Free Body Diagram often called FBD is a way of representing all the forces acting on a body at a particular instant in a simpler form. It enables the calculation of the net force acting on the body and its direction of motion by making a symbolic diagram of all the forces acting on a body.

In this article, we will learn in detail about the Free Body Diagram, what are its features, how to make it, and solve some examples based on it.

What is Free Body Diagram?

Free Body Diagram in physics is very useful for representing the magnitude and direction of all the forces acting on a body at a given point of time (or in a given situation). Free Body diagram is the first step towards the analysis of how the body is going to behave as a result of the application of the forces. Free Body Diagram is also abbreviated as FBD.

FBD Definition

Free Body Diagram is a diagrammatic, graphic, symbolic representation of an object (complete or partial part of another object) in which all the acting forces are shown, with there relative magnitude and direction by directed arrows.

Features of Free Body Diagram

Free Body Diagrams typically have the following features:

• All the types of forces acting on the body are shown.
• Forces are shown with arrows where the direction of the arrow shows the direction of the force acting on the body, and size of the arrow represents the relative magnitude.
• Moments are shown by the curved arrows showing the direction of action.
• The diagram is presented in a well-defined coordinate system.

While drawing a free-body diagram some assumptions are made which are specific to the problem, and air resistance and drag forces are neglected unless it is mentioned.

How to Make Free Body Diagram

Follow the steps mentioned below to make Free Body Diagram.

Step 1: Mark Object Boundary: First of all identify the body for which the analysis has to take place, draw the boundary of the object.

Step 2: Identify Contact Surfaces: Once the body is identified and boundary is clear, we need to identify the contact surfaces of the body (any surface which body touches is the contact surface for the body), which can be identified by drawing a dot on the object boundary, when any surface touches the body. When there is a dot it is for sure that there is a contact force.

Identifying Contact surface

Step 3: Define a Coordinate System: Define a coordinate system and label clearly specify positive directions.

Defining coordinate system

Step 4: Identify Contact Forces: For every dot define the contact force acting at that dot with an arrow pointing away from the dot, (since the force is acting on the body it will always be away from the surface and towards the body) and label this forces.

Step 5: Draw other forces acting on the body such as Weight of the body, electric or magnetic force in case it also exists.

Drawing forces acting on the body

Step 6: In case the body have any resulting acceleration show that using an acceleration vector.

Showing acceleration acting on the body

Free Body Diagram in Physics

Free Body Diagram in physics can be made for several physical phenomena such as a body in motion is subjected to some load. In this section we will discuss FBD for following types

• Free Body Diagram of Circular Motion
• Free Body Diagram of Frictional Force
• Free Body Diagram of Friction on Inclined Plane

Free Body Diagram of Circular Motion

Consider a ball initially at the bottom of a circular path, let’s use try to understand the Free Body Diagram of the when it move on the circular path with a velocity of v. In this section we will learn how the different forces are acting on different positions of the ball in the circular path.

Free Body Diagram of the Ball at Rest

When the ball will be at rest it will have a its weight acting downwards (W = mg), which will cause a Normal Force (N) from the surface to act on the object.

FBD of the ball at rest

Free Body Diagram of Ball at the Bottom of the Path when moving with a velocity of v:

We know every object moving on a circular path with a velocity v of a circular path experiences a Centrifugal Force away from the center. So when the ball will start moving it will experience Centrifugal Force given as

C_f = mv²/r

where,

• m is the mass of the ball,
• v is the velocity with which the ball is moving and,
• r is the radius of the circular path,

Hence the free body diagram will look like as follows:

FBD of moving ball at bottom

Free Body Diagram of the Ball at the Middle of the Path when Moving with a Velocity of v:

We know every object moving on a circular path with a velocity v of a circular path experiences a Centrifugal Force away from the center, so when the ball will start moving and reach the horizontal position as shown, it will experience a forces (Centrifugal Force C_f = mv² / r) , which will cause a Normal Force(N) to come into action towards the center and weight will always be acting vertically downwards.

Hence the free body diagram will look like:

FBD of moving ball in middle

Free Body Diagram of the ball at the Topmost Position of the path when moving with a velocity of v:

When the ball will reach the highest position of the circular path, it will have its weight (W = mg) acting downwards, and Centrifugal Force (C_f = mv² / r), which will cause a Normal Force (N) to act towards the center of the path.

Hence the Free Body Diagram can be shown as:

FBD of moving ball at top

Free Body Diagram for Frictional Force

When a body is placed on a plane, instantaneously its Weight (W=mg) will start acting vertically downwards which will cause a Normal Force (N) from the ground to come into action. Now when the body is at rest the friction action of the body will be zero, but as soon as the body starts moving a friction (f = μN) will start acting opposite to the direction of motion.

Hence the Free Body Diagram of block placed on plane with coefficient of friction (μ), will look like as shown below where, [Tex]0 \leq f \leqslant \mu N [/Tex], is applicable

FBD for Frictional force

Free Body Diagram of Inclined Friction

Consider a body of mass m placed on an inclined plane, it weight will start acting vertically downwards, but friction and Normal Forces will act along and perpendicular to the inclined surface, so will consider a coordinate system where x axis is parallel to the inclined surface and y-axis is perpendicular to it.

FBD of Inclined Friction

Since inclined angle is making a θ angle with the horizontal, the component of weight parallel to inclined will make a 90 – θ angle with the vertical, hence the components of weight can be resolved as W_p = mgcosθ and W_|| = mgsinθ. See the figure:

Free Body Diagram of Inclined Friction with Co-ordinate system

After, Resolution of Weight Component along perpendicular and parallel to the inclined plane is shown below:

FBD of Inclined Friction after Resolution

Now the normal force (N) will start acting perpendicular to the surface of the inclined and a friction (f = μN) will act parallel to the surface of the inclined. Hence the free body diagram will look like:

FBD on the inclined plane with friction

Significance of Free Body Diagram

Free Body diagram is quite helpful in physics to analyze any object. The significance of Free Body diagram:

• Free Body Diagram helps in better understanding of the various forces acting on the body.
• Free Body Diagram can help in predicting the dynamics/behaviour of the body.
• Free Body Diagram can help in finding a suited point to apply a force to feature a motion of the body.

Also, Learn

• Net Force
• Circular Motion
• Gravitational Force

Examples of Free Body Diagram

Example 1: Draw the Free Body Diagram of mass M, as given below.

Solution:

Consider the Block A: When the mass M, is suspended using the two ropes, it weight(Mg) will start acting downward, which will cause tension in the ropes, let use name this tensions in the ropes as T1 and T2, then we can have our initial FBD as shown below:

Now, the tension in the strings will act such that, it will try to balance the weight of the ball (Mg), so we can resolve the tension T1 and T2, in there corresponding vertical and horizontal component.

Resolution of T1: Since T1 is at an angle β with the vertical, therefore the component of T1 along the vertical will become, T1cosβ and the component along the horizontal will become T1sinβ.

Resolution of T2: Since T1 is at an angle α with the vertical, therefore the component of T2 along the vertical will become, T2cosα and the component along the horizontal will become T2sinα.

Hence, we can draw the final FBD, will all the forces resolved along the vertical and horizontal components only, as below:

Example 2: A block is at rest on a platform with coefficient of friction μ is pulled by a force F acting at an angle θ, with the horizontal as show draw the free body diagram of the block.

Solution:

When the block is placed on the platform, its weight (Mg) will starting acting vertically downwards.

The weight acting downwards on the body will cause a normal force (F) from platform to act in the vertically upward direct.

Now when the force F will come into picture, since it is inclined at and angle θ, with the horizontal it will have to components one along the horizontal (Fcosθ) and the other along the vertical (Fsinθ)

Since there is no other force in the horizontal force in the horizontal direction other than Fcosθ, this will try to move to body on the platform which will cause the friction to act in the direction opposite to the direction of motion, hence the FBD of the body will look like:

Free Body Diagram Practice Questions

Q1: Draw the Free Body Diagram of mass M and m, when they are suspended as shown in the figure given below.

Free Body Diagram Practice Question 3

Q2: Draw the Free Body Diagram for the string ball system when they are arranged as shown below:

Free Body Diagram Practice Question 2

Q3: Draw the free body diagram for block A and block B shown in the figure.

Free Body Diagram Practice Question 3

Free Body Diagram FAQs

What is a FBD in Physics?

FBD (Free Body Diagram) is a diagrammatic, graphic and symbolic representation of an object (complete or partial part of another object) in which all the acting forces are shown, with there relative magnitude and direction by directed arrows.

What are Components of FBD in Physics?

The FBD has mainly three components namely the co-ordinate system, body, and the forces acting on the body.

How to draw Free Body Diagram in Physics?

To draw a FBD, we first draw the object of interest by drawing all the forces acting on it and resolving all force vectors into defined x and y components.

What is Normal Force?

Normal force is a contact force, which a surface applies on the contacting body and is perpendicular to the contacting surfaces.

What are Advantages of Free Body Diagram?

FBD helps in clear visualization of all the forces acting on body and to calculate the resulting reactions of these forces.