286. We have seen that the velocity ratio is 193; therefore, to raise 100 lbs. 1 foot, we find that 1·43 × 193 = 276 units of energy must be expended: of this only 100 units, or 36 per cent., is usefully employed; the rest being consumed in overcoming the friction of the screw. Thus nearly two-thirds of the energy applied to such a screw is wasted. Hence we find that friction does not permit the load to run down, since less than fifty per cent. of the applied energy is usefully employed ([Art. 222]). This is one of the valuable properties which the screw possesses.
287. We may contrast the screw with the pulley-block ([Art. 199]). They are both powerful machines: the latter is bulky and economical of power, the former is compact and wasteful of power; the latter is adapted for raising weights through considerable distances, and the former for exerting pressures through short distances.
Fig. 44.
THE SCREW-JACK.
288. The importance of the screw as a mechanical power justifies us in examining another of its useful forms, the screw-jack. This machine is used for exerting great pressures, such for example as starting a ship which is reluctant to be launched, or replacing a locomotive upon the line from which its wheels have slipped. These machines vary in form, as well as in the weights for which they are adapted; one of them is shown at d in [Fig. 44], and a description of its details is given in [Table XVII]. We shall determine the powers to be applied to this machine for overcoming resistances not exceeding half a ton.
289. To employ weights so large as half a ton would be inconvenient if not actually impossible in the lecture room, but the required pressures can be produced by means of a lever. In [Fig. 44] is shown a stout wooden bar 16' long. It is prevented from bending by means of a chain; at e the lever is attached to a hinge, about which it turns freely; at a a tray is placed for the purpose of receiving weights. The screw-jack is 2' distant from e, consequently the bar is a lever of the second order, and any weight placed in the tray exerts a pressure eightfold greater upon the top of the screw-jack. Thus each stone in the tray produces a pressure of 1 cwt. at the point d. The weight of the lever and the tray is counterpoised by the weight c, so that until the tray receives a load there is no pressure upon the top of the screw-jack, and thus we may omit the lever itself from consideration. The screw-jack is furnished with an arm d g; at the extremity g of this arm a rope is attached, which passes over a pulley and supports the power b.
290. The velocity ratio for this screw-jack with an arm of 33", is found to be 414, by the method already described ([Art. 283]).
291. To determine its mechanical efficiency we must resort to experiment. The result is given in Table XVII.