The Great Pyramid of Cheops at El Gizeh, Egypt had height H = 147 m before its topmost stone fell. Its base is a square with edge length L = 230 m. Its volume V is equal to L 2H/3.
Find:
(a) the original height of its center of mass above the base
(b) the work required to lift the blocks into place from the base level
Find:
(a) the original height of its center of mass above the base
(b) the work required to lift the blocks into place from the base level
-
what are the assumptions?
that the surfaces are flat rather than steps? that the pyramid is solid (ie. no chambers inside)? that the density of the construction material is uniform? to find work, we must know mass or density and it's distribution...
if we look at entire pyramid, volume is
V=b*h/3
base is rectangular so b=L^2 and therefore
V=2592100m^3
assuming uniform density, and center of gravity will be at elevation x and half mass (volume) will be below and half above that point.
therefore we need to find h such that h=H-x
length of new base is of course going to be smaller (similarity of triangles)
work required is E=m*g*x
that the surfaces are flat rather than steps? that the pyramid is solid (ie. no chambers inside)? that the density of the construction material is uniform? to find work, we must know mass or density and it's distribution...
if we look at entire pyramid, volume is
V=b*h/3
base is rectangular so b=L^2 and therefore
V=2592100m^3
assuming uniform density, and center of gravity will be at elevation x and half mass (volume) will be below and half above that point.
therefore we need to find h such that h=H-x
length of new base is of course going to be smaller (similarity of triangles)
work required is E=m*g*x