Topic Eight (1.8): Resolving Vectors

Introduction

Resolving force vectors is the opposite of adding forces, you will be given the diagonal resultant force vector and be required to work out the pair of forces at right angles. Just as we can add two vectors for a resultant, we can break resultants down into components. We can pick any pair of 90° directions, and those components will act independently of each other. These are known as the ‘horizontal component’ and the ‘vertical component’.

For example, a resultant force vector that is drawn diagonally up and to the right can be resolved into a force to the right and a force acting upwards. You should learn how to do this by drawing a scale diagram on graph paper, and also using trigonometry.

Reading

Edexcel International AS/A Level Physics Student Book 1 pages 26 to 27

Tasks

Complete the following:

Read pages 26 to 27 of the textbook.

WATCH – Finding Horizontal and Vertical Components (Purple555) Links to an external site.

SIMULATION – Resolution of a Force into Components (Walter Fendt) Links to an external site. Practice various angles and calculate the resultant components, then check your answers.

WATCH – Inclined Planes (Udacity) Links to an external site.

WATCH – The Secret to Solving Inclined Plane Problems (Michael Kocher) Links to an external site.

COMPLETE – Gameboard: ‘Adding Vectors’ (Isaac Physics) Links to an external site.

COMPLETE – Gameboard: ‘B1 Components of a Vector’ (Isaac Physics) Links to an external site.

Complete the questions on page 27. You will find the answers in General Resources under the heading Textbook Answers. Download Textbook Answers.

Top Tips

Make sure that you understand the following key points:

A ‘force vector’ is shown by a straight arrow.
Resolving a (resultant) force vector requires working out the pair of forces at right angles that add up to the resultant.
Practise using scale diagrams and trigonometry to solve these problems.
Avoid confusion: Always draw a labelled sketch diagram and analyse it carefully.
Be clear which is your positive direction and stick to it consistently.
If $F$ is a force and $LaTeX: \theta$ $\theta$ is its angle from horizontal, then the horizontal component is $LaTeX: F\ cos\ \theta$ $F\ cos\ \theta$ and the vertical component is $LaTeX: fsin\ \theta$ $fsin\ \theta$ .
With sloping surfaces, pick your 90° directions as parallel and perpendicular to the plane.
Always check your calculator is in the correct mode – in this case degrees – when resolving vectors.

Key Terms

Add the following key terms with definitions to your word list:

Force vector
Resolution
Resolving vectors
Horizontal component
Vertical component
Catapult