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4. THE INCLINED PLANE.
The inclined plane is properly the second elementary power, and may be defined the lifting of a load by regular instalments. In principle it consists of any right line not coinciding with, but laying in a sloping direction to, that of the horizon; the standard of comparison of which commonly consists in referring the rise to so many parts in a certain length or distance, as 1 in 100, 1 in 200, &c., the first number representing the perpendicular height, and the latter the horizontal length in attaining such height, both numbers being of the same denomination, unless otherwise expressed; but it may be necessary to remark, that the inclination of a plane, the sine of inclination, the height per mile, or the height for any length, the ratio, &c., are all synonymous terms.
The advantage gained by the inclined plane, when the power acts in a parallel direction to the plane, is as the length to the height or angle of inclination: hence the rule. Divide the weight by the ratio of inclination, and the quotient equal the power that will just support that weight upon the plane. Or, multiply the weight by the height of the plane, and divide by the length,-the quotient is the power.
Ex. Required the power or equivalent weight capable of supporting a load of 350 lbs. upon a plane of 1 in 12, or 3 feet in height and 36 feet in length.
Note. The weight multiplied by the length of the base, and the product divided by the length of the incline, the quotient equal the pressure or downward weight upon the incline.
Table showing the Resistance opposed to the Motion of Carriages on
005 00333 0025 ·002 0016700143 00125 00111
applied to any other incline, the amount of traction on a level for carriages on railway inclines, it may with equal propriety be Note. Although this Table has been calculated particularly
Application of the preceding Table.
1. What weight will a tractive power of 150 lbs. draw up an incline of 1 in 340, the resistance on the level being estimated at 1th part of the insistent weight?
In a line with 40 in the left-hand column and under 200 is........
-21097 lbs. weight drawn up the plane.
2. What weight would a force of 150 lbs. draw down the same plane, the friction on the level being the same as before?
Friction on the level=100417
Gravity of the plane-00294 subtract
=121915 lbs. weight drawn down the plane.
Example of incline when velocity is taken into account.
A power of 230 lbs., at a velocity of 75 feet per minute, is to be employed for moving weights up an inclined plane 12 feet in height and 163 feet in length, the least velocity of the weight to be 8 feet per minute; required the greatest weight that the power is equal to.
230 x 75 x 163
12 × 8
=29288 lbs., or 13.25 tons.
TABLE OF INCLINED PLANES,
Showing the ascent or descent per yard, and the corresponding ascent or descent per chain, per mile; and also the ratio.
The wedge is a double inclined plane, consequently its principles are the same: Hence when two bodies are forced asunder by means of the wedge in a direction parallel to its head,-Multiply the resisting power by half the thickness of the head or back of the wedge, and divide the product by the length of one of its inclined sides; the quotient is the force equal to the resistance.
Ex. The breadth of the back or head of a wedge being 3 inches, and its inclined sides each 10 inches, required the power necessary to act upon the wedge so as to separate two substances whose resisting force is equal to 150 lbs.
Note. When only one of the bodies is moveable, the whole breadth of the wedge is taken for the multiplier.
The screw, in principle, is that of an inclined plane wound around a cylinder which generates a spiral of uniform inclination, each revolution producing a rise or traverse motion equal to the pitch of the screw, or distance between two consecutive threads,-the pitch being the height or angle of inclination, and the circumference the length of the plane when a lever is not applied; but the lever being a necessary qualification of the screw, the circle which it describes is taken, instead of the screw's circumference, as the length of the plane hence the mechanical advantage is, as the circumference of the circle described by