As pictured, two blocks of mass \(2m\) are connected by a rope of tension \(T_3\) and pulled along a frictionless surface. Another (massless) rope of tension \(T_2\) connects the two blocks to a (frictionless) pulley of mass \(m/2\), which is a disk of radius \(R\). The (massless) rope continues with tension \(T_1\) on the other side of the pulley to a hanging mass of mass \(m\).
Referring to the image, the tensions in the ropes satisfy:
Referring to the image, the magnitude of the acceleration of the system is:
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