How to Calculate Resultant Forces Using Vector Diagrams

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Understanding Resultant Forces and Vector Diagrams

When multiple forces act on an object, they can be replaced by a single force called the resultant force, which has the same effect. While many examples involve forces acting parallel to each other, this guide focuses on calculating the resultant when forces act at an angle.

Step-by-Step Guide to Using Vector Diagrams

1. Define the Scale

Choose a scale to represent the forces, for example, 1 cm equals 1 Newton.

2. Draw the Forces

  • Draw a free body diagram showing the object as a point.
  • Use a ruler to draw the first force vector to scale (e.g., 10 cm for 10 N).
  • Use a protractor to measure and draw the angle between the forces (e.g., 30°).
  • Draw the second force vector to scale at the correct angle (e.g., 8 cm for 8 N).

3. Construct the Parallelogram

  • Copy the second force vector and place it at the head of the first vector.
  • Copy the first force vector and place it at the head of the second vector.
  • Draw lines to complete the parallelogram.

4. Draw the Resultant Vector

  • Draw a vector from the tail of the first force to the opposite corner of the parallelogram.
  • Measure the length of this vector to find the magnitude of the resultant force.

5. Calculate the Resultant Force

  • Convert the measured length back to Newtons using the scale (e.g., 17.5 cm = 17.5 N).
  • Use a protractor to measure the angle of the resultant force if needed.

Example Problem

Two forces of 10 N and 8 N act at a 30° angle. Using the method above, the resultant force is found to be 17.5 N.

Practice Problem

Calculate the resultant force for two forces of 280 N and 320 N acting at a 20° angle.

  • Choose a scale (e.g., 1 cm = 40 N).
  • Draw vectors to scale and construct the parallelogram.
  • Measure the resultant vector length (e.g., 14.8 cm).
  • Calculate the resultant force (14.8 cm × 40 N/cm = 592 N).

Tips for Exams

  • Draw vector diagrams as accurately as possible.
  • Examiners allow a small range of answers for the resultant force.
  • Use a ruler and protractor for precision.

Additional Resources

For more practice, refer to the Vis Vision workbook linked in the video description, which contains numerous questions on vector diagrams and resultant forces. Additionally, you can explore the following resources for a deeper understanding of related concepts:

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