5/7 The homogeneous slender rod has a uniform cross sec- tion and is bent into a circular arc of radius a. Determine the x- and y-coordinates of the mass center of the rod by direct integration. 15° a y 45° x PROBLEM 5/7
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- 5/56 Locate the mass center of the slender rod bent into the shape shown. y 300 mm 150 mm5/4 Specify the x-, y-, and z-coordinates of the mass center of the quarter-cylindrical shell. 360 mm 120 mm Problem 5/4The welded assembly is made of a uniform rod having a mass of 2 kg per meter of length and two thin rectangular plates having a mass of 18 kg per square meter.Calculate the coordinates of the mass center of the assembly. x-coordinate, in mm y-coordinate, in mm z-coordinate, in mm
- Locate the mass center of the homogeneous solid body whose volume is determined by revolving the shaded area through 360° about the z-axis. 340 mm 200 mm r = kz3 Answer: 7 = i mm5/65 Using the methods of this article, determine the sur- face area A and volume V of the body formed by revolving the rectangular area through 360° about the z-axis. x 2 12 mm 35 mm PROBLEM 5/65 8 mmLocate the mass center of the homogeneous solid body whose volume is determined by revolving the shaded area through 360° about the z-axis. 245 mm r = kz³ Answer: Z = i 120 mm mm
- The gear drives a shaft which carries three masses of 4 kg, 3 kg and 2.5 kg, all attached to a circular disc. The masses are located at radial distances of 75 mm, 85 mm and 50 mm and at the angular positions of 45°, 135° and 240° respectively. The angular positions are measured anti-clockwise from the reference line along the x- axis. Analytically determine the amount of the balancing-mass required at a radial distance of 75 mm, in order to achieve static balance of the shaft. Verify this by use of the graphical method.Locate the center of mass (x, y, z) of thehomogeneous block assembly.Determine the x-, y-, and z-coordinates of the mass center of the homogeneous body shown. The hole in the upper surface is drilled completely through the object. 20 20 25 15 10 10 40 Dimensions in millimeters Answers: I= i mm y = mm Z = i mm
- The homogeneous slender rod has a uniform cross section and is bent into a circular arc of radius a. Determine the x- and y-coordinates of the mass center of the rod by direct integration.A rotating shaft carries three unbalanced masses of 4 kg, 3 kg, and 2.4 kg at radial distances of 75 mm, 85 mm and 50 mm and at the angular positions of 45°, 135° and 240° respectively. The planes of taken as the reference plane and the various distances are to be considered from this plane. Determine unbalanced masses, as well as planes of the countermasses are shown in the figure. Plane C₁ is to be the amounts and locations of the counterweights at planes C₁ and C₂ required for complete balance. 225- 200 7- C₂ 240° 3 135° 2 45°1 C₁(RP)h y g(x) density p = 800 kg m³ Determine the cone's radius of gyration about the x-axis. 2h x An engineering student has modelled a truncated cone in CAD software by rotating the coloured area about the x-axis. The y-coordinate can be described by the equation g(x) = + 1 and the cup has constant 6 The cone has dimensions h = 1 m and l = 6 m. X