direction) forces.
Resolving Forces Using Vector Diagrams
- A force can act entirely in the horizontal or vertical direction, or at an angle with components in both.
- When a force acts at an angle, it can be broken into horizontal (x) and vertical (y) components.
- The two components must be at right angles (perpendicular) to each other.
- To resolve a force, draw a vector diagram to scale showing its direction and magnitude.
Example Problem: 100 N Force at 35°
- Draw axes and use a protractor to mark the 35° angle from the horizontal.
- Use a scale (e.g., 1 cm = 10 N) to draw the 100 N force (10 cm long).
- Draw dotted lines from the head of the force vector to the axes to form a right triangle.
- Measure the length of the horizontal and vertical components on the diagram.
- Horizontal component: 8.3 cm = 83 N; vertical component: 5.7 cm = 57 N.
Practice Problem: 75 N Force at 20°
- Draw the vector at 20° to the horizontal using the same scale.
- Draw dotted lines to the axes and measure the component lengths.
- Horizontal component: 7 cm = 70 N; vertical component: 2.5 cm = 25 N.
Tips for Exams
- Remove any faint construction lines in the final answer, showing only the vectors.
- Clearly label magnitudes for both components in your diagram.
Key Terms & Definitions
- Resolve a Force — To split a force into two perpendicular components (horizontal and vertical).
- Vector Diagram — A scaled drawing showing the direction and magnitude of forces.
- Component — One part of a force acting in a specific direction (usually x or y).
Action Items / Next Steps
- Practice drawing and resolving forces using vector diagrams.
- Try more questions on resolving forces from the recommended workbook.