Forces - 5.1.4 Resultant Forces (GCSE Physics AQA)

Resultant Forces

Examples of Forces

Isolated Systems

In AQA exams, you will have to draw and explain forces acting on an isolated system. By this, we mean that you don’t need to worry about external forces associated with the surroundings.

Free Body Diagrams

We can draw free body diagrams to illustrate all the forces acting on an object. A free body diagram will have arrows to represent the different forces exerted on an object.

As previously mentioned, force is a vector (see section ‘Forces as Vectors’). This means that each force on a free body diagram has both magnitude and direction:

• The size of the arrow shows the magnitude of the force.
• The direction of the arrow will show the direction of the force

Resultant Forces

Combining Forces

• We can combine forces together. When multiple forces act on an object, you can replace them with a single force. The single force can be represented by one arrow on a diagram.
• The single force will be called the resultant force. The resultant force is the combined effect of all the other forces added together.

We can calculate the overall resultant force of both parallel and nonparallel forces. This is called resolving a force.

Resolving Parallel Forces

We can calculate the resultant force of two forces that act in a straight line, as shown in the diagrams below.

Think about this as a simple sum. We can add together forces in a line:

First, assign positive or negative to each direction. It’s easiest to say that the arrows pointing to the right are positive, whereas the arrows pointing to the left are negative. Now you can perform a simple sum, as shown in the diagram

• Horizontal forces – horizontal forces can be combined together. We have a forward and backward direction. You can assign positive and negative directions too each direction – e.g. forces in the forward direction can be positive (+ve), and forces in the backward direction can be negative (-ve).
• Vertical forces – vertical forces can also be combined together. We have an upward and downward direction. Again, assign positive and negative directions – e.g. forces in the upward direction can be positive (+ve), and forces in the downward direction can be negative (-ve).

Resolving Non-Parallel Forces

Above, we worked on combining two forces in a straight line (parallel) to get one resultant force. Well, we can also resolve two non-parallel forces to work out the resultant force. For us to do this, the two components need to be at right angles to each other.

For example, imagine we wish to work out the resultant force on the dog caused by pulling on his lead. We could break this up into a vertical and horizontal component. These components are at a right angle to each other. When combined, they will form the resultant force.

Using Vector Diagrams to Determine the Horizontal and Vertical Forces

We can use vector diagrams to help us resolve forces into a vertical and horizontal component. Vector diagrams represent forces as vectors, which have both magnitude and direction. In the exam, they’ll give you a scale (e.g. 1cm = 10N) so that you can measure distances and correlate them to force.

Question: There are two forces acting on an object, one horizontal (4N) and one vertical (7N). The forces are perpendicular to each other. What is the size of the resultant force? (2cm = 1N)

1. Draw the horizontal and vertical forces. Draw the horizontal and vertical forces in a vector diagram. When you draw the components, use a vector – i.e. the magnitude of the vector will be the size of the force and the direction of the vector will be the direction of the force. For example, the 3N vertical force would be 6cm according to the scale given in the question.
2. Work out the resultant force. The resultant force is the hypotenuse between the vertical and horizontal forces. However, from the diagram we can see the direction will be in between the horizontal and vertical forces, so we have to re-arrange our triangle, as shown in the diagram below.
3. Use a ruler to measure the resultant force. Measure the length of the vertical force.

You can also do this process backwards to work out the resultant force if you are given the horizontal and vertical components.

Special Case: Equilibrium Situations

When we use the term equilibrium, we mean that all the forces in the situation are balanced. The resultant force will be equal to zero.

In AQA exams, we can be given specific questions relating to forces in equilibrium. To see if an object is in equilibrium, we can use vectors:

1. Draw all the forces. Drawing out the forces should be your first step in this question. Label them all clearly onto a diagram.
2. Use a ruler to measure the forces. Measure the lengths of the vectors using a ruler. This will make sure that you are drawing the forces to scale.
3. Rearrange the forces to make a shape. Once you have labelled the forces on a diagram, you can rearrange them to make a shape. If there are 3 forces, it will form a triangle. As you can see in the diagram below, the beginning of one arrow will be touching the end of another arrow.
4. Check that there is no resultant force. When forces are in equilibrium, there will not be any resultant force. To check that this, make sure that all the arrows join together to form a closed shape (in Fig 13, the arrows form a closed triangle).