The two pulleys are fastened together and are used to hoist the cylinder of mass m. The

Chapter 6, Problem 6/86

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The two pulleys are fastened together and are used to hoist the cylinder of mass m. The fraction k can vary from near zero to one. Derive an expression for the tension T required to raise the cylinder at a steady speed if the coefficient of friction for the bearing of radius \(r_0\) is \(\mu\), a small enough value to permit the substitution of \(\mu\) for sin \(\phi\), where \(\phi\) is the friction angle. The mass of the pulley unit is \(m_0\). Evaluate your expression for T if m = 50 kg, \(m_0\) = 30 kg, r = 0.3 m, \(k=\frac{1}{2}, r_0=25 \mathrm{~mm}\), and \(\mu=0.15\).