277. The inclined plane as a mechanical power is often used in the form
of a wedge or in the still more disguised form of a screw. A wedge is
an inclined plane which is forced under the load; it is usually moved
by means of a hammer, so that the efficiency of the wedge is augmented
by the dynamical effect of a blow.
278. The screw is one of the most useful mechanical powers which we
possess. Its form may be traced by wrapping a wedge-shaped piece of
paper around a cylinder, and then cutting a groove in the cylinder
along the spiral line indicated by the margin of the paper. Such a
groove is a screw. In order that the screw may be used it must revolve
in a _nut_ which is made from a hollow cylinder, the internal diameter
of which is equal to that of the cylinder from which the screw is cut.
The nut contains a spiral ridge, which fits into the corresponding
thread in the screw; when the nut is turned round, it moves backwards
or forwards according to the direction of the rotation. Large screws
of the better class, such as those upon which we shall first make
experiments, are always turned in a lathe, and are thus formed with
extreme accuracy. Small screws are made in a simpler manner by means of
dies and other contrivances.
279. A characteristic feature of a screw is the inclination of the
thread to the axis. This is most conveniently described by the number
of complete turns which the thread makes in a specified length of
the screw, usually an inch. For example: a screw is said to have ten
threads to the inch when it requires 10 revolutions of the nut in order
to move it one inch. The shape of the thread itself varies with the
purposes for which the screw is intended; the section may be square or
triangular, or, as is generally the case in small screws, of a rounded
form.
280. There is so much friction in the screw that experiments are
necessary for the determination of the law connecting the power and the
load.
281. We shall commence with an examination of the screw by the
apparatus shown in Fig. 43.
The nut A is secured upon a stout frame; to the end of the screw hooks
are attached, in order to receive the load, which in this apparatus
does not exceed 224 lbs.; at the top of the screw is an arm E by which
the screw is turned; to the end of the arm a rope is attached, which
passing over a pulley D, carries a hook for receiving the power C.
[Illustration: FIG. 43.]
282. We first apply the principle of work to this screw, and calculate
the relation between the power and the load as it would be found if
friction were absent. The diameter of the circle described by the end
of the arm is 20"·5; its circumference is therefore 64"·4. The screw
contains three threads in the inch, hence in order to raise the load 1"
the power moves 3 × 64"·4 = 193" very nearly; therefore the velocity
ratio is 193, and were the screw capable of working without friction,
193 would represent the mechanical efficiency. In actually performing
the experiments the arm E is placed at right angles to the rope leading
to the pulley, and the power hook is weighted until, with a slight
start, the arm is steadily drawn; but the power will only move the arm
a few inches, for when the cord ceases to be perpendicular to the arm
the power acts with diminished efficiency; consequently the load is
only raised in each experiment through a small fraction of an inch, but
quite sufficient for our purpose.