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Vector Mechanics For Engineers
- 1. An excavator encounters a reaction force of 7600 lb from the ground, normal to line AC, as shown. The shaded structural members (Dipperstick (FH), Mainboom (ADK), bucket, and hydraulic cylinders) have a combined weight of 15000 lb and a horizontal mass center located midway between points C and G. ΑΠΟ G 3 ft 6 in. 40° E Mainboom 3 ft 4 in. 39 ft Dipperstick H Bucket 7600 lb C ANNAL Questions: (a) Dismember the shaded structural members (with labeled points A-H) from the tractor and sketch a free-body diagram showing external and exposed internal forces. (b) Compute the force in the hydraulic cylinder strut BD and the pin reactions at A in the given position.arrow_forwardDetermine the magnitude of the moment about A ( lb in) that produces the 125 lb force necessary to raise the window and whose line of action is the same as that of the shock absorber CB 20.5 in. 4.38 in. A B C 7.62 in. 17.2 in.arrow_forwardA 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 Note: It must be solved using the graphic method, not the equations method.arrow_forward
- Locate mass A at 35 mm from support X. 4.4. Locate mass B at 96.5 mm from support X. 4.5. Locate mass C at 122.7 mm from support X. 4.6. Position mass A at zero degrees and D at 90o from A. 4.7. Rotate the shaft by hand and release it. As the shaft is released masses should remain in any angular position. 4.8. Change the angular position of masses B and D till the shaft is statically balanced. 4.9. Rotate the shaft with the motor at high speed and notice the reaction of the system. High vibration and noise indicate that the system is out of balance. 4.10. Change the position of the mass D till the system is dynamically balanced.arrow_forwardA 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_forward
- EXERCISE 5.16 The origin of the xyz coordinate system coincides with the centroid of the upper face of the box. The mass of the box is 10 kg. Determine Ixx, Iyy, and Ixy as functions of 0. Rectangular parallelepiped b/2 as b/2 G az F02 fc2 m = pabc, Lxx = 1/2m (b²+ c²), Iyy = 1/2m(a² + c²), z = - 1/2m (a² + b²). 20 mm 80 mm- 40 mm ·xarrow_forward3.104 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 light fixture of negligible mass, has three applied forces acting on it as shown. |F,| = 4 kN 1.2 m 1.2 m 1.2 m 2.8 m |F,| = 6 kN - y 45° |F,| = 5 kN Using the coordinate system shown, determine in kilonewtons the x component of the reaction force at o - Rox Answer:arrow_forward
- Each 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_forwardAn object in the shape of a thin ring has radius a and mass M. A uniform sphere with mass m and radius R is placed with its center at a distance x to the right of the center of the ring, along a line through the center of the ring, and perpendicular to its plane . What is the gravitational force that the sphere exerts on the ring-shaped object? Show that your result reduces to the expected result when x is much larger than a.arrow_forwardPractice Problem 2.4.16: The couple acts on the handlesof a steering mechanism. In the position shown, themoment applied by the couple about the z-axis is zero.Determine the distance b.Use F = 200i − 110j − 80k kN.arrow_forward
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