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Equilibrium and the Force of Gravity
Figure 13.1. Weight of an object balanced by a single force.
Figure 13.1 shows a body of arbitrary shape balanced by a single force. The origin of the
coordinate system is defined such that it coincides with the
center of gravity
of the object,
which is the point upon which the balancing force acts. An object that is supported at its center of
gravity will be in static equilibrium, independent of the orientation of the object. If the body is in
equilibrium, the net force acting on it must be zero. Figure 13.1 shows that
Since the body is in equilibrium
and therefore
In obtaining this result
we have assumed that the gravitational acceleration is the same for
every point of the body
. The net torque acting on the body is given by
Since the body is in static equilibrium
and therefore
This shows that r
cm
= 0 or r
cm
is parallel to g. We conclude that
for a body to be in equilibrium,
its center of mass must coincide with its center of gravity
.
Sample Problem 13-1

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