Laws Of Motion

§§ MOTION OF BODIES CONNECTED BY STRINGS 

i) When two bodies of masses m₁ and m₂ are tied to the ends of a light string placed on the smooth horizontal surface, these are pulled by a force F. 

                  

    acceleration of the system  \( a = \frac{F} {{m_1 + m_2 }} \)                
    Tension in the string  \( T = m_1 a \)
              \( T = \frac{{m_1 F}} {{m_1 + m_2 }} \)

ii) If in the above example three bodies are pulled with a force F. 

                     

Acceleration produced in the system \( a = \frac{F} {{m_1 + m_2 + m_3 }} \) 
Tension produced in the string between the blocks m₁ and m₂ is \( T_1 = m_1 a = \frac{{m_1 F}} {{m_1 + m_2 + m_3 }} \) 
Tension produced in the string between m₂ and m₃ \( T_2 = \left( {m_1 + m_2 } \right)a \) 
         \( T_2 = \frac{{\left( {m_1 + m_2 } \right)F}} {{m_1 + m_2 + m_3 }}\left( {\because F - T_2 = m_3 a} \right) \)