Biomedical Engineering Reference
In-Depth Information
Fig. 3.5
Representation of
the proposed experiment for
the determination of the
C.G., showing the applied
forces and the effect of
torque which produces
counterclockwise rotation
of the sheet from the initial
to final situation. At the final
situation, the torque is zero.
In the repetition of the
experiment, the sheet is
suspended through axis 2
of rotation
axis of rotation
1
d
C.G.
initial situation
W
1
2
1
C.G.
W
W
final situation
repetition of the experiment
determination of the C.G. is achieved by repeating the previous procedure, fixing
the sheet of paper through the second axis of rotation, and drawing another vertical
line passing through the axis as shown in Fig.
3.5
. The center of gravity must also
lie along this second line. The only way for one point to fall on two different lines is
to be located at their intersection. This point corresponds to the C.G. of the body.
In short, the method of the plumb line used to locate the center of gravity, C.G.,
of a body consists in suspending it from a point, and, at equilibrium, a vertical line
which corresponds to the line of action of the weight force is drawn. This procedure
is repeated one or more times, suspending the body from a different point each time.
The C.G. must lie on both lines of action, and the only point which belongs to both
lines is that of the intersection. For two-dimensional (three-dimensional) objects, it
has to be suspended by at least two (three) different axes of rotation.
It is interesting to point out that, as the C.G. is the point of the body where its
weight is considered to be applied, we shall be able to equilibrate the body by
hanging or supporting it from a point such that the line of action of the force that
supports it passes through its C.G.
The C.G. of the human body or parts of it has been obtained using cadavers by
the practical method of the plumb line.
Exercise 3.3
Cut out any flat figure as illustrated in the figure of Exercise 3.3, from
cardboard, and locate its center of gravity by the method of the plumb line.
