GCSE Finding the resultant force, using the parallelogram rule

Finding the resultant force, using the parallelogram rule

We can use the parallelogram rule to find the resultant force of two forces that do not act along the same line. 

Lets look at an example:

An airplane that has a forward thrust force and it is experiencing a sideways cross wind force which pushes the airplane side ways. As a result the plane will fly in a diagonal direction.

We can use the parallelogram rule to work out the resultant  diagonal force using the forward thrust force and sideways wind force.

Now we need to draw two parallel lines to form a parallelogram, as shown below.

Now draw a diagonal line from where the forces originate to where red lines meet as shown below.

These are all based on scale drawings. We will assume each square is 1cm. 

The wind force 500N = 2 squares long = 2cm. 

This means that 1cm = 250N.

Now measure the purple line. If the purple line is 8.25cm, then it is 8.25cm x 250N = 2060N as a resultant diagonal force. 

Please NOTE on your screen the length of the arrows will not match due to the screen resolution.  If you draw this out on  a piece of square paper, then you can follow with the example.

Another example

Two men are trying to pull a weight along the ground. One man pulls with a force of 160N, this is represented by a line of length 8cm. The other man pulls with a force of 145N, this is represented by a line of 7.25cm. The angle between the men is 62 degrees. 

Please NOTE on your screen the length of the arrows will not match due to the screen resolution.  If you draw this out on  a piece of square paper, then you can follow with the example.

We need to calculate the resultant force. 

The first step is to measure the force arrows, in this case, it has been done in the diagram above. However, often the questions have just the force written next to them. 

This is so you can work out the scale. So, if one force arrow is 8cm = 160N, then 1cm = 20N.

Now, we need to complete the parallelogram as show below.

Now draw a line from the origin of the forces to where the blue lines meet as shown below.

Now measure this green line. On our diagram it is 12.5cm. Using the scale of 1cm = 20 N, 12.5cm = 250N.

On the next page we will show you how to deal with the model zip line questions, which can be tricky!