168. I have here a wooden pulley 3"·5 in diameter; the hole is lined with brass, and the pulley turns very freely on an iron spindle. I place the rope and hooks upon the groove. Brass rubbing on iron has but little friction, and when 7 lbs. is placed on each hook, 0·5 lb. added to either will make it descend and raise up the other. Let 14 lbs. be placed on each hook, 0·5 lb. is no longer sufficient; 1 lb. is required: hence when the weight is doubled the friction is also doubled. Repeating the experiment with 21 lbs. and 28 lbs. on each side, the corresponding weights necessary to overcome friction are 1·5 lbs. and 2 lbs. In the four experiments the weights used are in the proportion 1, 2, 3, 4; and the forces necessary to overcome friction, 0·5 lb., 1 lb., 1·5 lbs., and 2 lbs., are in the same proportion. Hence the friction is proportional to the load.
WHEELS.
169. The wheel is one of the most simple and effective devices for overcoming friction. A sleigh is an admirable vehicle on a smooth surface such as ice, but it is totally unadapted for use on common roads; the reason being that the amount of friction between the sleigh and the road is so great that to move the sleigh the horse would have to exert a force which would be very great compared with the load he was drawing. But a vehicle properly mounted on wheels moves with the greatest ease along the road, for the circumference of the wheel does not slide, and consequently there is no friction between the wheel and the road; the wheel however turns on its axle, therefore there is sliding, and consequently friction, at the axle, but the axle and the wheel are properly fitted to each other, and the surfaces are lubricated with oil, so that the friction is extremely small.
170. With large wheels the amount of friction on the axle is less than with small wheels; other advantages of large wheels are that they do not sink much into depressions in the roads, and that they have also an increased facility in surmounting the innumerable small obstacles from which even the best road is not free.
171. When it is desired to make a pulley turn with extremely small friction, its axle, instead of revolving in fixed bearings, is mounted upon what are called friction wheels. A set of friction wheels is shown in the apparatus of [Fig. 66]: as the axle revolves, the friction between the axles and the wheels causes the latter to turn round with a comparatively slow motion; thus all the friction is transferred to the axles of the four friction wheels; these revolve in their bearings with extreme slowness, and consequently the pulley is but little affected by friction. The amount of friction in a pulley so mounted may be understood from the following experiment. A silk cord is placed on the pulley, and 1 lb. weight is attached to each of its ends: these of course balance. A number of fine wire hooks, each weighing 0·001 lb., are prepared, and it is found that when a weight of 0·004 lb. is attached to either side it is sufficient to overcome friction and set the weights in motion.
ENERGY.
172. In connection with the subject of friction, and also as introductory to the mechanical powers, the notion of “work,” or as it is more properly called “energy,” is of great importance. The meaning of this word as employed in mechanics will require a little consideration.
173. In ordinary language, whatever a man does that can cause fatigue, whether of body or mind, is called work. In mechanics, we mean by energy that particular kind of work which is directly or indirectly equivalent to raising weights.
174. Suppose a weight is lying on the floor and a stool is standing beside it: if a man raise the weight and place it upon the stool, the exertion that he expends is energy in the sense in which the word is used in mechanics. The amount of exertion necessary to place the weight upon the stool depends upon two things, the magnitude of the weight and the height of the stool. It is clear that both these things must be taken into account, for although we know the weight which is raised, we cannot tell the amount of exertion that will be required until we know the height through which it is to be raised; and if we know the height, we cannot appreciate the quantity of exertion until we know the weight.
175. The following plan has been adopted for expressing quantities of energy. The small amount of exertion necessary to raise 1 lb. avoirdupois through one British foot is taken as a standard, compared with which all other quantities of energy are estimated. This quantity of exertion is called in mechanics the unit of energy, and sometimes also the “foot-pound.”