Experimental Mechanics / A Course of Lectures Delivered at the Royal College of Science for Ireland

by Robert S. Ball

INTRODUCTION.

151. The pulley forms a good introduction to the important subject of the mechanical powers. But before entering on the discussions of the next few chapters, it will be necessary for us to explain what is meant in mechanics by “work,” and by “energy,” which is the capacity for performing work, and we shall therefore include a short outline of this subject in the present lecture.

152. The pulley is a machine which is employed for the purpose of changing the direction of a force. We frequently wish to apply a force in a different direction from that in which it is convenient to exert it, and the pulley enables us to do so. We are not now speaking of these arrangements for increasing power in which pulleys play an important part; these will be considered in the next lecture: we at present refer only to change of direction. In fact, as we shall shortly see, some force is even wasted when the single fixed pulley is used, so that this machine certainly cannot be called a mechanical power.

153. The occasions upon which a single fixed pulley is used are numerous and familiar. Let us suppose a sack of corn has to be elevated from the lower to one of the upper stories of a building. It may of course be raised by a man who carries it, but he has to lift his own weight in addition to that of the sack, and therefore the quantity of exertion used is greater than absolutely necessary. But supposing there be a pulley at the top of the building over which a rope passes; then, if a man attach one end of the rope to the sack and pull the other, he raises the sack without raising his own weight. The pulley has thus provided the means by which the downward force has been changed in direction to an upward force.

154. The weights, ropes, and pulleys which are used in our windows for counterpoising the weight of the sash afford a very familiar instance of how a pulley changes the direction of a force. Here the downward force of the weight is changed by means of the pulley into an upward force, which nearly counterbalances the weight of the sash.

FRICTION BETWEEN A ROPE AND
AN IRON BAR.

155. Every one is familiar with the ordinary form of the pulley; it consists of a wheel capable of turning freely on its axle, and it has a groove in its circumference in which the rope lies. But why is it necessary to give the pulley this form? Why could not the direction of the rope be changed by simply passing it over a bar, as well as by the more complicated pulley? We shall best answer this question by actually trying the experiment, which we can do by means of the apparatus of [Fig. 34 (see page 90)]. In this are shown two iron studs, g, h, 0"·6 diameter, and about 8" apart; over these passes a rope, which has a hook at each end. If I suspend a weight of 14 lbs. from one hook a, and pull the hook b, I can by exerting sufficient force raise the weight on a, but with this arrangement I am conscious of having to exert a very much larger force than would have been necessary to raise 14 lbs. by merely lifting it.

156. In order to study the question exactly, we shall ascertain what weight suspended from the hook b will suffice to raise a. I find that in order to raise 14 lbs. on a no less than 47 lbs. is necessary on b, consequently there is an enormous loss of force: more than two-thirds of the force which is exerted is expended uselessly. If instead of the 14 lbs. weight I substitute any other weight, I find the same result, viz. that more than three times its amount is necessary to raise it by means of the rope passing over the studs. If a labourer, in raising a sack, were to pass a rope over two bars such as these, then for every stone the sack weighed he would have to exert a force of more than three stones, and there would be a very extravagant loss of power.

157. Whence arises this loss? The rope in moving slides over the surface of the iron studs. Although these are quite smooth and polished, yet when there is a strain on the rope it presses closely upon them, and there is a certain amount of force necessary to make the rope slide along the iron. In other words, when I am trying to raise up 14 lbs. with this contrivance, I not only have its weight opposed to me, but also another force due to the sliding of the rope on the iron: this force is due to friction. Were it not for friction, a force of 14 lbs. on one hook would exactly balance 14 lbs. on the other, and the slightest addition to either weight would make it descend and raise the other. If, then, we are obliged to change the direction of a force, we must devise some means of doing so which does not require so great a sacrifice as the arrangement we have just used.