# Rope Tension Between Blocks#

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 $$m$$.

## Part 1#

Referring to the image, the tensions in the ropes satisfy:

• $$T_3$$ > $$T_2$$ > $$T_1$$

• $$T_3$$ > $$T_2$$ = $$T_1$$

• $$T_3$$ = $$T_3$$ = $$T_1$$

• $$T_3$$ < $$T_2$$ < $$T_1$$

• $$T_3$$ < $$T_2$$ = $$T_1$$

## Part 2#

Referring to the image, the magnitude of the acceleration of the system is:

• $$a = \frac{4}{21} g$$ $$\rm{ \frac{m}{s^2} }$$

• $$a = \frac{g}{4}$$ $$\rm{ \frac{m}{s^2} }$$

• $$a = \frac{g}{2}$$ $$\rm{ \frac{m}{s^2} }$$

• $$a = g$$ $$\rm{ \frac{m}{s^2} }$$

• $$a = \frac{2}{3} g$$ $$\rm{ \frac{m}{s^2} }$$