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 \(m\).

Ropes and Pulleys

Part 1#

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

Answer Section#

  • \(T_3\) > \(T_2\) > \(T_1\)

  • \(T_3\) > \(T_2\) = \(T_1\)

  • \(T_3\) = \(T_3\) = \(T_1\)

  • \(T_3\) < \(T_2\) < \(T_1\)

  • \(T_3\) < \(T_2\) = \(T_1\)

Part 2#

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

Answer Section#

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

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

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

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

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


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