Resolving a Single Force Using Vector Diagrams

Overview

• Objective: Use vector diagrams to resolve a single force into two component forces.
• Audience: Higher-tier students.

Key Concepts

Vector Diagrams for Forces

• A vector diagram can show how a force can be split into components.
• Components are parts of the force acting in different directions, typically horizontal (x-direction) and vertical (y-direction).

Types of Forces

• Horizontal Force: Entirely in the horizontal direction.
• Vertical Force: Entirely in the vertical direction.
• Diagonal Force: Has both horizontal and vertical components.

Steps to Resolve a Force

1. Identify Force Direction

   • Determine the angle of the force relative to the horizontal.

2. Draw Axes

   • Use x and y-axes to determine the direction of the components.

3. Draw Force Vector

   • Scale the vector diagram (e.g., 1 cm = 10 Newtons).
   • Measure the angle of the force using a protractor.
   • Draw the vector representing the force using a ruler.

4. Determine Components

   • Draw dotted lines from the vector head to the axes to create a right-angled triangle.
   • Draw horizontal and vertical components along the axes.

5. Measure and Calculate

   • Measure the length of each component using a ruler.
   • Calculate the magnitude using the scale.

Example Problem

• Force: 100 Newtons
• Angle: 35 degrees with the horizontal

Solution Steps

1. Scale: 1 cm = 10 Newtons
2. Draw Vector: 10 cm length for 100 Newtons at 35 degrees.
3. Measure Components:
   • Horizontal component: 8.3 cm (83 Newtons)
   • Vertical component: 5.7 cm (57 Newtons)

Practice Problem

• Force: 75 Newtons
• Angle: 20 degrees with the horizontal

Solution Steps

1. Scale: 1 cm = 10 Newtons
2. Draw Vector
3. Measure Components:
   • Horizontal component: 7 cm (70 Newtons)
   • Vertical component: 2.5 cm (25 Newtons)

Additional Resources

• For more practice, refer to the revision workbook available from the provided link.