Chapter 6 Rigid body6-1 Two blocks are connected by a light string passing over a pulley of radius 0.25m and moment of inertia I. The blocks move(towards the right) with an acceleration of 1.00m/s2 along their frictionless inclines as shown in figure. (a)Draw free-body diagrams for each of the two blocks and the pulley. (b) Determine FT1 and FT2, the tensions in the two parts of the string. (c) Find the net torque acting on the pulley, and determine its moment of inertia, I.6-2 Two masses, m1=35.0kg and m2=38.0kg , are connected by a rope that hangs over a pulley as shown in the figure. The pulley is a uniform cylinder of radius 0.30m and mass 4.8kg, Initially, m1 is on the ground and m2 rests 2.5m above the ground. If the system is released, use conservation of energy to determine the speed of m2 just before it strikes the ground. Assume the pulley bearing is frictionless.6-3 Two masses M1, M2 connected by a cord passing over a pulley of radius R0 and moment of inertial I as shown in the figure. Mass M1 slides on the horizontal surface with coefficient of friction k, and M2 hangs freely. Determine a formula for (a) the angular momentum of the system about the pulley axis, as a function of the speed v of mass M1 and M2, and (b) the acceleration of the system.6-4 A tall, cylindrical chimney falls over when its base is ruptured. Treat the chimney as a thin rod of length 55.0 m. At the instant it makes an angle of 35.00 with the vertical as it falls, what are (a) its angular speed, (b) the radial acceleration of the top, and (c) the tangential acceleration of the top.(Hint: Use energy considerations, not a torque. (d) At what angle is the tangential acceleration equal to g?6-5 At the instant the displacement of a 2.00 kg object relative to the origin is , its velocity is (2.0)4(3.)dmijkrr(6.0/)3.(.0/)vmsijskrrAnd it is subject to a force . Find (a) the (.)84FNijkracceleration of the object, (b) the angular momentum of the object about the origin, (c) the torque about the origin acting on the object, and (d) the angle between the velocity of the object and the force acting on the object.6-6 At time t, gives the position of a 3.0 kg particle 224.0(6.)rtitjrrelative to the origin of an xy coordinate system ( is in meters and t is in rvseconds) (a) Find an expression for the torque acting on the particle relative to the origin . (b) Is the magnitude of the particles angular momentum relative to the origin increasing, decreasing, or unchanging? 6-7 In Fig. , a 1.0 g bullet is fired into a 0.50 kg block attached to the end of a 0.60 m nonuniform rod of mass of 0.50kg. The block-rod-bullet system then rotates in the plane of the figure, about a fixed axis at A. The rational inertia of the rod along that axis at A is 0 060 kg .m2 . Treat the block as a particle. (a) What then is the rotational inertia of the block-rod-bullet system about point A? (b) if the angular speed of the system about A just after impact is 4.5rad/s, What is the bullets speed just before impact?6-8 In Fig., a small 50 g block slides down a frictionless surface through height h=20 cm and then sticks to a uniform rod of mass 100 g and length 40 cm. The rod pivots about point O through angle before momentarily stopping. Find .Ans: 6-1. (b)75N (c) 21.7Ikgm6-2. v = 1.4 m/s.6-3 . (a) (b) 0120(/).LRMIRv 22120/(/)KaMgIR6-4 (a) (b) ar =5.32 m/s2 .3 rads(c) (d) = 41.8.284m/.ta6-5 (a) = (3.00 m/s2) (4.00 m/s2) + (2.00 m/s2) .a i j k(b) = (42.0 kg.m2/s) + (24.0 kg.m2/s) + (60.0 kg.m2/s) .L i j k(c) = (8.00 N.m) (26.0 N.m) (40.0 N.m) .ri j k(d) = cos148.0/(7.35 10.8) = 127.6-6 (a) (b) the angular momentum increases in proportion to t2. 48tkNm()v6-7 (a) I = 0.24 kg m2. (b) v0 = 1.8 103 m/s6-8 1cos(0.5)3