The nut a is secured upon a stout frame; to the end of the screw hooks are attached, in order to receive the load, which in this apparatus does not exceed 224 lbs.; at the top of the screw is an arm e by which the screw is turned; to the end of the arm a rope is attached, which passing over a pulley d, carries a hook for receiving the power c.
Fig. 43.
282. We first apply the principle of work to this screw, and calculate the relation between the power and the load as it would be found if friction were absent. The diameter of the circle described by the end of the arm is 20"·5; its circumference is therefore 64"·4. The screw contains three threads in the inch, hence in order to raise the load 1" the power moves 3 × 64"·4 = 193" very nearly; therefore the velocity ratio is 193, and were the screw capable of working without friction, 193 would represent the mechanical efficiency. In actually performing the experiments the arm E is placed at right angles to the rope leading to the pulley, and the power hook is weighted until, with a slight start, the arm is steadily drawn; but the power will only move the arm a few inches, for when the cord ceases to be perpendicular to the arm the power acts with diminished efficiency; consequently the load is only raised in each experiment through a small fraction of an inch, but quite sufficient for our purpose.
Wrought iron screw, square thread, diameter 1"·25, with 3 threads to the inch, length of arm 10"·25; nut of cast iron, bearing surfaces oiled, velocity ratio 193, useful effect 36 per cent., mechanical efficiency 70; formula P = 0·0143 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 | 28 | 0·4 | 0·4 | 0·0 |
| 2 | 56 | 0·8 | 0·8 | 0·0 |
| 3 | 84 | 1·2 | 1·2 | 0·0 |
| 4 | 112 | 1·6 | 1·6 | 0·0 |
| 5 | 140 | 2·0 | 2·0 | 0·0 |
| 6 | 168 | 2·4 | 2·4 | 0·0 |
| 7 | 196 | 2·7 | 2·8 | +0·1 |
| 8 | 224 | 3·3 | 3·2 | -0·1 |
283. The results of the experiments are shown in [Table XVI]. If the motion had not been aided by a start the powers would have been greater. Thus in experiment 6, 2·4 lbs. is the power with a start, when without a start 3·2 lbs. was found to be necessary. The experiments have all been aided by a start, and the results recorded have been corrected for the friction of the pulley over which the rope passes: this correction is very small, in no case exceeding 0·2 lb. The fourth column contains the values of the powers computed by the formula P = 0·0143 R. This formula has been deduced from the observations in the manner described in the Appendix. The fifth column proves that the experiments are truly represented by the formula: in each of the experiments 7 and 8, the difference between the calculated and observed values amounts to 0·1 lb., but this is quite inconsiderable in comparison with the weights we are employing.
284. In order to lift 100 lbs. the expression 0·0143 R shows that 1·43 lbs. would be necessary: hence the mechanical efficiency of the screw is 100 ÷ 1·43 = 70. Thus this screw is vastly more powerful than any of the pulley systems which we have discussed. A machine so capable, so compact, and so strong as the screw, is invaluable for innumerable purposes in the Arts, as well as in multitudes of appliances in daily use.
285. It is evident, however, that the distance through which the screw can raise a weight must be limited by the length of the screw itself, and that in the length of lift the screw cannot compete with many of the other contrivances used in raising weights.