You and your group are working at a company that designs equipment to be used in gyms and fitness centers. Your supervisor has an idea for a new piece of exercise equipment. The figure below shows the apparatus. The long, vertical spring is attached to the floor at the lower end and at the upper end to a rope that passes over a cylinder of mass M and radius R. At the other end of the rope is a handle from which a person can hang. In operation, a fitness center customer of mass m hangs from the handle at the end of the rope. By pumping his body up and down at the right frequency, as if he is doing chin-ups, the customer can achieve a resonance vibration in which he is vibrating up and down with a maximum amplitude. Many Calories are expended by the customer in setting himself in vibration and building up a large amplitude. During the vibration, the rope does not slide on the cylinder, so the cylinder rotates back and forth in periodic motion along with the customer. The cylinder has a mass of M = 50.0 kg and a radius of R = 0.400 m, and the spring constant is k = 450 N/m. Work with your group to determine the period (in s) of the resonance vibration of a 95.0 kg customer hanging from the handle and pumping up and down.
You and your group are working at a company that designs equipment to be used in gyms and fitness centers. Your supervisor has an idea for a new piece of exercise equipment. The figure below shows the apparatus. The long, vertical spring is attached to the floor at the lower end and at the upper end to a rope that passes over a cylinder of mass M and radius R. At the other end of the rope is a handle from which a person can hang. In operation, a fitness center customer of mass m hangs from the handle at the end of the rope. By pumping his body up and down at the right frequency, as if he is doing chin-ups, the customer can achieve a resonance vibration in which he is vibrating up and down with a maximum amplitude. Many Calories are expended by the customer in setting himself in vibration and building up a large amplitude. During the vibration, the rope does not slide on the cylinder, so the cylinder rotates back and forth in periodic motion along with the customer. The cylinder has a mass of M = 50.0 kg and a radius of R = 0.400 m, and the spring constant is k = 450 N/m. Work with your group to determine the period (in s) of the resonance vibration of a 95.0 kg customer hanging from the handle and pumping up and down.
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