The block-and-tackle system is released from rest with all cables taut. Neglect the mass and friction of all pulleys and determine the acceleration of each cylinder and the tensions T₁ and T₂ in the two cables.

.) The figure shows a vertical force applied tangentially to a uniform cylinder of weight F. The coefficient of static friction between the cylinder P and all surfaces is 0.500. The force P is increased in magnitude until the cylinder begins to rotate. In terms of F, find the maximum force magnitude P that can be applied without causing the cylinder to rotate. Suggestion: show that both friction forces will be at their maximum values when the cylinder is on the verge of slipping.

A hoop of mass 3.00 kg and radius 1.00 m is moving at 3π rad/s across a horizontal surface. The coefficient of friction between the hoop and the surface is 0.65. Calculate how far the hoop will travel before it comes to rest.

A 6.25 g quarter sits 25 cm from the axis of rotation on a turnable. The maximum period of rotation without the quarter slipping is 1.8 seconds. What must the coefficient of static friction be in order to keep the quarter from sliding outward when the turntable is in motion?