bee29400_ch12_690-726.indd Page 713 11/27/08 11:40:43 PM user-s172 /Volumes/204/MHDQ077/work%0/indd%0 Problems 12.35 A 500-lb crate B is suspended from a cable attached to a 40-lb trolley A which rides on an inclined I-beam as shown. Knowing that at the instant shown the trolley has an acceleration of 1.2 ft/s2 up and to the right, determine (a) the acceleration of B relative to A, (b) the tension in cable CD. T C 12.36 During a hammer thrower’s practice swings, the 7.1-kg head A of the hammer revolves at a constant speed v in a horizontal circle as shown. If r 5 0.93 m and u 5 60°, determine (a) the tension in wire BC, (b) the speed of the hammer’s head. 25° D A B Fig. P12.35 B C q r A Fig. P12.36 12.37 A 450-g tetherball A is moving along a horizontal circular path at a constant speed of 4 m/s. Determine (a) the angle u that the cord forms with pole BC, (b) the tension in the cord. B 1.8 m q A C Fig. P12.37 713 38 A single wire ACB of length 80 in.indd Page 714 714 11/26/08 Kinetics of Particles: Newton’s Second Law 6:37:12 PM user-s173 /Volumes/204/MHDQ077/work%0/indd%0 12. A d B q2 q1 C Fig. P12. Knowing the u1 5 60° and u2 5 30° and that the tension is the same in both portions of the wire.41 A 100-g sphere D is at rest relative to drum ABC which rotates at a constant rate.1 N. determine the speed v.4 m. P12. determine the range of the allowable values of the velocity v of the sphere if neither of the normal forces exerted by the sphere on the inclined surfaces of the drum is to exceed 1.39 A single wire ACB passes through a ring at C that is attached to a 12-lb sphere which revolves at a constant speed v in the horizontal circle shown.38. and P12. determine (a) the angle u2 (b) the speed v. passes through a ring at C that is attached to a sphere which revolves at a constant speed v in the horizontal circle shown.bee29400_ch12_690-726. 0. Knowing that u1 5 50° and d 5 30 in.40 12.39. 12. 12.40 Two wires AC and BC are tied at C to a 7-kg sphere which revolves at a constant speed v in the horizontal circle shown. Neglecting friction. P12.2 m A D C 70° 30° B Fig.6 lb.41 . and that the tension in both portions of the wire is 7. determine the range of values of v for which both wires remain taut. Knowing that u1 5 55° and u2 5 30° and that d 5 1. A 35° B Fig. a 12-lb model C of the earth is attached to wires AC and BC and revolves at a constant speed v in the horizontal circle shown.44 A child having a mass of 22 kg sits on a swing and is held in the position shown by a second child. 12.2-lb flyballs of a centrifugal governor revolve at a constant speed v in the horizontal circle of 6-in. and DE and requiring that the links support only tensile forces.42 As part of an outdoor display.43 The 1. A 3 ft C 40° 15° A B 20° 1. radius shown.bee29400_ch12_690-726. (b) immediately after the swing is released. BC. P12.43 D 30° E 1.44 Fig. Determine the range of the allowable values of v if both wires are to remain taut and if the tension in either of the wires is not to exceed 26 lb. AD. Neglecting the mass of the swing.2 lb B Fig.indd Page 715 11/27/08 11:41:04 PM user-s172 /Volumes/204/MHDQ077/work%0/indd%0 Problems *12. P12. determine the tension in rope AB (a) while the second child holds the swing with his arms outstretched horizontally.42 C *12. Neglecting the weights of links AB. determine the range of the allowable values of v so that the magnitudes of the forces in the links do not exceed 17 lb. P12.2 lb 715 . 46 12. where the speed of B is 4. Knowing that the coefficient of kinetic friction between a sled and the run is 0.bee29400_ch12_690-726. A 60 ft 40 ft B C D 140 ft Fig. determine the tangential component of the acceleration of the sled (a) just before it reaches B. P12. Determine the tension in the cable (a) at the top C of the swing. determine the force exerted on a 160-lb driver by the seat of his 3100-lb car as the car.10 and that the speed of the sled is 25 ft/s at B. (b) just after it passes C.45 A 60-kg wrecking ball B is attached to a 15-m-long steel cable AB and swings in the vertical arc shown.47 . and section BC is straight and forms an angle of 20° with the horizontal.47 The portion of a toboggan run shown is contained in a vertical plane. P12. Sections AB and CD have radii of curvature as indicated. (b) at the bottom D of the swing. (a) Determine the radius of curvature r of the vertical profile of the road at A.46 During a high-speed chase. P12. a 2400-lb sports car traveling at a C 20° B D Fig.2 m/s. A r Fig. passes through A. (b) Using the value of r found in part a.indd Page 716 716 11/26/08 Kinetics of Particles: Newton’s Second Law 6:37:13 PM user-s173 /Volumes/204/MHDQ077/work%0/indd%0 12.45 speed of 100 mi/h just loses contact with the road as it reaches the crest A of a hill. traveling at a constant speed of 50 mi/h. A 12. 49 A 54-kg pilot flies a jet trainer in a half vertical loop of 1200-m radius so that the speed of the trainer decreases at a constant rate. respectively. 12. (See Sample Prob.5 N and neglecting the effect of friction. determine (a) the force exerted by the belt on the package just after it has passed point A.6 for the definition of rated speed. (b) the coefficient of static friction between the tires and the track under the prevailing conditions. which rotates in the vertical plane at a constant rate such that v 5 3 m/s. P12.indd Page 717 11/26/08 6:37:14 PM user-s173 /Volumes/204/MHDQ077/work%0/indd%0 Problems 12. θ θ Fig.49 12.48 A series of small packages. P12.4. P12. P12. each with a mass of 0. v A 900 mm B O q Fig. determine (a) the banking angle u.50 12. are dis- charged from a conveyor belt as shown.) Knowing that a racing car starts skidding on the curve when traveling at a speed of 180 mi/h.51 717 . Knowing that the pilot’s apparent weights at points A and C are 1680 N and 350 N.48 C 1200 m B A Fig. 12. (b) the angle u defining the point B where the packages first slip relative to the belt. determine the range of values of u for which block B is in contact with the face of the cavity closest to the axis of rotation O. (c) the minimum speed at which the same car could negotiate the curve. determine the force exerted on her by the seat of the trainer when the trainer is at point B. Knowing that the spring exerts on block B a force of magnitude P 5 1.5 kg.50 A 250-g block fits inside a small cavity cut in arm OA.bee29400_ch12_690-726. Knowing that the coefficient of static friction between each package and the conveyor belt is 0. 1 m/s A B 250 mm Fig.51 A curve in a speed track has a radius of 1000-ft and a rated speed of 120 mi/h. 53 Tilting trains. yet do not feel any side force. The tilting feature of the cars also increases passenger comfort by eliminating or greatly reducing the side force Fs (parallel to the floor of the car) to which passengers feel subjected. determine the required angle of tilt f if passengers are to feel side forces equal to 10% of their weights. 12. Express your answer in terms of the radius r of the curve.54 12. (See Sample Prob. prefer to reduce. As it enters a curve. the banking angle u. For the train of Prob. are designed to travel safely at high speeds on curved sections of track which were built for slower.6 for the definition of rated speed. each car is tilted by hydraulic actuators mounted on its trucks.52 A car is traveling on a banked road at a constant speed v. therefore. . P12. but not eliminate that force. (b) the required angle of tilt f if the passenger is to feel no side force.53 and P12. 12. Designers.54 Tests carried out with the tilting trains described in Prob. Deter- mine the range of values of v for which the car does not skid. determine (a) the magnitude of the side force felt by a passenger of weight W in a standard car with no tilt (f 5 0).53.indd Page 718 718 11/27/08 Kinetics of Particles: Newton’s Second Law 7:00:29 PM user-s172 /Volumes/204/MHDQ077/work%0/indd%0 12. For a train traveling at 100 mi/h on a curved section of track banked through an angle u 5 6° and with a rated speed of 60 mi/h. 12. conventional trains. such as the American Flyer which will run from Washington to New York and Boston.) f q Fig.53 revealed that passengers feel queasy when they see through the car windows that the train is rounding a curve at high speed.bee29400_ch12_690-726. and the angle of static friction fs between the tires and the pavement. 12. Knowing that a 5 40° and that the rod rotates about the vertical AC at a constant rate of 5 rad/s. Knowing that the coefficients of friction are ms 5 0. determine the value of r for which the collar will not slide on the rod if the effect of friction between the rod and the collar is neglected. A Fig.58 Fig. radius is cut in a flat plate which rotates about the vertical AD at a constant rate of 14 rad/s. Knowing that the trunk undergoes a constant tangential acceleration of 0.35 and mk 5 0. C 12. P12. P12. Knowing that r 5 8 in.60 2. and P12. 0.56 A small.5 m B 719 . P12. P12. C D 12. 300-g collar D can slide on portion AB of a rod which is bent as shown. E q A B Fig.55 A small.indd Page 719 11/26/08 6:37:16 PM user-s173 /Volumes/204/MHDQ077/work%0/indd%0 Problems 12.24 m/s2. P12. 200-g collar D can slide on portion AB of a rod which is bent as shown.59 v 12. 0.55.57 26 in. determine whether the block will slide in the slot if it is released in the position corresponding to (a) u 5 80°. and that the rod rotates about the vertical AC at a constant rate of 10 rad/s. (b) u 5 40°.30. B r D a 12.56. (b) a 5 45°.6-lb collar D can slide on portion AB of a rod which is bent as shown. Also determine the magnitude and the direction of the friction force exerted on the block immediately after it is released. determine the range of values of the speed v for which the collar will not slide on the rod if the coefficient of static friction between the rod and the collar is 0. (b) the magnitude of the force required to free a tuft if the average mass of a tuft is 1. Indicate for each case the direction of the impending motion. If the polisher is started so that the fleece along the circumference undergoes a constant tangential acceleration of 4 m/s2.8-lb block E is designed to slide in the slot as the plate rotates.60 A turntable A is built into a stage for use in a theatrical production. A small.58 A semicircular slot of 10-in. Knowing that the rod rotates about the vertical AC at a constant rate and that a 5 30° and r 5 600 mm. determine the smallest allowable value of the coefficient of static friction between the collar and the rod if the collar is not to slide when (a) a 5 15°. determine the coefficient of static friction between the trunk and the turntable. v A Fig.57 A small. 12.6 mg. It is observed during a rehearsal that a trunk B starts to slide on the turntable 10 s after the turntable begins to rotate. determine (a) the speed v of a tuft as it leaves the pad. small tufts of fleece from along the circumference of the 225-mm-diameter polishing pad are observed to fly free of the pad.25.bee29400_ch12_690-726.59 Three seconds after a polisher is started from rest.