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A free body diagram, also called a force diagram, is a pictorial representation often used by physicists and engineers to analyze the forces acting on a body of interest. A free body diagram shows all forces of all types acting on this 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 torques or 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.
A free body diagram consists primarily of a sketch of the body in question and arrows representing the forces applied to it. The selection of the body to sketch may be the first important decision in the problem solving process. For example, to find the forces on the pivot joint of a simple pair of pliers, it is helpful to draw a free body diagram of just one of the two pieces, not the entire system, replacing the second half with the forces it would apply to the first half.
The sketch of the free body need to include only as much detail as necessary. Often a simple outline is sufficient. Depending on the analysis to be performed and the model being employed, just a single point may be the most appropriate. If rotation of the body and torque is in consideration, it is best to draw the shape. Free body diagrams are named as such because the diagram isolates the body, hence free, from all other interacting bodies, and the diagram focuses on one specific body. Neighboring free body diagrams in the same big picture may be necessary in order to consider the other interacting bodies of the situation.
All external contacts, constraints, and body forces are indicated by vector arrows labeled with appropriate descriptions. The arrows show the direction and magnitude of the various forces. To the extent possible or practical, the arrows 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, normal force, drag, tension, or a human force due to pushing or pulling. When in a non-inertial reference frame, fictitious forces, such as centrifugal pseudoforce may be appropriate.
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: mgsin(θ) in the x and mgcos(θ) in the y, where θ is the angle between the ramp and the horizontal.
All external contacts and constraints are left out and replaced with force vectors as described above.
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. Of those two forces, the FBD for just the ball should only include the force that the table applies to the ball. Including the forces which the free body applies to other objects in addition to the forces applied to the free body would always result in zero net force, whether the object was in equilibrium or not, because each pair must be exactly equal and opposite, according to Newton's Third Law of Motion, and so cancel each other.
Internal forces, forces between various parts that make up the system that is being treated as a single body, are omitted. For example, if an entire truss is being analyzed to find the reaction forces at the supports, the forces between the individual truss members are not included.
Any velocity or acceleration is left out. These may be indicated instead on a companion diagram, called a "Kinetic diagram", "Inertial response diagram", or the equivalent, depending on the author.
The free body diagram reflects the assumption and simplifications made in order to analyze the system. If the body in question is a satellite in orbit for example, and all that is required is to find its velocity, then a single point may be the best representation. On the other hand, the brake dive of a motorcycle cannot be found from a single point, and a sketch with finite dimensions is required.
Force vectors must be carefully located and labeled to avoid assumptions that presuppose a result. For example, in the accompanying diagram of a block on a ramp, the exact location of the resulting normal force of the ramp on the block can only be found after analyzing the motion or by assuming equilibrium.
Other simplifying assumptions that may be considered include two-force members and three-force members.
A simple free body diagram, shown above, of a block on a ramp illustrates this.
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