=132. Value of Friction.=--_Friction always hinders motion_ and whenever one body moves over or through another the energy used in overcoming the friction is transformed into heat which is taken up by surrounding bodies and usually lost. Friction is therefore the great obstacle to perfect efficiency in machines. Friction, however, like most afflictions _has its uses_. We would find it hard to get along without it. Without friction we could neither walk nor run; no machines could be run by belts; railroad trains, street cars, in fact all ordinary means of travel would be impossible, since these depend upon friction between the moving power and the road for propulsion. [Illustration: FIG. 110.--Timken roller bearings. As used in the front wheel of an automobile.] =133. Coefficient of Friction.=--The ratio between the friction when motion is just starting and the force pushing the surfaces together is called the _coefficient of friction_. If the block in Fig. 111 is drawn along the board with uniform motion, the reading of the spring balances indicates the amount of friction. Suppose the friction is found to be 500 g., and the weight of the block to be 2000 g. Then the coefficient of friction for these two substances will be {500/2000} = {1/4}, or 25 per cent. =134. Laws of Friction, Law I.=--_The friction when motion is occurring between two surfaces is proportional to the force holding them together._ Thus if one measures the friction when a brick is drawn along a board, he will find that it is doubled if a second brick is placed on the first. On brakes greater pressure causes greater friction. If a rope is drawn through the hands more pressure makes more friction. [Illustration: FIG. 111.--A method for testing the friction between surfaces.] =Law II.=--_Friction is independent of the extent of surface in contact._ Thus a brick has the same friction drawn on its side as on its edge, since, although the surface is increased, the weight is unchanged. =Law III.=--Friction is greatest at starting, but after starting is practically the same for all speeds. =135. Fluid Friction.=--When a solid moves through a fluid, as when a ship moves through the water or railroad trains through the air, the resistance encountered is not the same as with solids but increases with the square of the velocity for slow speeds and for high speeds at a higher rate. This is the reason why it costs so much to increase the speed of a fast train, since the resistance of the air becomes the prominent factor at high speeds. The resistance to the motion of a ship at high speed is usually considered to increase as the cube of the velocity so that to double the speed of a boat its driving force must be eight times as great. Important Topics 1. Friction: two kinds; sliding and rolling. 2. Four ways of reducing friction. 3. Uses of friction. 4. Coefficient of friction. Three laws of friction. 5. Fluid friction. Exercises