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 vvb4. 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 w = 4pqpxq 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.
The friction of the axis of the pulley is as the weight w, its angular velocity, the diameter of the axis directly, and the diameter of the pully inversely. A power of 100 pounds, with the addition of 50 pounds, will only draw up 500 with a tackle of 5; and 15 pounds over a single pully will draw up only 14 pounds.
8. In the screw, there is a great deal of friction: those with sharp threads have more friction than those with square threads; and endless screws have more than either. Screws, with a square thread, raise a weight with more ease than those with a sharp thread.
In the common screw the friction is so great, that it will sustain the weight in any position given, when the power is taken off; and therefore the friction is at least equal to the power. From whence it will follow, that in the screw, the power must be to the weight or resistance, at least as twice the perpendicular height of a thread to the circumference described by one revolution of the power; if it be able to raise the weight, or only sustain it. This friction of the screw is of great use, as it serves to keep the weight in any given position.