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.
Wrought iron screw, square thread, diameter 2", pitch 2 threads to the inch, arm 33"; nut brass, bearing surfaces oiled; velocity ratio 414; useful effect, 28 per cent.; mechanical efficiency 116; formula P = 0·66 + 0·0075 R.
| Number of Experiment. | R. Load in lbs. | Observed power in lbs. | P. Calculated power in lbs. | Difference of the observed and calculated powers. |
|---|---|---|---|---|
| 1 | 112 | 1·4 | 1·5 | +0·1 |
| 2 | 224 | 2·2 | 2·3 | +0·1 |
| 3 | 336 | 3·3 | 3·2 | -0·1 |
| 4 | 448 | 4·1 | 4·0 | -0·1 |
| 5 | 560 | 5·0 | 4·9 | -0·1 |
| 6 | 672 | 5·7 | 5·7 | 0·0 |
| 7 | 784 | 6·5 | 6·5 | 0·0 |
| 8 | 896 | 7·4 | 7·4 | 0·0 |
| 9 | 1008 | 8·1 | 8·2 | +0·1 |
| 10 | 1120 | 9·0 | 9·1 | +0·1 |
292. It may be seen from the column of differences how closely the experiments are represented by the formula. The power which is required to raise a given weight, say 600 lbs., may be calculated by this formula; it is 0·66 + 0·0075 × 600 = 5·16. Hence the mechanical efficiency of the screw-jack is 600 ÷ 5·16 = 116. Thus the screw is very powerful, increasing the force applied to it more than a hundredfold. In order to raise 600 lbs. one foot, a quantity of work represented by 5·16 × 414 = 2136 units must be expended; of this only 600, or 28 per cent., is utilized, so that nearly three-quarters of the energy applied is expended upon friction.
293. This screw does not let the load run down, since less than 50 per cent. of energy is utilised; to lower the weight the lever has actually to be pressed backwards.
294. The details of an experiment on this subject will be instructive, and afford a confirmation of the principles laid down. In experiment 10 we find that 9·0 lbs. suffice to raise 1,120 lbs.; now by moving the pulley to the other side of the lever, and placing the rope perpendicularly to the lever, I find that to produce motion the other way—that is, of course to lower the screw—a force of 3·4 lbs. must be applied. Hence, even with the assistance of the load, a force of 3·4 lbs. is necessary to overcome friction. This will enable us to determine the amount of friction in the same manner as we determined the friction in the pulley-block ([Art. 207]). Let x be the force usefully employed in raising, and y the force of friction, which acts equally in either direction against the production of motion; then to raise the load the power applied must be sufficient to overcome both x and y, and therefore we have x + y = 9·0. When the weight is to be lowered the force x of course aids in the lowering, but x alone is not sufficient to overcome the friction; it requires the addition of 3·4 lbs., and we have therefore x + 3·4 = y, and hence x = 2·8, y = 6·2.
That is, 2·8 is the amount of force which with a frictionless screw would have been sufficient to raise half a ton. But in the frictionless screw the power is found by dividing the load by the velocity ratio. In this case 1120 ÷ 414 = 2·7, which is within 0·1 lb. of the value of x. The agreement of these results is satisfactory.