Free body diagram

A free body diagram is a pictorial representation often used by physicists and engineers to analyze the forces acting on a free body. It shows all contact and non-contact forces acting on the body. Drawing such a diagram can aid in solving for the unknown forces or the equations of motion of the body. Creating a free body diagram can make it easier to understand the forces, and moments, in relation to one another and suggest the proper concepts to apply in order to find the solution to a problem. The diagrams are also used as a conceptual device to help identify the internal forces, (for example shear forces and bending moments in beams), which are developed within structures.cite book
title = Introduction to Statics and Dynamics
last = Ruina
first = Andy
coauthors = Rudra Pratap
year = 2002
pages = 79-105
publisher = Oxford University Press
url = http://ruina.tam.cornell.edu/Book/RuinaPratapNoProblems.pdf
format = PDF
accessdate = 2006-08-04] cite book
title = Engineering Mechanics: Statics & Dynamics
edition = Eleventh Edition
last = Hibbeler
first = R. C.
year = 2007
publisher = Pearson Prentice Hall
id = ISBN 0-13-22150-4
pages = 83–86]

Components

The free body diagram starts with a sketch or just an outline of the free body. All external contacts and contraints are left out.

All external contacts, constraints, and body forces are replaced by vectors, representing the different forces acting on the object. The vectors show the direction and magnitude of the various forces. To the extent possible or practical, the vectors should indicate the point of application of the force they represent.

Only the forces acting on the object are included. These may include forces such as friction, gravity, the normal force, drag, or simply contact force due to pushing. When in a non-inertial reference frame, fictitious forces may be appropriate. Each vector should point in the direction of the force it represents, and be labeled with the magnitude of that force.

Forces which the free body applies to other objects are not included. For example, if a ball rests on a table, the ball applies a force to the table, and the table applies an equal and opposite force to the ball. The FBD of the ball only includes the force that the table causes on the ball.

A coordinate system is usually included, according to convenience. This may make defining the vectors simpler when writing the equations of motion. The "x" direction might be chosen to point down the ramp in an inclined plane problem, for example. In that case the friction force only has an "x" component, and the normal force only has a "y" component. The force of gravity will still have components in both the "x" and "y" direction: "mg"sin(theta) in the "x" and "mg"cos(theta) in the "y", where theta is the angle between the ramp and the horizontal.

Example

A simple free body diagram, shown above, of a block on a ramp illustrates this.
* All external supports and structures have been replaced by the forces they generate. These include::* "mg": the product of the blocks mass and the constant of gravitation acceleration: its weight.:* "N": the normal force of the ramp.:* "F_f": the friction force of the ramp.
* The force vectors show direction and point of application and are labeled with their magnitude.
* It contains a coordinate system that can be used when describing the vectors.

ee also

* Classical Mechanics

References