Work Done in Overturning a Body
المؤلف:
GEORGE A. HOADLEY
المصدر:
ESSENTIALS OF PHYSICS
الجزء والصفحة:
P-86
2025-11-05
43
The work that must be done to overturn a body is a measure of its stability. When a cylinder lies upon its side, the only work necessary to overturn it is to overcome the friction between it and the surface upon which it lies, since the center of gravity moves in a horizontal line. If, however, the body is a cube, the center of gravity is raised a distance ab every time it is turned over, and the work done is just the same as would be done in lifting the cube through the height ab (Fig. 1).
Fig.1
A brick lying on a table upon its side has greater stability than one standing on end. The work necessary to overturn it in each case is expressed by the formula Work = W × ab.
In both cases shown in Fig. 1 the highest position of the center of gravity is the same, but the original heights above the table are unequal and so the product W × ab is greater in A than in B.
FIG.2
Demonstration. -Get a brass ball such as is used on the ends of curtain poles. Remove the screw, enlarge the hole, and pour in a little melted lead When the lead has cooled in position A, put the ball in any other position, as B, and since a vertical line from the center of gravity C does not fall within the base D, the ball will roll and the center of gravity will fall until it reaches the lowest possible position, when a vertical line from C will fall within the base of support, and the ball will be in a condition of stable equilibrium.
FIG. 3
The principle of this demonstration is applied in making one kind of oil cans. The ordinary form is conical (Fig. 4, А), and' if it is overturned, the oil escapes. But when the base is made in the form of a hemisphere and loaded with a little lead in the bottom (a), the can will always right itself and the oil will be retained.
FIG.4
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