Free Body Diagram

What is a Free Body Diagram?

Free Body Diagrams (FBD) are useful aids for representing the relative magnitude and direction of all forces acting upon an object in a given situation. The first step in analyzing and describing most physical phenomena involves the careful drawing of a free-body diagram. In a free body diagram, the size of the arrow denotes the magnitude of the force while the direction of the arrow denotes the direction in which the force acts.

A free body diagram is defined as:

A free-body diagram is a graphic, dematerialized, symbolic representation of the body (structure, element or segment of an element) in which all connecting “pieces” have been removed.

Features of Free Body Diagram

A free-body diagram is a diagram that is modified as the problem is solved. Normally, a free body diagram consists of the following components:

  • A simplified version of the body (most commonly a box)
  • A coordinate system
  • Forces are represented as arrows pointing in the direction they act on the body
  • Moments showed as curved arrows pointing in the direction they act on the body

The number of forces acting on a body depends on the specific problem and the assumptions made. Commonly, air resistance and friction are neglected.

Exclusions in Free Body Diagram

Some of the things that a free body diagram excludes are as follows:

  • Bodies other than the free body diagram
  • Constraints
  • Internal Forces
  • Velocity and Acceleration Vectors

What is the purpose of a free body diagram?

Free body diagrams are tools that are used to visualize the force and moments applied to a body and to calculate the resulting reactions in many types of mechanics problems.

How to make a free body diagram?

In the section, we will explain the step-by-step procedure of drawing a free body diagram:

1. Identify the Contact Forces

Identify the Contact Forces

To identify the forces acting on the body, draw an outline of the object with dotted lines as shown in the figure. Make sure to draw a dot when something touches the object. When there is a dot, it indicates that there is at least one contact force acting on the body. Draw the force vectors at the contact points to represent how they push or pull on the object.

Contact points to represent how they push or pull on the object

2. After identifying the contact forces, draw a dot to represent the object that we are interested in. Here, we are only interested in determining the forces acting on our object.

3. Draw a coordinate system and label positive directions.

4. Draw the contact forces on the dot with an arrow pointing away from the dot. The arrow lengths should be relatively proportional to each other. Label all forces.

5. Draw and label our long-range forces. This will usually be weight unless there is an electric charge or magnetism involved.

6. If there is acceleration in the system, then draw and label the acceleration vector.

Common Mistakes made while drawing a free body diagram
  • Avoid drawing forces of the object acting on other objects
  • The direction of the different types of forces is denoted wrong.

The direction of different forces:

  1. Weight is always down
  2. Friction is always parallel to the contact surface,
  3. The normal force is always perpendicular to the contact surface, and tension only pulls.

Free Body Diagram Examples

In this section, we have listed free diagrams considered under different scenarios.

1. A bottle is resting on a tabletop. Draw the forces acting on the bottle.

Forces acting on the bottle

2. An egg is free-falling from a nest in a tree, neglecting the air resistance, what would the free body diagram look like?

An egg is free-falling from a nest

3. If a rightward force is applied to a book in order to move it across a desk at a constant velocity. Considering only the frictional forces and neglecting air resistance. A free-body diagram for this situation looks like this:

A free-body diagram where a rightward force is applied

4. A skydiver is descending at a constant velocity. Considering the air resistance, the free body diagram for this situation would like the following:

A skydiver is descending at a constant velocity

Free Body Diagram Solved Problem

Example: Draw a free body diagram of three blocks placed one over the other as shown in the figure.

A free body diagram of three blocks placed one over the other

Solution:

The forces acting on the individual elements of the system are shown below:

Forces acting on the individual elements of the system

Description of Forces acting on each block:

The forces on block “C” are:

WC=mCg= its weight, acting downward

NB= normal reaction on “C” due to the upper surface of block B, acting upward

The forces on block “B” are:

WB=mBg= its weight, acting downward

NB= normal reaction on “B” due to the lower surface of block C, acting downward

NA= normal reaction on “B” due to the upper surface of block A, acting upward

The forces on the block “A” are :

WA=mAg= its weight, acting downward

NA= normal reaction on “A” due to the lower surface of block B, acting downward

NO= normal reaction on “A” due to horizontal surface, acting upward

The FBD of the blocks as points with external forces are shown here.

FBD of the blocks as points with external forces

Frequently Asked Questions – FAQs

What is the definition of a free body diagram?

A free-body diagram is a graphic, dematerialized, symbolic representation of the body (structure, element or segment of an element) in which all connecting “pieces” have been removed.

What does a free body diagram represent?

Free-body diagrams represent the relative magnitude and direction of all forces acting upon an object in a given situation.

How to draw a free body diagram?

While drawing a free body diagram, we draw the object of interest by drawing all the forces acting on it and resolve all force vectors into x– and y-components. Separate free body diagrams should be drawn for each object in the problem.

What is the free body diagram indicative of?

Free body diagrams are used to visualize the forces and moments applied to a body and to calculate the resulting reactions in many types of mechanics problems.

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