Force diagrams
Adding and subtracting forces in a straight line Forces at an angle
Parallelogram of forces Uses of force diagrams Vector diagrams

Click for larger image Forces are vectors, that is they are described by a magnitude and a direction. For example, if a marble was pushed across a table with a force of 20 newton applied, due North would describe the force used to move the marble. One way of showing forces in direction and magnitude is by using force diagrams. In this system, an arrow is drawn in the direction of the force, the length of the line being proportional to the magnitude of the force.

By using force diagrams it is possible to estimate the resultant force - that is the net force exerted on an object.

Click for larger imageAdding and subtracting forces in a straight line
If an object is being pushed in one direction by a force of 20 newton, and another force of 20 newton is applied in exactly the opposite direction, then the resultant force is 20 - 20, or zero newton. With no resultant force, the motion of the object will not change. If it is stationary, it will stay that way, if it is moving, it will keep moving in the same direction and speed.

Click for larger image Increasing the first force by 5 newton means that the object will accelerate in the direction of action of this new force, and the resultant force is 25 - 20, or 5 newton.

When forces are in a straight line the resultant force is simply the arithmetical sum of, or difference between, the two forces.

Forces at an angle
Once forces are applied at an angle to each other the calculation becomes more complex. The simplest way of finding the resultant force, when two forces are applied, is by a technique called a parallelogram of forces, where the force can be estimated from the diagram.

Parallelogram of forces
Click for larger image A parallelogram is a four sided figure where both opposite sides are of the same length, and parallel to each other. To estimate a resultant force it is first necessary to draw the direction and magnitude of each force. The parallelogram is completed by drawing in the two other sides parallel to the two forces and the diagonal measured. This diagonal represents the resultant force. Click for larger image

Uses of force diagrams
Click for larger image Tugs are often used to tow large ships. Two tugs pulling at an angle produce a resultant force that can be calculated. Two people pulling on a tree trunk to drag it out of the ground can calculate their resultant force - and can be out of the way of the trunk when it falls!

The resultant of any two forces can be calculated using the parallelogram of forces.

Vector diagrams
Three or more forces can also be estimated, using vector diagrams. In fact, the force diagrams used above are based on vector diagrams. In vector diagrams, each force is represented by its vector arrow and added in turn. The resultant force is measured from the tail of the first force to the head of the last.

Copyright owned by the State of Victoria (Department of Education and Early Childhood Development). Used with Permission.

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Glossary
 
Magnitude Proportional Resultant Force