Theory and Applications

A thin sheet lies along the portion of the plane x + y + z = 1 in the first octant. The density of the sheet is

a. Partition the sheet into a finite number of subpieces to show that the work done by gravity to move the sheet straight down to the xy-plane is given by

where g is the gravitational constant.

b. Find the total work done by evaluating the surface integral in part (a).

c. Show that the total work done equals the work required to move the sheet’s center of mass straight down to the xy-plane.