Drawing Flawless Free Body Diagrams.

Here we intend to learn the first step to solve a mechanics problem. When we talk of force, we need a specification so as how is the force acting on the body. This further means that the magnitude as well as direction and the point of action of this force are necessary to ascertain the motion of the body. The problem where we consider all the forces acting on an object, pictorially, is the free-body diagram (FBD). In other words, a free-body diagram is a picture of the physical situation we are analyzing, and which depicts all of the relevant forces acting on the objects of interest.



Steps for getting the FBD for the objects under consideration.


1.The complexity of the FBD is dependent upon the idealized model you are applying in that situation. In other words, if your model indicates ignoring a force, it shouldnsinglequotet show up in the FBD. Let’s say for example that we neglect the air drag for the motion of a particle projected in the x-y plane. If in this situation, we are asked to indicate the forces acting on the particle during the flight, the FBD shouldn’t include the air drag.


2.When creating a free-body diagram, you must orient it in a coordinate system, typically a two-dimensional one. This is almost always done so that the force of gravity is pulling straight down (in the negative-y direction). Itsinglequotes generally preferred to orient things so that any horizontal movement will be in the positive-x direction (i.e. to the right), although so long as you maintain the same orientation you will get physically identical results.


3. Identifying the forces: The best way to list the forces acting on the objects under consideration, is by classifying them under two heads, i.e. Contact Forces and Field Forces.


3.1 Contact Forces: Identification of the contact forces is mechanical in a sense that we just need to identify the contacts that the object is making with the system components other than it. For eg: FBD of a book kept on the table at rest would (under the influence of no force other than gravity)indicate just a single contact force, which is the normal reaction from the table balancing its weight.


Consider the following case:




The FBD in the above diagram indicates that the object is in contact with a) the string: hence the tension force; b) Fluid: hence the buoyant force. Air pressure has been neglected and hence not included in the FBD.


Examples of contact forces generally encountered are: Friction, Normal Reaction, Tension, Air Drag, Viscous Drag, Buoyant Force, etc.


3.2 Field Forces: Forces which exert their influence without being in direct contact with the object are field forces. For eg: The gravitational force, the electro-magnetic force, etc. are field forces that we generally encounter in mechanics problems.


The idea here is to identify the field that the object under consideration is under the influence of, and include all the relevant forces in the FBD. For eg: A charged particle projected in the x-y plane, with an electric field present in the space surrounding it, would have both the gravitational and the electromagnetic forces indicated as the field forces in FBD.

So, considering that only the gravitational field is present then the complete FBD of the body will be:

Please note that both weight and buoyant  force act on the center of the mass, they are shown here in different lines just for the sake of clarity.


4. Point of action and direction: Many a times we encounter more than just particles in the physical situations. When forces act on rigid bodies, or objects of finite dimensions, the degrees of freedom increase. Hence, it is absolutely essential to know the point of action and direction of the forces acting, subject to the selection of the coordinate system. For finite sized objects, the scaled down figures (FBD’s) should clearly indicate the points of action and direction.


All that remains now is to resolve the forces and apply Newton’s Laws of Motion, Torque Equations etc. to solve the Classical Mechanics Problem. A flawless FBD is what helps us to arrive at the force/torque equations from the problem statement. Hence, drawing the flawless FBD is absolutely critical.