Free-body diagrams

A free body diagram is a special example of a vector diagram and is used throughout the study of physics. It is a simplified representation of an object in a problem and is used by students and practicing engineers to breakdown a sometimes complex situation into a more easily understood and solvable problem. For example, a free body diagram may be used in order to determine the forces acting upon a car that is parked on a hill.

In order to complete a free body diagram you must understand the different forces that are acting upon an object as well as the magnitude, direction and location of the forces.

Components of the free-body diagram

A free body diagram can consist of many different things, however there a few components that are necessary in order to create a useful diagram. The first and most important component is the object and shown via a simple box, the size and shape of the object is not important.

The second component of the diagram is the force which is represented in the diagram using a simple arrow (¬ ). However, the direction the arrow is pointing and the size of the arrow is important and useful when doing the final calculation. The direction of the arrow reveals the direction which the force is acting and the size of the arrow is a representation of the magnitude of force. Each arrow in the diagram is labeled to indicate the exact type of force.

There is no hard and fast rule about the number of forces which must be drawn in a free-body diagram. The only rule for drawing free-body diagrams is to depict all the forces which exist for that object in the given situation.

Types of forces used in a free-body diagram

Although there are many forces that can be used or considered in creating a free-body diagram, following is a list of the more common forces along with a description of each;

• Gravity
• Normal force
• Frictional
• Push or Pull
• Tension

The first force that can be considered and probably the most widely experienced force is the force of gravity or gravitational force. The acceleration that is due to gravity (if on Earth) is roughly g = 9.8 m/s² and is represented with the formula F = m g. Where g is the acceleration of gravity and m is the mass of the object.

Friction is a force that is related to the normal because it too is due to the surface that the object is in contact with. Unlike the normal force, which is perpendicular, the frictional force is always parallel to the surface the object is resting upon. Also, the force of friction impedes or opposes motion, so the vector representing it always points opposite the direction of movement.

There are two types of friction that can act upon an object, one is static friction. This type of friction occurs when the object is resting and is the force that makes it difficult to start moving an object. The other type of friction is kinetic, this type of friction occurs when the object is in motion. This is the force that causes objects to slow down and eventually stop.

Push or pull is also a force that could be acting upon an object. For example if wind is blowing into the sail of a sailboat it would be represented in a free body diagram as a pushing force. On the other hand, if a child has a rope attached to a wagon and is moving it down the street, the force making the wagon move is the force of pulling.

The last of the common forces used in creating a free-body diagram is the force of tension. Tension is the force that results if two forces are pulling on the ends of an object.

Creating the free-body diagram

When creating a free-body diagram you should first examine the physical situation presented to you and determine the forces that are present. Then determine the direction in which each force is acting, as well as the relative magnitude of the force. Finally, draw a box and add arrows for each existing force in the appropriate direction and be sure to label each arrow according to its type.