We have here supposed the weight to be sustained upon the inclined
plane by a hard plane fixed at right angles to it. But the power
necessary to sustain the weight will be the same in whatever way it is
applied, provided it act in the direction of the plane. Thus, a cord
may be attached to the weight, and stretched towards A, or the hands of
men may be applied to the weight below it, so as to resist its descent
towards B. But in whatever way it be applied, the amount of the power
will be determined in the same manner. Suppose the weight to consist
of as many pounds as there are inches in A B, then the power
requisite to sustain it upon the plane will consist of as many pounds
as there are inches in A C, and the pressure on the plane will
amount to as many pounds as there are inches in B C.
From what has been stated it may easily be inferred that the less the
elevation of the plane is, the less will be the power requisite to
sustain a given weight upon it, and the greater will be the pressure
upon it. Suppose the inclined plane A B to turn upon a hinge
at B, and to be depressed so that its angle of elevation shall be
diminished, it is evident that as this angle decreases the height of
the plane decreases, and its base increases. Thus, when it takes the
position B A′, the height A′ C′ is less than the former
height A C, while the base B C′ is greater than the former
base B C. The power requisite to support the weight upon the plane
in the position B A′ is represented by A′ C′, and is as much
less than the power requisite to sustain it upon the plane A B,
as the height A′ C′ is less than the height A C. On the
other hand, the pressure upon the plane in the position B A′ is
as much greater than the pressure upon the plane B A, as the base
B C′ is greater than the base B C.
(287.) The power of an inclined plane, considered as a machine, is
therefore estimated by the proportion which its length bears to its
height. This power is always increased by diminishing the elevation of
the plane.
Public-domain text, read in full here on John Shaqi.
Reviews
Reviews
No reviews yet
Be the first to share your thoughts on this work.
Elsewhere in the archive
Join the Discussion
Join the discussion
Sign in to leave a comment or review.
Sign InorCreate an account