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Phys011 / HKUST / Fall 2007
Homework 6 (Chapter 10)
20. Rigid rods of negligible mass lying along the y axis connects three particles (Fig. P10.20). The system rotates about the x axis with an angular speed of 2.00 rad/s. Find (a) the moment of inertia about the x axis and the total rotational kinetic energy evaluated from . I2 and (b) the tangential speed of each particle and the total kinetic energy evaluated from . mivi2. (c) Compare the answers for kinetic energy in parts (a) and (b).
Fig. P10.20
35. A block of mass m1 = 2.00 kg and a block of mass m2 = 6.00 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.250 m and mass M = 10.0 kg. These blocks are allowed to move on a fixed block-wedge of angle
= 30.0 as in Figure P10.35. The coefficient of kinetic friction is 0.360 for both blocks. Draw free-body diagrams of both blocks and of the pulley. Determine Fig. P10.35
(a) the acceleration of the two blocks, and
(b) the tensions in the string on both sides of the pulley.
42. Consider the system shown in Fig. P10.42 with m1 = 20.0 kg, m2 = 12.5 kg, R = 0.200 m, and the mass of the uniform pulley M = 5.00 kg. Object m2 is resting on the floor, and object m1 is 4.00 m above the floor when it is released from rest. The pulley axis is frictionless. The cord is light, does not stretch, and does not slip on the pulley. Calculate the time interval required for m1 to hit the floor. How would your answer change if the pulley were massless?
Fig. P10.42
46. A solid sphere is released from height h from the top of an incline making an angle with the horizontal. Calculate the speed of sphere when it reaches the bottom of the incline (a) in the case that it rolls without slipping and (b) in the case that it slides frictionlessly without rolling. (c) Compare the time intervals required to reach the bottom in cases (a) and (b).
49. (a) Determine the acceleration of the center of mass of a uniform solid disk rolling down an incline making an angle with the horizontal. Compare this acceleration with that of a uniform hoop. (b) What is the minimum coefficient of friction required to maintain pure rolling motion for the disk?
57. A long, uniform rod of length L and mass M is pivoted about a horizontal, frictionless pin through one end. The rod is released , almost from rest in a vertical position as shown in fig. P10.57. At the instant the rod is horizontal, find (a) its angular speed, (b) the magnitude of its angular acceleration, (c) the x and y components of the acceleration of its center of mass, and (d) the components of the reaction force at the pivot.
Fig. P10.57
63. The blocks as shown in Fig. P10.63 are connected by a string of negligible mass passing over a pulley of radius 0.250 m and moment