IIT (NTSE/Olympiad)

Newton's Laws Of Motion & Friction

8. Motion of bodies in contact

8. Motion of connected Bodies
Case (A) :
For two Bodies :
F is the pull on body A of mass m₁. The pull of A on B is exercised as tension through the string connecting A and B. The value of tension throughout the string is T only.
But this manifests as a pull T on B and a "reaction pull" T on A the free body diagram in this case are shown as follows.

Note : The spring is massless
Free body diagrams :

For body A	For body B

R₁= m₁g F – T = m_1a	R₂= m₂g T = m₂a

⇒

Case (B) :
For Three bodies :

Free body diagrams :

For A	For B	For C
R₁= m₁g T₁= m₁a	R₂= m₂g T₂– T₁= m₂a ⇒ T₂= m₂a + T₁ T₂= (m₂ + m₁)a	R₃= m₃g F – T₂= m₃a ⇒ F = m₃a + T₂ = m₃a + (m₁ + m₂)a F = (m₁ + m₂ + m₃)a