FREE BODY DIAGRAM

Free-Body Force Diagams
* The purpose of a free-body force diagram is to assist you in trying to determine the net force acting on a body. It is only the net force to which Newton's Second Law can be applied and not each individual force seperately.

Useful mental overseer questions to reflect on are:

How shall I define the system?
What are the forces acting on the system?
In which directions are they pushing or pulling on the system?
Do I have them all? Do I have too many?
Are any of the forces I have sketched non-existent? What is the source of the force?
Constructing a free-body force diagram:
* Select an object or group of objects to focus on as the "body", i.e. the system.

* Sketch the body by itself, "free" of its surroundings. The body could be represented by a single point located at the body's center of mass.

* Draw only those forces that are acting directly on the body. Include both the magnitude and the direction of these forces.

* Except for rotational problems, you can normally sketch the forces as though they were acting through a single point at the center of mass of the body. It is useful to draw the force-vectors with their tails at the center of mass.

* Do not include any forces that the body exerts on it surroundings, they do not act on the body. However, there is always an equal reaction force acting on the body.

*For a compound body you do not need to include any internal forces acting between the body's subparts, since these internal forces come in action-reaction pairs which cancel each other out because of Newton's Third Law.

*Choose a coordinate system and sketch it on the free-body diagram. If you choose one of the axes to be parallel to the object's acceleration, it can sometimes simplify the equations you have to solve.


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Example 1:
Suppose that a block is pushed to the left on a surface with friction by a horizontally applied force, and that the block is connected by a cord passing through a frictionless pulley to a hanging weight.

Let T represent the tension in the cord and f the force of friction acting on the block.



Free-Body Diagram
for Block A Free-Body Diagram
for Block B


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Example 2.



Suppose two blocks of different masses are pushed along a frictionless surface by a force applied at an angle.

Let FBA be the force that block B exerts on block A, and FAB be the force that block A exerts on block B.


Free-Body Diagram for Block A Free-Body Diagram for Block B

Free-Body Diagram for the System of Both Blocks

Observe that the applied force Fapp only acts on block A and not block B. It does affect block B but it does not act directly upon B. Changing Fapp would change the magnitude of FAB, the force that block A exerts on B.

Also observe that when both blocks together are considered to be a single system, then the FAB and FBA become internal forces and cancel each other out.