Newton’s laws of motion | Basic Physics for IIT JAM PDF Download

Free Body Diagram

The Free body diagram (FBD) is representation of all forces acting on independent bodies. To draw FBD we assume the body to be a point mass and then we mark all forces acting on it. A suitable coordinate axis may be drawn to resolve the forces along X and Y direction. Some common external forces are discussed below: 

1. Weight: The weight of body is w = mg as shown in figure
                   

2. Normal forces: When a body is in contact with any surface then the surface will exert normal force N ( reaction force). The direction of normal force is perpendicular to the plane of surface.   If a Block of mass m is lying on any surface, the surface will push the block in perpendicular direction w.r.t. the plane of the surface with magnitude  N and at the same time by Newtons third law the block will push the contact surface with same magnitude but opposite in direction.  

Example 1: A Force F of 20N acts on a block m₁ =  5  kg such that m₂ = 3 Kg is in contact with m₁ and m₃ = 2 Kg as shown in figure.

(i) Find acceleration of each block  

 (ii) Find contact force in each block 

Solution: (i) All are moving with same acceleration(ii) Free body diagram  

3. Tension: Force F is exerted on mass m through string .Then any section of the string is pulled by two equal and opposite forces. Any one of these forces is called tension. Tension always gives pulling effect to mass. In the Figure, the force F is acted on mass m through string so there is tension T in the string giving pulling effect.

Now let us analyze another system in which two masses m₁ and m₂ are attached with a string and force F is acted on the mass m₁ as shown in figure. Due to force F tension T is developed in the string. If one will draw free body diagram for m₁ the tension will act towards left and if free body diagram draw for m₂ the tension will act towards right. In both the case tension will produce pulling effect on mass m₁ and m₂.

String is massless show there is same tension acts on is part of the string. 

Free body diagram for mass m₁ and  m₂

 If the rope is massless the tension in string is same for all sections of string other wise it will depend on mass of segment of the rope. 

Example 2:   Figure shows a block of  mass m₁ and m₂  attached to mass less string. Another  mass m₃  attached to mass m₂ with different mass less  string . All contact surface are Smooth. Mass  m₂ can move vertical downward direction under influence of Gravitation field g. Find the acceleration of each mass and tension in both string.

Solution: All forces  act on  the system  shown in figure T and  T₁ are Tension  in first and second string, m₁g is weight of mass m₁ . The weight of other   particle will balanced with their normal force exerted by the surface . Hence length of  each string is fixed so  all three particle will move will same acceleration . 

The free body diagram and equation of motion for mass m₁