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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- Mirror the triangle shown below along a 45° - axis. ) (1,3) P₂ D P₁ 45° (1, 1)! (3, 3)Q.3 Find the volume of a parallelepiped if four of its eight vertices are A(0, 0, 0), B(2, -3,0), C(5, -4, 3), and D(0, 2, 1).Compare the magnitudes of the equilibrant vectors measured from the experiment with those obtained from the graphical and component methods. Example: A: 200 g 60° above +x axis B: 300 g 45° above -x axis C: 400 g 30°below -x-axis A, A cos a = 1.96 N x cos 60° = 0.98 N B₂B cos b = 2.94 N x cos 135º = -2.08 N C, C cos g = 3.92 N x cos 210°= -3.39 N R₂-A, + B + C₂ = -4.49 N A, A sin a = 1.96 N x sin 60° = 1.70 N By B sin b = 2.94 N x sin 135º = 2.08 N C, C sin g = 3.92 N x sin 210° = -1.96 N Ry= Ay+ By + Cy = 1.82 N Questions: I: (a) A: 200 g along +x axis B: 100 g 45° above -x axis A₂ = A cos a = B₂ =B cos b = R₂-A₂+ B₁₂= A₂ = A sin a = B, = B sin b = R₂ = A + B₂ = R=(R₂. R₂):_ Quadrant R = √ (R₂²+R₂²) = Direction:q=tan [R, /R.] (c) A: 100 g along -y axis B: 200 g along -x axis A = A cos a = B = B cos b = R₂-A₂+ B₂ = A = A sin a = B, B sin b = R=A, +B₂ = R=(R₁, R₂): Quadrant R = √ (R₂²+R₂²) = Direction:q tan¹ [R, /R]
- F2 X- axis y-axis Figure (1) Q1] Answer the following questions: For figure (1): The object is subjected to two forces F1 = 25 N, and F2= 50 N. Set « = 30° , 0 = 45° , and ß = 30°. 1 - What is the magnitude of the resultant of these two forces? a) 39 2 - What is the direction of the resultant force measured counterciockwise from the positive x-axis? None of themDraw a line AB of length 120 mm and by construction obtain a point P dividing AB internally in the ratio (a) 3:5 (b) 4:7. Measure AP (to the nearest half mm).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 (-)
- 2. Determine the coordinate angle for F2 and R = 450 N then express each force acting on the bracket as Cartesian vector. b. Determine the magnitu de and coordinate direction angles of 450 the resultant force acting on the bracket. 60 452 F = 600 N Fig.P2-60, Mechanics of Materials, R.C. Hibbeler, 12th ed1. Find the components of . 2. A Find the components of T2- (Reminder: cos(a) =) 3. Find the angle between and 2. 4. Find the magnitude of the projection of r2 along/parallel to T = 6m 30° 40° Z 8 60° r₁= r₂ = √2 120° 45⁰ a 0 = Y= 2 = 9 m optionalProblem 1. Three circles are tangent externally. The distance between their centers are 60 m, 73 m, and 85 m. Find the radius of the largest circle. Problem 2. Six congruent circles are arranged in a way that each circle is tangent to at least two other circles. If the radius of each circle is 2 m, find the perimeter of the polygon formed by connecting the centers of each circle. Problem 3 If y varies inversely as z and y = 23 when z = 45,000, find y when z = 54,000. Problem 4 From a window of a building 5.25m above the ground, the angle of elevation of the top of a nearby building is 35.6 degrees and the angle of depression of its base is 28.2 degrees. What is the height of the nearby building? Problem 5 From a point A (Elev. 042.5), the angle of elevation of the top of the tower is 35 degrees, from a point B 325 m nearer angle of elevation of the top of the tower is 55 degrees. What is the elevation of the top of the tower? the tower and 18.65 m below the point A, the
- For the planar area symmetrical with respect to the x-axis in the figure, the cross-section dimensions are a = 1 cm and c = 3 cm, the radius of the semicircle is c. a) Find the center of gravity of this area. b) Find the volume of the object formed by rotating this area 180° around the x-axis. 4a k C - C → 2a a → X 不Q3/A For the figure below, the resultant is.: * 20 Ν 75 N 450 50 N 150 N 259 80 N Q3/B) The direction of the resultant approximately is * Q3/C/SumFx= * Q3/D/SumFy: *Show conv D +z axis 01) Given the figure, AB=5m, BC= 8m and AG= 7m and pt 0 is origin. Determine the following: 250 N B *y axis 1) What is magnitude of R and Cr in pt G? 20 kN m 1689 Ibt (Unit must be in N and kN-m) 1269 pounds 2) What is the magnitude of R and Cr in pt 0? +x axis (Unit must be in N and kN-m) 3) Unit Vector of R in the system. 4) Direct Cosines of Cr in pt 0.