Question

Find the acceleration of the three weights shown in fig. Assume pulleys are frictionless. Also, find the tension in the cables. 

Answer 1

$200-T_1=m_1a_1$

$40-T_2=-m_2(a_1+a_2)$

$60-T_2=m_3(-a_1+a_2)$

$-T_1+2T_2=0$

From this system of linear equations

$a_1=3.51\ (m/s^2)$

$a_2=2.7\ (m/s^2)$

$T_1=129.7\ (N)$

$T_2=64.86\ (N)$