265. The friction of the truck upon the glass plate is always very
small, and is shown to have but little variation at those inclinations
of the plane which we used. But when the friction is large, we shall
not be justified in neglecting its changes at different elevations,
and we must adopt more rigorous methods. For this inquiry we shall
use the pine plank and slide already described in Art. 117. We do not
in this case attempt to diminish friction by the aid of wheels, and
consequently it will be of considerable amount.
266. In another respect the experiments of Table XIII. are also in
contrast with those now to be described. In the former the load was
constant, while the elevation was changed. In the latter the elevation
remains constant while a succession of different loads are tried. We
shall find in this inquiry also that when the proper allowance has been
made for friction, the theoretical law connecting the power and the
load is fully verified.
267. The apparatus used is shown in Fig. 33; the plane, is, however,
secured at one inclination, and the pulley C shown in Fig. 32 is
adjusted to the apparatus, so that the rope from the pulley to the
slide is parallel to the incline. The elevation of the plane in the
position adopted is 17°·2, so that its length, base, and height are in
the proportions of the numbers 1, 0·955, and 0·296. Weights ranging
from 7 lbs. to 56 lbs. are placed upon the slide, and the power is
found which, when the slide is started by the screw, will draw it
steadily up the plane. The requisite power consists of two parts, that
which is necessary to overcome gravity acting down the plane, and that
which is necessary to overcome friction.
[Illustration: FIG. 42.]
268. The forces are shown in Fig. 42. R G, the force of gravity, is
resolved into R L and R M; R L is evidently the component acting down
the plane, and R M the pressure against the plane; the triangle G L R
is similar to A B C, hence if R be the load, the force R L acting down
the plane must be 0·296 R, and the pressure upon the plane 0·955 R.
269. We shall first make a calculation with the ordinary law that
the friction is proportional to the pressure. The pressure upon the
plane A B, to which the friction is proportional, is not the weight of
the load. The pressure is that component (R M) of the load which is
perpendicular to the plane A B. When the weights do not extend beyond
56 lbs., the best value for the coefficient of friction is 0·288 (Art.
141): hence the amount of friction upon the plane is