A vertical rod of mass 4 kg is hanging on a rope and a 3-kg cat is grasping the bottom end of the rod. The rope is cut off and the frightened cat begins to run up on the rod. While the rod is falling

Question

A vertical rod of mass 4 kg is hanging on a rope and a 3-kg cat is grasping the bottom end of the rod. The rope is cut off and the frightened cat begins to run up on the rod. While the rod is falling vertically, the cat remains at the same height, with respect to the ground. The acceleration of the rod is k g /4 m/s² where g is the acceleration due to gravity. Find k .

TestHub · Accepted Answer

Since the cat remains at the same height with respect to the ground, it is in equilibrium, so the rod must push it up with a force equal to its weight:

$T = weight of cat = 3 g$

By Newton's third law the cat pushes the rod down with the same force. The net downward force on the rod is therefore $T + 4 g = 3 g + 4 g$ , and

$a_{ro d} = \frac{3 g + 4 g}{4} = \frac{7 g}{4} m/s^{2} \Rightarrow k = 7$

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