Part 164

It is hardly possible to lay down general rules for computing the quantity of friction, because it depends upon a multiplicity of circumstances, as the structure, firmness, elasticity, &c. of bodies rubbing against each other. Some authors make the friction upon a horizontal plane, equal to ¹⁄₃d of the weight to be moved; while others have found it to be considerably less. But however this be, the doctrine of friction, as ascertained by the latest experiments, may be summed up in the following manner.

1. When one body rests on another upon a horizontal plane, it presses it with its whole weight, which being equally reacted upon, and consequently the whole effect of its gravity destroyed by the plane, it will be absolutely free to move in any horizontal direction by any the least power applied thereto, provided both the touching surfaces be smooth.

2. But since we find no such thing as perfect smoothness in the surfaces of bodies, arising from their porosity and peculiar texture, it is easy to understand, that when two such surfaces come together, the prominent parts of the one will, in some measure, fall into the concave parts of the other; and therefore, when an horizontal motion is attempted in one, the fixed prominent parts of the other will give more or less resistance to the moving surface, by holding and retaining its parts; and this is what we call friction.

3. Now since any body will require a force equal to its weight, to draw it over a given obstacle, it follows that the friction arising to the moving body, will always be in proportion to its weight only, and not to the quantity of the surface, by which it bears upon the resisting plane or surface. Thus if a piece of wood 4 inches wide, and 1 thick, be laid upon another fixed piece of the same wood, it will require the same weight to draw it along, whether it be laid on its broad or narrow side.

4. For, though there be 4 times the number of touching particles on the broad side (cetæris paribus) yet each particle is pressed with only ¹⁄₄th of the weight, that those are on the narrow side, and since 4 times the number multiplied by one fourth of the weight, it is plain the resistance is equal in both places, and so requires the same force to overcome it.

5. The reason why friction is proportional to the weight of the moving body, is, because the power applied to move the body must raise it over the prominent parts of the surface on which it is drawn; and this motion of the body, as it is not upright, will not require a power equal to its whole weight; but being in the nature of the motion on an inclined plane, it will only require a part of its own weight, which will vary with the various degrees of smoothness and asperity.

6. It is found by experiment, that a body, may be drawn along by nearly ¹⁄₃d of its weight; and if the surfaces be hard and well polished, by less than ¹⁄₃d part; whereas, if the parts be soft or rugged, it will require a much greater weight.

The ingenious Mr. Emerson, in his Principles of Mechanics, has given the following rules deduced from experiments; but they require some variation under different circumstances, which must be left to the judgment of the artist.

1. Wood and all metals, when greased, have nearly the same friction; and the smoother they are, the less friction they have; yet metals may be so far polished as to increase friction by the cohesion of their parts.

Wood slides easier upon the ground in wet weather than in dry, and easier than iron in dry weather; but iron slides easier than wood, in wet weather. Lead makes a great deal of resistance. Iron or steel running in brass, makes the least friction of any. In wood acting against wood, grease makes the motion twice as easy, or rather ²⁄₃ds easier. Wheel-naves, greased or tarred, go 4 times easier than when wet.

Metals oiled make the friction less than when polished, and twice as little as when unpolished.

In general, the softer or rougher the bodies, the less or greater their friction.

2. As to particular cases: a cubic piece of soft wood of 8 pounds weight, moving upon a smooth plane of soft wood, at the rate of 3 feet per second; its friction is about ¹⁄₃d of the weight of it; but if it be rough, the friction is little less than one half the weight.

Upon the same supposition, other soft wood upon soft wood very smooth, the friction is bout ¹⁄₄th of the weight.

Soft wood upon hard, or hard wood upon soft, ¹⁄₅th or 1-half of the weight. Hard wood upon hard wood, ¹⁄₇th or ¹⁄₈th of the weight.

Polished steel moving upon steel or pewter, ¹⁄₄th of the weight; moving on copper or lead, ¹⁄₅th of the weight; on brass, ¹⁄₅th of the weight. Metals of the same sort have more friction than different sorts.

The friction, cæteris paribus, increases with the weight almost in the same proportion. The friction is also greater with a greater velocity, but not in proportion to it, except in very few cases. A greater surface also causes somewhat more friction, with the same weight and velocity; yet friction may sometimes be increased by having too little surface to move on; as upon clay, &c. where the body sinks.

3. The friction arising from the bending of ropes about machines, differs according to their stiffness, the temper of the weather, degree of flexibility, &c., but, cæteris paribus, the force or difficulty of bending a rope is as the square of the diameter of the rope, and its tension, directly; and the diameter of the cylinder or pulley it goes about, reciprocally.

A rope of 1 inch diameter, whose tension or weight drawing it is 5 pounds, going over a pully 3 inches diameter, requires a force of 1 pound to bend it.

4. The resistance of a plane moving through a fluid is as the square of the velocity; and putting v = velocity in feet in a second; it is equal to the weight of a column of the fluid, whose base is the plane, and height

vv ----. b4

And in a globe it is but half so much.

5. As to the mechanic powers, the single lever makes no resistance by friction; but if, by the motion of the lever in lifting the fulcrum, or place of support, be changed further from the weight, the power will be decreased thereby.

6. In any wheel of any machine, running upon an axis, the friction on the axis is as the weight upon it, the diameter of the axis, and the angular velocity. This sort of friction is but small.

7. In the pully, if p, q, be 2 weights, and q the greater; and

4pq w = -----, pxq

then w is the weight upon the axis of the single pulley; and it is not increased by the acceleration of the weight q, but remains always the same.

The friction of the pullies is very considerable, when the sheaves rub against the blocks; and by the wearing of the holes and axles.