between planes For each of the following 2-dimensional shapes, determine the highest order rotation axis of symmetry. 3. (b)
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Q: Sketch the plane of the axis from the following Miller indices. (i) (2 1̅ 1)
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- Use integration to verify the formula given in Table 9.2 for Ixy of a half parabolic complement.J 5: !!!Please show it mathematically, not theorysecond moments=475.15 Determine, using the method of composite areas, the second moments of area of part 2 about the y-axis [units^4]. Determine, using the method of composite areas, the second moments of area of part 3 about the y-axis [units^4]. Determine, using the method of composite areas, the total second moments of area of of the composite about the y-axis [units^4].
- 29 - Find the center of gravity M (x,y,z) of the three-dimensional homogeneous ABCD wire in the figure by using the coordinate set. The dimensions of the wire are a= 24 cm, b= 36 cm. In which of the following options are the coordinates of the AB part of the homogeneous wire in the x, y and z axes given correctly?A) (36 ; 24 ; 12)B) (18 ; 12 ; 0)C) (36 ; 12 ; 0)D) (36 ; 24 ; 0)E) (36 ; 12 ; 24)3 29knd. A cylinder of 50 mm diameter and height 60 mm is resting on base in H.P. A circular hole of 20 mm diameter is drilled , so that the axis of the hole is perpendicular to V.P and bisects the axis of cylinder at right angles . Draw the development of the lateral surface of the cylinder with the slot . Draw neatly with pencil and take correct values must**Determine and locate the resultant of the system shown in fig (3). If you know that the values of Ax=240 N. Ay=2000 N. F=160 N, N=2400N, W=400 N and M=2N.m
- 24 - Constant thickness homogeneous planar plate in the figure coordinates of the center of gravity M (Xm, Ym) of the surface area, Find it on the (x, y) set. t = 3 cm and a = 9 cm. Find the coordinates (Xm; Ym) of the rectangle extracted from this planar plate in the x and y axes.A) (9; 15)B) (9; 13)C) (9; 25.5)D) (9; 18)E) (9; 22.5)A hexagonal plane of side 30 mm has a corner in the V.P. The surface of the plane isinclined at 45° to the V.P. and perpendicular to the H.P. Draw its projections. Assume thatthe diagonal through the corner in the V.P. is parallel to the H.P.The triangular plate is fixed at its base, and its apex A is given a horizontal displacement of 5 mm. Suppose that a= 640 mm
- 6 - Find the center of gravity M of the three-dimensional homogeneous wire ABCD in the figure using the (x, y, z) coordinate set. The dimensions of the wire are a = 24 cm, b = 36 cm. Which of the following is the correct coordinates of the BC part of the homogeneous wire in the x, y and z axes?A) (36; 12; 24)B) (18; 12; 0)C) (36; 24; 12)D) (36; 12; 0)E) (36; 24; 0)19 - Find the center of gravity M of the three-dimensional homogeneous wire ABCD using the coordinate set (x, y, z) in the figure. The dimensions of the wire are a = 20 cm, b = 30 cm. Which of the following is the correct coordinates of the BC part of the homogeneous wire in the x, y and z axes?A) (30; 20; 10)B) (30; 10; 0)C) (15; 20; 20)D) (30; 20; 0)E) (30; 20; 20)It is common to hang objects on doorknobs and over-the-door hooks. There is a limit to the amount of weight that a door can hold because of the forces exerted on the hinges. A door of height h = 2.5 m and width h/2 has a mass of M = 36 kg. The mass is distributed uniformly, so the center of mass is located at the geometric center of the door. One hinge is located a distance h/4 from the top of the door. The second hinge is a distance h/4 from the bottom of the door. Refer to (a) in the figure. The door’s weight is supported entirely by the two hinges and each hinge supports half of the weight. In other words, the vertical force exerted by each hinge is exactly one half of the total weight, including any additional load. For this problem, take the positive y-direction to be directly upward and the positive x-direction pointing from the hinge side of the door to the knob side. 1.) calculate the force, with its sign in Newtons that the upper hinge exerts on the door in the x axis.…