THE COEFFICIENT VARIES WITH
THE WEIGHTS USED.
140. In a subsequent lecture we shall employ as an inclined plane the plank we have been examining, and we shall require to use the knowledge of its friction which we are now acquiring. The weights which we shall then employ range from 7 lbs. to 56 lbs. Assuming the ordinary law of friction, we have found that 0·27 is the best value of its coefficient when the loads range between 14 lbs. and 112 lbs. Suppose we only consider loads up to 56 lbs., we find that the coefficient 0·288 will best represent the experiments within this range, though for 112 lbs. it would give an error of nearly 3 lbs. The results calculated by the formula F = 0·288 R are shown in Table V., where the greatest difference is 0·7 lb.
Friction of pine upon pine; the mean values of the friction given in [Table II]. (corrected for the friction of the pulley) compared with the formula F = 0·288 R
| Number of Experiment. | R. Total load on slide in lbs. | Corrected mean value of friction. | F. Calculated value of friction. | Discrepancies between the observed and calculated frictions. |
|---|---|---|---|---|
| 1 | 14 | 4·7 | 4·0 | -0·7 |
| 2 | 28 | 8·2 | 8·1 | -0·1 |
| 3 | 42 | 12·2 | 12·1 | -0·1 |
| 4 | 56 | 15·8 | 16·1 | +0·3 |
141. But we can replace the common law of friction by the more accurate law of [Art. 137], and the formula computed so as to best harmonise the experiments up to 56 lbs., disregarding the higher loads, is F = 0·9 + 0·266 R. This formula is obtained by the method referred to in [Art. 137]. We find that it represents the experiments better than that used in [Table V]. Between the limits named, this formula is also more accurate than that of [Table IV]. It is compared with the experiments in [Table VI]., and it will be noticed that it represents them with great precision, as no discrepancy exceeds 0·1.
Friction of pine upon pine; the mean values of the friction given in [Table II]. (corrected for the friction of the pulley) compared with the formula F = 0·9 + 0·266 R.
| Number of Experiment. | R. Total load on slide in lbs. | Corrected mean value of friction. | F. Calculated value of friction. | Discrepancies between the observed and calculated frictions. |
|---|---|---|---|---|
| 1 | 14 | 4·7 | 4·6 | -0·1 |
| 2 | 28 | 8·2 | 8·3 | +0·1 |
| 3 | 42 | 12·2 | 12·1 | -0·1 |
| 4 | 56 | 15·8 | 15·8 | 0·0 |