A classical mechanics problem by Tanay Kibe

Consider a pulley as shown. A string is placed on the pulley. The string is massless and the pulley has friction. Consider the two tensions \(T_1\) and \(T_2\), with \( T_1>T_2\).

The coefficient of friction is \(k\). Find the ratio \( \dfrac{ T_1}{T_2}\) when the string is just about to slip over the pulley.

Details and Assumptions:

  • Take \(k =\frac1\pi , \theta = \pi\).

  • Use the approximation \(e = 2.71\).

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