Mechanics: The Science of MachineryBond, A. Russell (Alexander Russell)
History
Mechanics: The Science of Machinery
Bond, A. Russell (Alexander Russell)
Machinery; Mechanical engineering; Mechanics
Although a force is something that cannot be pictured it can be
represented graphically by means of a line, letting the direction of
the line represent the direction of the force and the length of the
line the strength of the force. In Figure 58 we may measure off 3
inches from _O_ to _a_ to indicate the 3-pound force and 4 inches
from _O_ to _b_ to represent the 4-pound force and 5 inches from _O_
to _c_ to represent the 5-pound force. Now if from _a_ a line is
drawn parallel to _O b_ and from _b_ a line is drawn parallel to _O
a_ we shall have a parallelogram _a O b d_, and if we extend the line
_O c_ it will bisect the parallelogram, running diagonally from _O_
to _d_, and this diagonal will be found to measure exactly 5 inches
which represents the 5-pound force. This is what is known as the
_parallelogram of forces_. It shows us the resultant of any two forces
that are not directly opposite and it gives us the direction as well
as the strength or magnitude of this resultant. It is only because we
happen to choose the forces 3, 4 and 5 that the angle at _O_ is a right
angle. In Figure 59, where the forces are all equal, our parallelogram
is lozenge-shaped and the line _O d_ is just as long as the line _O a_
and _O b_, showing that its magnitude is the same as that of the two
forces that balanced it.
[Illustration: FIG. 57.--BALANCED FORCES--UNEQUAL WEIGHTS]
The greater the angle between the two lifting forces the less weight
can they lift. If two men are carrying a ten-pound satchel, each will
be lifting five pounds, if the pull is directly upward; but this is a
rather inconvenient way of carrying the bag and usually they pull at a
slight angle from the vertical, and so each must carry more than half
the weight. If they move so far apart that the angle between them is
more than 120 degrees, each will be carrying more than the full weight
of the bag.
[Illustration: FIGS. 58 AND 59.--PARALLELOGRAMS OF FORCES]
SAILING AGAINST THE WIND
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