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The ultimate purpose of a free body diagram is to develop a math model to answer a question. This math model will look like a set a equations. In order to be successful at this, the you must know when each force in the previous section applies to a problem and in which direction is points. Below is summary.

Force Name	Math Symbol	Formula	When it is present	Direction
weight	w	w=mg	On any big object, like a planet.	Always down -to the planet's center
normal force		...	when two surfaces touch	perpendicular to the surface
Friction			When the problem indicates	parallel to the surface & opposite the direction of motion
Tension	T	...	When ropes, chains or an object being stretched is involved	parallel to the rope. You can't push with a rope.
Net force	Fnet	...	When a body is changing speed or direction	In the direction of the acceleration
This list will grow as the course progresses. You must know the information in this table to be successful at free body diagrams.

Example

Question Answer Two trucks have a rope connecting their under carriages.The begin to have a "Tug of War." The trucks drift to the right at a constant velocity. Draw a free body digram for each truck and the rope.

To develop the math model a set of equations will be created. The set of equations varies from problem to problem.

To create a equation the force will be added in one or more directions. This is called summing and the math symbol that is used to indicate this is the capital Greek letter sigma, "Σ." If the forces are going to be summed in the x-direction, then the summation looks like the one shown below.

To indicate that the forces are added up in the y-direction the symbol below is used.

The next step is to show what these summed forces will equal. They will either equal zero or a net force. If the body is moving at a constant velocity then the summation will equal zero. (Recall that a body at rest is moving at a constant velocity of zero.) If the body is accelerating, then the summation will equal F_net or as it is sometimes written, ma_net.

Constant Velocity	Acceleration
	...If it accelerates in the "x" direction. ...If it accelerates in the "y" direction.

These summations do not need to be the same. One may be equal to zero and the other may be equal to ma_net.