A
free body diagram is a pictorial representation often used by physicists and engineers to analyze the forces acting on a
free bodyFree body is the generic term used by physicists and engineers to describe an object—be it a bowling ball, a spacecraft, pendulum, a television, or anything else—which can be considered as moving as a single unit. The object doesn't have to be "free" in the usual sense of the...
. A free body diagram shows all
contactIn physics, a contact force is a force between two objects that are in contact with each other. This is distinct from a non-contact force, or action-at-a-distance force , such as gravity or magnetic attraction/repulsion.A contact force has two components...
and
non-contactA non-contact force is any force applied to an object by another body that is not in direct contact with it. The most common example of a non-contact force is gravity. A non-contact force is different from a contact force, which is a force applied to a body by another body that is in contact with it...
forceIn physics, a force is any agent that causes a change in the motion of a free body, or that causes stress in a fixed body. It can also be described by intuitive concepts such as a push or pull that can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a...
s acting on the body. Drawing such a diagram can aid in solving for the unknown forces or the
equations of motionIn physics, equations of motion are equations that describe the behavior of a system as a function of time...
of the body. Creating a free body diagram can make it easier to understand the forces, and
momentsIn physics, the term "moment" can refer to many different concepts:*Moment of force is a synonym for torque, an important basic concept in physics, civil engineering, and mechanical engineering. In the context of mechanical engineering, the terms are not necessarily interchangeable, but one or the...
, in relation to one another and suggest the proper concepts to apply in order to find the solution to a problem.
A
free body diagram is a pictorial representation often used by physicists and engineers to analyze the forces acting on a
free bodyFree body is the generic term used by physicists and engineers to describe an object—be it a bowling ball, a spacecraft, pendulum, a television, or anything else—which can be considered as moving as a single unit. The object doesn't have to be "free" in the usual sense of the...
. A free body diagram shows all
contactIn physics, a contact force is a force between two objects that are in contact with each other. This is distinct from a non-contact force, or action-at-a-distance force , such as gravity or magnetic attraction/repulsion.A contact force has two components...
and
non-contactA non-contact force is any force applied to an object by another body that is not in direct contact with it. The most common example of a non-contact force is gravity. A non-contact force is different from a contact force, which is a force applied to a body by another body that is in contact with it...
forceIn physics, a force is any agent that causes a change in the motion of a free body, or that causes stress in a fixed body. It can also be described by intuitive concepts such as a push or pull that can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a...
s acting on the body. Drawing such a diagram can aid in solving for the unknown forces or the
equations of motionIn physics, equations of motion are equations that describe the behavior of a system as a function of time...
of the body. Creating a free body diagram can make it easier to understand the forces, and
momentsIn physics, the term "moment" can refer to many different concepts:*Moment of force is a synonym for torque, an important basic concept in physics, civil engineering, and mechanical engineering. In the context of mechanical engineering, the terms are not necessarily interchangeable, but one or the...
, 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.
Construction
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
pliersPliers are a type of hand tool used to hold objects firmly, or for cutting and bending tough materials such as wire. Generally, pliers consist of a pair of metal levers joined at a pivot positioned closer to one end of the levers, creating short jaws on one side of the pivot, and longer handles on...
, 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.
What is included
The sketch of the free body need 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.
All external contacts, constraints, and body forces are indicated by vector arrows labeled with appropriate descriptions. The arrows show the direction and
magnitudeThe magnitude of a mathematical object is its size: a property by which it can be compared as larger or smaller than other objects of the same kind; in technical terms, an ordering of the class of objects to which it belongs....
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
frictionFriction is the force resisting the relative lateral motion of solid surfaces, fluid layers, or material elements in contact. It is usually subdivided into several varieties:...
,
gravityGravitation is a natural phenomenon by which objects with mass attract one another. In everyday life, gravitation is most commonly thought of as the agency which lends weight to objects with mass. Gravitation causes dispersed matter to coalesce, thus accounting for the existence of the Earth, the...
,
normal forceIn physics, the normal force is the component, perpendicular to the surface of contact, of the contact force exerted by, for example, the surface of a floor or wall, on an object, preventing the object from entering the floor or wall...
,
dragIn fluid dynamics, drag refers to forces that oppose the relative motion of an object through a fluid . Drag forces act in a direction opposite to the oncoming flow velocity...
, or simply contact force due to pushing. When in a
non-inertial reference frameA non-inertial reference frame is a reference frame that is not an inertial reference frame. As such, the laws of physics in such a frame do not take on their most simple form, as required by the special principle of relativity...
,
fictitious forceA fictitious force, also called a pseudo force, d'Alembert force or inertial force, is an apparent force that acts on all masses in a non-inertial frame of reference, such as a rotating reference frame...
s, such as centrifugal force may be appropriate.
A
coordinate systemIn mathematics and its applications, a coordinate system is a system for assigning an n-tuple of numbers or scalars to each point in an n-dimensional space. This concept is part of the theory of manifolds. "Scalars" in many cases means real numbers, but, depending on context, can mean complex...
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 planeThe inclined plane is one of the original six simple machines; as the name suggests, it is a flat surface whose endpoints are at different heights. By moving an object up an inclined plane rather than completely vertical, the amount of force required is reduced, at the expense of increasing the...
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(theta) in the
x and
mgcos(theta) in the
y, where theta is the angle between the ramp and the horizontal.
What is excluded
All external contacts and constraints are left out and replaced with force arrows 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. The FBD of the ball only includes the force that the table causes on the ball.
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
trussIn architecture and structural engineering, a truss is a structure comprising one or more triangular units constructed with straight slender members whose ends are connected at joints referred to as nodes. External forces and reactions to those forces are considered to act only at the nodes and...
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 "Kinetic diagrams", "Inertial response diagrams", or the equivalent, depending on the author.
Assumptions
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.
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 mass of the block and the constant of gravitation acceleration: its weight.
- N: the normal force of the ramp.
- Ff: 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.
See also
- Classical Mechanics
In the fields of physics, classical mechanics is one of the two major sub-fields of study in the science of mechanics, which is concerned with the set of physical laws governing and mathematically describing the motions of bodies and aggregates of bodies geometrically distributed within a certain...
- Force field analysis
Force field analysis is an influential development in the field of social science. It provides a framework for looking at the factors that influence a situation, originally social situations. It looks at forces that are either driving movement toward a goal or blocking movement toward a goal...
- applications of force diagram in social science
- Shear and moment diagrams
Shear and bending moment diagrams are analytical tools used in conjunction with structural analysis to help perform structural design by determining the value of shear force and bending moment at a given point of an element. Using these diagrams the type and size of a member of a given material can...