Torque on Discs & Pulleys Practice Problems

A 3.0 kg bag resting on the ground is tied to a vertical cord. The cord of negligible mass passes through a cylinder with a groove in which a cord can run. The other end of the cord is attached to a 6.0 kg ball, as shown in the figure. The cylinder is 4.0 cm in radius and has a mass of 1.25 kg. The friction force about the rotation axis produces a torque of 1 N•m. Calculate the time needed for the 6.0 kg ball to hit the ground if it is released from a height of 1.25 m without initial speed.

A building employs a dual counterweight system with two elevator cars. Elevator Car A has a mass of 1200 kg and starts at the tenth floor. Elevator Car B, with a mass of 1250 kg, begins at the second floor. They are connected by a steel cable that runs over a pulley that is free to rotate about a fixed axis at the top of the shaft. The pulley is a solid cylinder with a radius of 0.80 meters and a mass of 100 kg. Find the acceleration of each elevator car as they move in the shaft.

A sled connected by a strong line wraps around a large wheel at the top of a snowy slope. The wheel can rotate, offering some resistance due to friction. Starting from rest, find the speed of the sled after it has slid 1.50 meters down the slope. The coefficient of friction for all contact surfaces is μ = 0.050. Hint: $a=g \frac{m(\sin \theta-\mu \cos \theta)-\mu M)}{\left(m+\frac{1}{2} M\right)}$

A cable car and a counterweight are connected by a cable passing over a pulley. The pulley has a radius of 0.30 meters and an unknown moment of inertia, denoted as I. The system accelerates at 0.75 m/s² as the cable car moves uphill and the counterweight descends. Determine the magnitude of the net torque acting on the pulley and its moment of inertia.

Consider an elevator system with a 500.0 kg cabin and a 450.0 kg counterweight connected by a massless, inextensible cable over a solid cylindrical drum (radius 1.0 m, mass 400.0 kg). Initially at rest, the cabin descends and the counterweight rises when released. Determine the acceleration of both the cabin and the counterweight.