Chapter 10, Problem 69P

Compute the center of mass/ centroid of the region R = {(x, y): 1 ≤ x ≤ 3, 0 ≤ y ≤ x^2. Show the graph

8.72 Locate the centroid of the volume generated by revolving the area shown about the line AB. Use numerical integration. B Answer: x = 12 in. y = 3.83 in z = 0 42 in.- -12 in. 693 in. 8.49 in. 9.90 in. 10.95 in 1200 in

3. Determine the distance y to the centroid for the beam's cross sectional area; then determine the moment of inertia about the x' axis. 25 mm 50 mm 100 mm 75 mm C 25 mm 25 mm 75 mm- 50 mm 100 mm 25 mm -X

Find the centroid of the region bounded by the graphs of the functions y = 7², y = x² + 4 The centroid is at (ī, j) where = 23

Locate the centroid of the plane area shown if r = 46 in.    X¯¯¯�¯ : 1.07  Numeric Response 1.Edit Unavailable. 1.07 correct.in. Y¯¯¯�¯ : 20.8  Numeric Response 2.Edit Unavailable. 20.8 correct.in. The horizontal x-axis is drawn through the centroid C of the area shown, and it divides the area into two component areas A1 and A2. Determine the first moment of each component of area with respect to the x-axis if w = 50 mm and b = 25 mm.    The first moment of the area above the x-axis is 53  Numeric Response 1.Edit Unavailable. 53 correct.× 103 mm3. The first moment of the area below the x-axis is -53  Numeric Response 2.Edit Unavailable. -53 correct.× 103 mm3.

The cross-sectional area shown below has dimensions h = 152 mm, t₁ = 23 mm, t₂ = 21 mm, and b = 245 mm. Determine the y-coordinate of the centroid (y), where y is the signed distance from the z-axis to the z-axis. The z-y axes pass through the centroid of the cross section and are positive in the directions shown. y = 60.33 1 t₁ 1 Y b mm B h

Determine the second moments with respect to The x- and y-axes through the centroid of the area. 7 in. 7 in. 7 in. 7 in. 6 in.

250 mm 3. A thin brass rod of uniform cross section is bent into the shape shown to the right. Find the center of gravity. Ans. X = 205 mm, y =255 mm, 7 = 75mm 750 mm %3D D 300 mm 500 mm

Determine the dimension b of the square cutout so that Ixy=0 for the region shown.