Question

Hi, I really just need help with number 8. The rest of the question is provided for context, thanks!

6.10 pts) A patient with a broken leg was placed in traction using the system shown below at left. Once the cast is off of the foot, the system can be modeled as shown at right where mi is the mass of the cast. In a most unfortunate incident, the cast slips off of the patient's foot and is flung by the traction system. In this problem, model the pulleys as massless, the system as frictionless, and assume the rope rolls over the pulleys without slipping. a. Use Newton's laws to find an expression for the acceleration of m2, the counterweight, in terms of m, m2, and g. b. From your expression, what must be true of m, and m2 for the acceleration to be zero, that is, the cast is not flung. c. If m1 m2, use kinematics to find the speed of the counterweight after it has fallen 2.0 m. m1 m2 m2 7. (10 pts.)* Repeat problem 6 part c using conservation of energy. 8. (10 pts.) Now suppose that you want to refine the model of the system above by considering the non zero mass of the pulleys. Model the pulleys as uniform disks. Assume that 1/4 of the mass of the cast- pulley system is the mass of disk A (so this disk has mass Im and the cast has massm,), and disc B has mass 1/8 mi a. Repeat problem 7 in the refined model to get a refined speed b. Find the tangential acceleration of the disk in pulley B using kinematics and your answer in part a. c. Find the net torque on pulley B if it's mass is 0.10 kg and its radius is 0.20 m d. What is the difference in the tension in the rope on the 2 sides of pulley B? On which side is it greater?

Answer 1

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