Free Body Diagrams (F.B.D.) on Inclines

A free body diagram is a simple sketch showing all the forces acting on an object when it is on its own (i.e. removed from its surrounding). 

Here are some guidelines for drawing Free Body Diagrams.

  • Forces are represented by vectors
  • A relative scale should be used to show the relative size of the forces whenever possible.
  • Only the forces acting on the object should be included not the forces that the object exerts on other objects.
  • All forces (vectors) should be drawn with respect to the center of gravity (or center of mass of the object). 
  • This point is usually located at the geometric center of the object

A. FBD for an object resting on a flat (horizontal) surface

Fis the elastic force pointing up 
Fis the force of gravity; pointing down
  • Note the symbols used to represent the forces Fe is the elastic Force, Fg is the force of gravity. 
  • Note also the arrow head on top of the symbol indicating that the Force is a vector.
  • Note the direction of the forces; Fe is up  while Fg is down.  
  • We say that these forces acting collinearly (in the same line of action)  are equal in magnitude and opposite in direction are in static equilibrium. 
  • When this happens the forces on an object are said to be balanced.

B. FBD for an object resting on an inclined plane

In the diaram below, an object with mass m rests on an incline.
Here the Normal Force Fstill points as predicted but notice that it is alwyas perpendicular to the plane where the object rests.
The force of gravity F  points straight down ytowards the centre of the Earth, as redicted. 
However, it is  the y component of the force of gravity that counterbalances the normal force collinearly.
The magnitude of the components of the force of gravity component can be calculated by trigonometric rules.