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Vector Mechanics for Engineers: Dynamics
- A shaft with 3 meters span between two bearings carries two masses of 10 kg and 20 kg acting at the extremities of the arms 0.45 m and 0.6 m long respectively. The planes in which these masses rotate are 1.2 m and 2.4 m respectively from the left end bearing supporting the shaft. The angle between the arms is 60°. The speed of rotation of the shaft is 200 r.p.m. If the masses are balanced by two counter-masses rotating with the shaft acting at radii of 0.3 m and placed at 0.3 m from each bearing centers, estimate the magnitude of the two balance masses and their orientation with respect to the X-axis, i.e. mass of 10 kg.arrow_forwardEXERCISE 5.31 The right triangular plate is welded to the shaft, which rotates at constant speed. Determine the force-couple acting at bearing A that is equivalent to the force system the bearings must exert to sustain this motion. a 61 aarrow_forward45 N Ans. (a) 34 N, 0=280 (b) dRA = 11.64 mm from B to the left; dRc3D62 mm below B 36 Dr. M.S. Meddah 3.116 A 160-N motor is mounted on the floor. Find the resultant of the weight and the forces exerted on the belt, and determine where the line of action of the resultant intersects the floor. 700 N 30° 50 mm -300 N 50 mm Final result: Resultant, R = 925.92 N and 0 = 11.840 x= -582.22 mm i.e. resultant intersects the floor 582.22 mm to the left of the vertical centerline through O. 37arrow_forward
- 2. Show that the gravitational self-energy (energy of assembly piecewise from infinity) 3GM? of a uniform sphere of mass M and radius R is U = - 5Rarrow_forwardThe telescoping arm ABC is used to provide an elevated platform for construction workers. The workers and the platform together have a mass of 200 kg and have a combined center of gravity located directly above C. For the position when θ=20°, determine (a) the force exerted at B by the single hydraulic cylinder BD, (b) the force exerted on the supporting carriage at A.arrow_forwardEach of the gears A and B has a mass of 10 kg and a radius of gyration of 190 mm, while gear Chas a mass of 2.5 kg and a radius of gyration of 80 mm. Consider that a couple M of constant magnitude 10 N-m is applied to gear C. 250 mm 250 mm 100 mm Determine the corresponding tangential force acting on gear A. The corresponding tangential force acting on gear A is 26.35 O N.arrow_forward
- 3.104 Five separate force-couple systems act at the corners of a piece of sheet metal, which has been bent into the shape shown. Determine which of these systems is equivalent to a force F = (10 lb)i and a couple of moment M = (15 lb - ftj + (15 lb - ft)k located at the origin. 5 Ib-ft 15 Ib-ft 5 Ib-ft 5 lb-ft 15 Ib-ft 10 lb 10 lb 15 Ib-ft B 2 ft 25 Ib-ft 10 lb 80 lb-ft 2.5 ft 10 lb 15 Ib-ft 2 ft 10 Ib 2 ft' 15 Ib-ft Fig. P3.104 Luarrow_forwardA uniform disk of mass m = 4 kg and radius r = 150 mm is supported by a belt ABCD that is bolted to the disk at B and C. If the belt suddenly breaks at a point located between A and B, draw the FBD and KD for the disk immediately after the break.arrow_forward1. Determine the angle ” between the table and the plane face of thehemisphere in its equilibrium position, if a solid hemisphere of radius 3m weighing 30kN rests on its convex surface on a level table. A body weighing 3 kN is attached to a point in the circumference of the plane face of the hemisphere. In addition, a force of 5 kN is applied at an angle of 60° from the horizontal level as shown.arrow_forward
- Joints at O and A are vertical hinges that can withstand force in all three coordinate directions and moment on the x and z axes. The mass of arm OA is 2.00 kg, that of arm AB is 2.50 kg, and tray C is 4.00 kg. The center of mass of each member is at its geometric center. Determine the reaction in O for the configuration shown.arrow_forwardB. F 4 in 6 in 8 in 20 in 3 in The model airplane shown above is supported by a single fixed support at F. The weight of the model can be idealized by 4 Ibs concentrated at point A, and 2 Ibs each concentrated at points B and C. Which of the following is closest to the magnitude of the couple moment reaction at point F that acts parallel to the y-axis? Assume that weight/gravity acts in the negative z direction. a) 8 lb-in b) O Ib-in c) 64 lb·in d) 172 Ib·inarrow_forwardThe 12ft pole AC (negligible mass) lies in the y-z plane and forms a 30° angle with the z-axis. The pole is held in place at point C by a ball-and-socket joint. Two cables, BD and BE, are fixed to the pole at point B (these represent two separate cables attached at B). A 110 lb force pulls downward at the end of pole AC in the vertical direction (y-direction). If the distance between B and C along the feet, determine the Reactions at C (ball-and-socket joint) The tension in cables BD and BE.arrow_forward
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