Topic Four (1.4): Adding Forces

Introduction

This topic explains how to add forces as vectors, so you can tell if an object is in force equilibrium (all forces balance, so no acceleration). When adding vectors, two plus two may not equal four, so learn the rules carefully! It also teaches ‘free body force diagrams’ – one of the most valuable and important tools in all of mechanics. Drawing all forces as arrows coming from an object’s centre can clearly show what is happening, avoiding any confusion. The focus of this section is to work out a resultant force.

You will be given a horizontal and vertical force arrow (force vector) and be required to work out the diagonal (resultant) force vector. For example, imagine a force to the right of $10\ N$, and an upwards force of $10\ N$. The resultant can be calculated using the trigonometric equation $a=\sqrt{b^2+c^2}$ (where $b$ and $c$ are the rightward and upward forces), or by drawing a scale diagram and measuring the hypotenuse. The answer is $14.1\ N$. Since the forces are equal the resultant force will be at 45^° to the horizontal. But for unequal forces you can also use the sin, cos and tan equations to calculate the angle.

Reading

Edexcel International AS/A Level Physics Student Book 1 pages 15 to 16

Tasks

Complete the following:

• Read pages 15 to 16 of the textbook.

READ – ‘Nose to Tail’ Vector Addition (PDF) Links to an external site.

• Practise drawing some vector additions on paper, adding ‘nose to tail’. Draw the first vector arrow, then start the next vector arrow at the point where the first arrow ends. The resultant is the arrow that would take you from the very start to the very end of all the drawn arrows.

WATCH – The Triangle and Parallelogram Rule for Vector Addition (YouTube) Links to an external site.

• Make careful note of figure G on page 16 – the free body force diagram. Representing an object as a dot, and considering just the forces acting on that object, drawing the force vectors as arrows, is a powerful tool that makes it simple to see if it is in equilibrium (all forces balance), or there is a resultant force (which will cause its velocity to change).

READ and WORK THROUGH - Drawing Free-body Force Diagrams (Physics Classroom) Links to an external site.

COMPLETE - Free Body Force Diagram Interactive (Physics Classroom) Links to an external site.

• Complete the questions on page 16. 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:

• It is always good to draw a vector diagram. Draw arrows ‘nose to tail’ to add vectors.
• An object is in force equilibrium if the vector sum of all the force arrows totals zero.
• Objects in force equilibrium have zero acceleration: Their speed and direction continue unchanged.
• Always draw a free body force diagram (all forces acting on a single object) to understand if it is in force equilibrium.
• Calculating a hypotenuse using trigonometry equations.
  • Draw a scale diagram and measure the resultant force (hypotenuse) with a ruler.
  • Work out the angle by measuring with a protractor.
  • Calculate the angle of the resultant force vector using the sin, cos and tan trigonometry equations.
• The vector addition rules shown in the textbook, work for all vectors, not just forces.

Key Terms

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

• Force
• Resultant force vector
• Horizontal component
• Vertical component
• Equilibrium
• Free-body force diagram
• Triangle and parallelogram rule