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 T1T_1 and T2T_2, with T1>T2 T_1>T_2.

The coefficient of friction is kk. Find the ratio T1T2 \dfrac{ T_1}{T_2} when the string is just about to slip over the pulley.

Details and Assumptions:

  • Take k=1π,θ=πk =\frac1\pi , \theta = \pi.

  • Use the approximation e=2.71e = 2.71.

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