13-102. Using a forked rod, a smooth cylinder P. having a

Chapter 13, Problem 13-102

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Using a forked rod, a smooth cylinder P, having a mass of \(0.4 \mathrm{~kg}\), is forced to move along the vertical slotted path \(r=(0.6 \theta) \mathrm{m}\), where \(\theta\) is in radians. If the cylinder has a constant speed of \(v_C=2 \mathrm{~m} / \mathrm{s}\), determine the force of the rod and the normal force of the slot on the cylinder at the instant \(\theta=\pi\) rad. Assume the cylinder is in contact with only one edge of the rod and slot at any instant. Hint: To obtain the time derivatives necessary to compute the cylinder's acceleration components \(a_r\) and \(a_\theta\), take the first and second time derivatives of \(r=0.6 \theta\). Then, for further information, use Eq. 12-26 to determine \(\dot{\theta}\). Also, take the time derivative of Eq.12-26, noting that \(\vec{v}=0\) to determine \(\ddot{\theta}\).