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Figure P10.67

68.The speed of a moving bullet can be determined by allowing the bullet to pass through two rotating paper disks mounted a distance d apart on the same axle (Fig. P10.68). From the angular displacement of the two bullet holes in the disks and the rotational speed of the disks, we can determine the speed v of the bullet. Find the bullet speed for the following data:  

d = 80 cm, = 900 rev/min, and = 31.0.

Figure P10.68

69.A uniform, hollow, cylindrical spool has inside radius R/2, outside radius R, and mass M (Fig. P10.69). It is mounted so that it rotates on a fixed horizontal axle. A counterweight of mass m is connected to the end of a string wound around the spool. The counterweight falls from rest at t = 0 to a position y at time t. Show that the torque due to the friction forces between spool and axle is

Figure P10.69

70.The reel shown in Figure P10.70 has radius R and moment of inertia I. One end of the block of mass m is connected to a spring of force constant k, and the other end is fastened to a cord wrapped around the reel. The reel axle and the incline are frictionless. The reel is wound counterclockwise so that the spring stretches a distance d from its unstretched position and is then released from rest.  (a) Find the angular speed of the reel when the spring is again unstretched.  (b) Evaluate the angular speed numerically at this point if I = 1.00 kg·m2, R = 0.300 m, k = 50.0 N/m, m = 0.500 kg, d = 0.200 m, and = 37.0°.

Figure P10.70

71.Two blocks, as shown in Figure P10.71, are connected by a string of negligible mass passing over a pulley of radius 0.250 m and moment of inertia I.

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