Mechanics: The Science of MachineryBond, A. Russell (Alexander Russell)
History
Mechanics: The Science of Machinery
Bond, A. Russell (Alexander Russell)
Machinery; Mechanical engineering; Mechanics
A simple form of inclined plane is pictured in Figure 17, which shows
a weight W being rolled up an incline. The effort required to carry it
to the top of the incline depends, of course, upon the steepness of the
incline. The drawing shows a rise of 3 feet on a slope 5 feet long, and
the weight of the wheel is, say 20 pounds. To find the effort required,
the weight is multiplied by the rise (20 × 3 = 60) and divided by
the length of the slope (60/5 = 12) and we find that it takes only
12 pounds to roll the 20-pound wheel to the top of the incline. This
holds true when the pull is parallel to the inclined face. If the
pull is parallel to the base of the incline, as in Figure 18, we must
divide by the length of the base instead of the length of the incline
(60/4 = 15) and we find that it takes 15 pounds of effort to pull the
weight up the incline. If the pull is exerted at an angle both to the
base and the inclined face, we have a problem that is slightly more
complicated and we need not go into it here because it involves a bit
of trigonometry. In all cases, however, it may be noted that the amount
of rope that is taken in, in hauling the weight up the incline, bears a
definite relation to the amount of effort required to raise the weight.
In Figure 17, 5 feet of rope must be pulled in, in order to raise the
weight 3 feet, so that ⅗ of 20 or 12 pounds is all that is required
to pull up the weight, while in Figure 18, 4 feet of rope is hauled
in for a lift of 3 feet, so that ¾ of 20 or 15 pounds is required to
pull up the weight. In this respect the inclined plane is exactly like
the lever or the pulley, for the _effort_ multiplied by the _distance_
through which it is exerted is always exactly equal to the _weight_
multiplied by the _distance_ through which it moves. Thus in Figure
17, the effort 12 pounds multiplied by the distance 5 = the weight 20
pounds times the distance 3, and in Figure 18, effort 15 x distance 4
= weight 20 x distance 3. Of course, we are ignoring the weight of the
rope and the friction which, in actual practice, are important factors
to be reckoned with.
[Illustration: FIG. 19.--ENDLESS SCREW OR WORM GEAR]
So far we have considered a fixed inclined plane, but when the inclined
plane is moved between the weight and a fixed base it is known as a
wedge, and in this case, too, the effort required to move the wedge
multiplied by the distance the wedge moves is equal to the weight
multiplied by the distance it is lifted.
Public-domain text, read in full here on John Shaqi.
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