Glass Plane 48" long, truck 1 lb. in weight, friction counterpoised; formula P = 0·0208 × h".
| Number of Experiment. | Height of plane. | Observed power in lbs. | P. Calculated power in lbs. | Differences of the observed and calculated powers. |
|---|---|---|---|---|
| 1 | 2" | 0·04 | 0·04 | 0·00 |
| 2 | 4" | 0·08 | 0·08 | 0·00 |
| 3 | 6" | 0·13 | 0·12 | -0·01 |
| 4 | 8" | 0·16 | 0·17 | +0·01 |
| 5 | 10" | 0·21 | 0·21 | 0·00 |
| 6 | 15" | 0·31 | 0·31 | 0·00 |
| 7 | 20" | 0·42 | 0·42 | 0·00 |
| 8 | 33" | 0·71 | 0·69 | -0·02 |
Thus for example, in experiment 6, where the height b e is 15", it is observed that the power necessary to draw the truck is 0·31 lb. The truck is placed in the middle of the plane, and the power is adjusted so as to be sufficient to draw the truck to the top with certainty; the necessary power calculated by the formula is also 0·31 lbs., so that the theory is verified.
264. The fifth column of the table shows the difference between the observed and the calculated powers. The very slight differences, in no case exceeding the fiftieth part of a pound, may be referred to the inevitable errors of experiment.
THE INCLINED PLANE WITH FRICTION.
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.
Fig. 42.