Given the triangle described by the homogenous point matrix: [2 2 0 11 P=2 5 0 1 5 5 0 1] Scale it to three-fourth size keeping the centroid in the same location.
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- 3一4 Problem 1 Find the centroidal coordinates for the following triangles using the integrals SycdA S dA and %3D = X vp S You may utilize symmetry when appropriate. (-3,4) (3,4) (0,0) a. (5,4) (5,1) b. (4'0) (0) C. ×て (3,4) す Th-てh:8018 (-)D 1- A B Find the center of gravity Mof the three dimensional homogeneous wire ABCD in the figure using the (x, y, z) coordinate set. The dimensions of the wire are a = 15 cm, b=27 cm. Which of the following is the correct coordinates of the homogeneous wire in the x, y and z axes ? A) (23,57; 17,14;11,43) B) (20,61 ; 13,03; 9,08) O C) (28,29; 13,71 ; 20,57) O DI (23,57; 11,43; 17,14) E) (28,29 ; 20,57; 13,71)The corners of a triangle are at (4, 4), (10, 8), and (12, 4). The diameter of a semi-circle ends at (4, 4) and (12, 4) and the semi-circle touches the x-axis. Find the distance of the centroid of the composite figure from the x-axis. 2.3 3.48 4.24 5.33
- For the area below, evaluate 1. The (x,y) coordinates of the centroid (please mark your origin or reference point on the diagram) 2. The 2nd moments and product of area in centroidal-based xy (horizontal-vertical) coordinates 3. The principal 2nd moments of area, and the direction of the first principal axis relative to the horizontal (x) axis (anticlockwise positive) 50 75 30 150 60 50 15 Figure 1: Cross section (all dimensions in mm) Quantity Xc (please mark your origin on the diagram) Yc (please mark your origin on the diagram) Ix ly Ixv I₁ I₂ a1 (please show the direction) Value 30 UnitsUse cylindrical shells to find the volume of the solid generated when the region enclosed by the given curves is revolved about the y-axis. 1 a = 0, 2 = 9, y = 0 2 +1' NOTE: Enter the exact answer. V =3) A right circular cone of 30 mm diameter and 60 mm height is cut from a cylinder of 50 mm diameter and 120 mm height as shown in the figure. Find the position of the CG of the body from its base. 50 Ans CG of the given section is at (0mm, 62.87mm,0mm)
- 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)A triangular plate is supported by a ball and socketat point A, a roller at point B, and a rope at point C. Thedimensions are given along the line of AB. Determine thereactions at all supports and report your answers in cartesianvector form. Free Body Diagram.For the triangular element shown below, determine the shape functions at the point P. (5,6) (34) 0 (4.5,6) 2 (8,5) H
- 1- In space ,the point can be specified by position vector r wnich is given by: A:r-ix+ jy c r=ix+ jy + kz B:r=ix+ D:r=ix13 - 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 = 24 cm, b = 36 cm. The coordinates of the AB part of the homogeneous wire in the x, y and z axes are given in the following:A) (36; 12; 0)B) (36; 24; 0)C) (36; 24; 12)D) (18; 12; 0)E) (36; 12; 24)In the fig. shown, compute the following : (1-2) the resultant, R 50 lb 6 in.- R = 40 lb |20 lb B (3) What is the angle of the Resultant with 6 in. Respect to the x- axis measured CW 6 in.- (4-6) how far from point C will the line of action of the R bisect the edge ABC? X = 50 Ib In the fig. shown, compute the following : (7-8) the total load of the beam w = (9-10) the reactions: R1 = 100 lb/ft 60 lb www.mathalino.com R2 = 3 ft 6 ft 4 ft R2