Chapter 9, Problem 84P

Using the method of composite areas, find the centroid of the truncated parabolic complement.

Use integration to find the centroidal coordinates for the volume obtained by revolving the area shown about the x-axis.

Use numerical integration to find the centroid of the volume generated by revolving the area shown about the x-axis.

Using integration, locate the centroid of the area under the n-th order parabola in terms of b, h, and n (n is a positive integer). (b) Check the result of part (a) with Table 8.1 for the case n = 2.

Small screws are used to fasten a piece of hardwood to the bracket that is formed from 1/20-in.-thick steel sheet metal. For steel, =0.283lb/in.3, and for hardwood, =0.029lb/in.3. Locate the center of gravity of the assembly.

Using the method of composite areas, find the dimension h that maximizes the centroid coordinate y of the plane region shown.

Verify the centroidal z-coordinate of the pyramid shown in Table 8.3 by integration.

The picture board and its triangular supporting bracket form a composite surface. Calculate the height h of the support that minimizes the centroidal z-coordinate of the assembly.

Compute the centroidal coordinates of the L-shaped region in terms of b and t using the method of composite areas.