A smooth plane of pine 72" × 11" carries a loaded
slide of pine 9" × 9"; one end of the plane
is gradually elevated until the slide, having
received a start, moves off uniformly.
+-----------+-----------------+------------+
|Number of | Total load on | Angle of |
|Experiment.|the slide in lbs.|inclination.|
+-----------+-----------------+------------+
| 1 | 14 | 14°·3 |
| 2 | 56 | 13°·0 |
| 3 | 112 | 13°·0 |
+-----------+-----------------+------------+
We see from this table also that the angle of friction is independent
of the load, but the angle is in this case less by 5° or 6° than was
found necessary to impart motion when a start was not given.
146. It is commonly stated that the coefficient of friction equals the
tangent of the angle of friction, and this can be proved to be true
when the ordinary law of friction is assumed. But as we have seen that
the law of friction is only approximately correct, we need not expect
to find this other law completely verified.
147. When the slide is started, the mean value of the angle of friction
is 13°·4. The tangent of this angle is 0·24: this is about 11 per cent.
less than the coefficient of friction 0·27, which we have already
determined. The mean value of the angle of friction when the slide
is not started is 19°·2, and its tangent is 0·35. The experiments of
Table I. are, as already pointed out, rather unsatisfactory, but we
refer to them here to show that, so far as they go, the coefficient of
friction is in no sense equal to the tangent of the angle of friction.
If we adopt the mean values given in the last column of Table I., the
best coefficient of friction which can be deduced is 0·41. Whether,
therefore, the slide be started or not started, the tangent of the
angle of friction is smaller than the corresponding coefficient of
friction. When the slide is started, the tangent is about 11 per cent.
less than the coefficient; and when the slide is not started, it is
about 14 per cent. less. There are doubtless many cases in which these
differences are sufficiently small to be neglected, and in which,
therefore, the law may be received as true.