But let us suppose, that the force which urges P is in a direction
P F, oblique to A B. Taking P F as the diagonal of a
parallelogram, whose sides are P D and P C (74), the force
P F is mechanically equivalent to two forces, expressed by the
lines P D and P C. But P D, being perpendicular to
A B, produces pressure without motion, and P C, being in
the direction of A B, produces motion without pressure. Thus
the effect of the force P F is distributed between motion and
pressure in a certain proportion, which depends on the obliquity of
its direction to that of the surface. The two extreme cases are, 1.
When it is in the direction of the surface; it then produces motion
without pressure: and, 2. When it is perpendicular to the surface; it
then produces pressure without motion. In all intermediate directions,
however, it will produce both these effects.
(130.) It will be very apparent, that the more oblique the direction
of the force P F is to A B, the greater will be that part
of it which produces motion, and the less will be that which produces
pressure. This will be evident by inspecting _fig. 26._ In this
figure the line P F, which represents the force, is equal to
P F in _fig. 25._ But P D, which expresses the pressure,
is less in _fig. 26._ than in _fig. 25._, while P C,
which expresses the motion, is greater. So long, then, as the obliquity
of the directions of the surface and the force remain unchanged, so
long will the distribution of the force between motion and pressure
remain the same; and therefore, if the force itself remain the same,
the parts of it which produce motion and pressure will be respectively
equal.
(131.) These general principles being understood, no difficulty can
arise in applying them to the motion of bodies urged on inclined planes
or curves by the force of gravity. If a body be placed on an unyielding
horizontal plane, it will remain at rest, producing a pressure on the
plane equal to the total amount of its weight. For in this case the
force which urges the body, being that of terrestrial gravity, its
direction is vertical, and therefore perpendicular to the horizontal
plane.
But if the body P, _fig. 25._, be placed upon a plane A B,
oblique to the direction of the force of gravity, then, according to
what has been proved (129), the weight of the body will be distributed
into two parts, P C and P D; one, P D, producing a
pressure on the plane A B, and the other, P C, producing
motion down the plane. Since the obliquity of the perpendicular
direction P F of the weight to that of the plane A B must be
the same on whatever part of the plane the weight may be placed, it
follows (130), that the proportion P C of the weight which urges
the body down the plane must be the same throughout its whole descent.
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