## What is a free body diagram?

The system of forces acting on a body tends to either rotate it or make the body undergo motion. In general, when an external agent exerts a force on a body, the body undergoes translational motion and rotational motion. The body has six degrees of freedom under the influence of that force. Here, three degrees of freedom are from the translational motion while the other three are from the rotation motion. However, sometimes the bodies are not allowed to undergo any motion and are fixed, under such conditions the body is said to be constrained.

A mechanical system consists of different bodies connected whose motions are constrained to analyze a particular body for its motion and forces, the body is drawn separately as a diagram that is isolated from the rest of the bodies. All the external forces and reactions are included in that body. The unknowns are then solved by a set of equilibrium equations. The isolated body which is drawn separately is known as a free body diagram (FBD).

## Forces in free body diagram

A constrained body may be fixed due to a variety of reasons that are in general difficult to analyze. Hence to analyze such bodies under equilibrium, the body first needs to be isolated from the support. Various forces acting on a free body are shown with the notation of vectors in the form of a diagram. Such diagrams are called free-body diagrams.

Two kinds of forces are generally shown in the free body diagram. They are external forces and reactive forces. External forces act due to the nature of the environment where the body is kept, as the frictional force. Whereas, reactive forces are the forces exerted on the body due to supports and contacts. The reactive forces occur generally due to action-reaction provided by the third law of motion given by Newton. The SI unit of force is Newton, where N is shown along with the vector notations in the diagram. There are ample conceptual questions that are asked in examinations. To show solutions to these kinds of conceptual questions requires a good problem-solving strategy, which can be tackled by first drawing a free-body diagram.

## Steps to draw a free-body diagram

Drawing a free-body diagram is the first step to show a solution to a given problem in mechanics. The basic steps in drawing free-body diagrams are outlined below:

1. A mechanical system is composed of several interconnected bodies that exert forces on one another. To analyze a body under equilibrium, the body of interest should be first identified.
2. The body of interest is then isolated from the rest of the bodies and drawn separately.
3. The drawn body should include all the external forces and reactive forces that are acting from the supports. The forces acting due to air resistances are usually neglected. This body must be drawn to scale. The forces are shown by a force arrow in a vector notation, where a vector is any quantity that has both magnitude and direction. The magnitude and unit of force, that is, newton (N) should be included near the arrow.
4. The first force that must be shown in a free-body diagram is the gravity force due to the self-weight of the body.
5. The second force that must be included in a free-body diagram is the force due to a normal reaction. The force acts on the body due to surface contact between the body and the surface where the body is resting.
6. Other forces such as the forces due to spring stiffness, tensile forces, compressive forces, and so on must be indicated.
7. Lastly, all the forces acting on the body due to the reactive forces must be shown in a free-body diagram.

For instance, consider objecting A resting on an inclined plane having a mass M, which is in contact with object B.

Under such conditions, the free-body diagram for object A that can be drawn is shown below.

Here, Mg is the force due to the self-weight of the body, Fb is the reactive force due to object B and N is the normal reactive force for the surface. As Mg is acting at an angle from the vertical y-axis, Mg should be resolved into two components, that is, x-components that act along x-axes and y-components that act along y-axes. Each coordinate of individual bodies should be shown in the xy-coordinate system. Friction forces should not be mentioned until the coefficient of friction is mentioned. When in problems, the magnitude of forces in Newton (N) is included, those magnitudes must be always included in a free-body diagram.

To determine an unknown force as Fb after drawing the free-body diagram, the three key equations known as the equilibrium equations must be applied.

## Free-body diagram with friction

Sometimes, in practical scenarios, the body under the action of external forces tends to undergo motion. Due to the motion, frictional forces act between the surface of the body and the plane at which the body is resting. In a free-body diagram, the frictional force should be shown in an opposite direction to the body's motion. This is because a frictional force is a force that acts opposite to the motion of a body to retard its motion. There are two kinds of frictional forces that are generally included in a free-body diagram problem. They are static friction and kinetic friction.

Consider a block of mass M, resting on a frictional surface with a coefficient of static friction ${\mu }_{s}$, under the action of an external force $F$.

The free-body for such a case can be drawn as shown below

Where, ${F}_{s}={\mu }_{s}N$, is the static frictional force induced in the body due to the tendency of the body to move, which acts in the opposite direction.

## Context and Applications

This topic is taught extensively in the undergraduate courses of bachelor of science. The topic is also taught during the first-year engineering courses of mechanical engineering and civil engineering.

• Bachelors in Science (Physics)
• Masters in Science (Physics)
• Bachelors in Technology (Mechanical)
• Masters in Technology (Mechanical)

## Practice Problems

1. Which of the following is the correct name of the drawing created by isolating the body from the supports?

1. Free-body diagram
2. Force diagram
3. Equilibrium diagram
4. All of these

Correct option- a

Explanation: A free-body diagram is a diagram, which is drawn by isolating the body of interest and by including all the relevant forces acting on it.

2. Which of the forces should be first shown in a free-body diagram?

1. Normal reaction
2. Gravity force
3. Reactive force
4. Frictional force

Correct option- b

Explanation: The force due to the self-weight of the body, that is, the gravity force should be first indicated in a free-body diagram. It is shown by a vector arrow pointing downwards.

3. Which of the following is true for a vector?

1. Any quantity that has only magnitude
2. Any quantity that has both magnitude and direction
3. Any quantity that has only direction
4. None of these

Correct option- b

Explanation: A vector is a quantity that has both magnitude and direction. A vector is shown by an arrow with the magnitude represented above it.

4. Which of the following is an external force?

1. Friction
2. Body forces
3. Gravity forces
4. None of these

Correct option- a

Explanation: Frictional forces are those forces that act external to the body. These forces arise due to the frictional effects due to the contact between the surfaces when the body has a tendency of motion or the body is already in motion. Hence these kinds of forces are external forces.

5. What of the following kinds of friction act on a body due to its motion?

1. Static friction
2. Dynamic friction
3. Both static and dynamic friction
4. All of these

Correct option- b

Explanation: When a body is in motion the frictional force that acts on a body is the dynamic friction.

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