() An hydraulic accumulator. pulley or the like. This question was answered fairly well, although a certain proportion of the candidates had evidently to rely on books for their knowledge of workshop processes. Sketches, with few exceptions, were extremely poor. It is desirable to draw attention again to the great advantage it is to students to encourage them to make sketches of the various machines and appliances with which they come in contact in the shops. The greatest weakness in the answers to this question was shown in the sketches of the details of the various machines, for example, such a detail as the stuffing-box of a hydraulic accumulator. (a) The question on the lathe was a favourite one, and, as a rule, was well answered. (6) Some curious designs of accumulators were sketched, and one candidate advised that milk should be mixed with the water to keep it (the water) from going bad. (c) Most of the sketches of the circular saw and saw bench were crude and out of proportion, and it was evident that this part of the question was, in some cases, attempted by candidates who were quite unfamiliar with a saw bench. (d) It was clear from the quality of the answers that this division of the question was attempted only by candidates who had had real foundry experience, but there were one or two most remarkable answers, so extraordinarily foolish as almost to force the Examiners to come to the conclusion that the candidate was deliberately writing nonsense. Q. 2. Answer only one of the following (a), (6) or (c) : (a) Describe how you would determine experimentally the coefficient of sliding friction between two pieces of metal of any convenient size when the speed of rubbing is low. (6) Describe how you would determine experimentally the modulus of rigidity of either a block of indiarubber or a steel rod. (c) Describe how you would determine the mechanical efficiency of either a Pelton waterwheel, or a small turbine; state carefully what measurements you would make, and what calculations would be needed. The answers on laboratory work were generally bad, and apparently most of the blame for this must be placed upon teachers. (a) In describing this experiment not one candidate in a hundred, who made use of the plan of sliding one piece of metal over another by means of a weighted string passing over a pulley, referred to the allowance which must be made for the friction of the pulley, though several made the perfectly senseless remark, “take a frictionless pulley and a perfectly flexible cord,” as if it were quite possible to find such things in any laboratory or workshop. (6) Very few candidates appeared to have any real knowledge of the modulus of rigidity, and it is evident that the subject of shear, which is the most important factor in the Strength of Materials, is almost neglected by the majority of teachers. Most of the candidates who made any attempt at this division of the question described experiments for finding either the modulus of tension, or the modulus of compression. Many of the answers were quite irrelevant and exceedingly absurd, one candidate stating "the centre of gravity is the modulus of rigidity in other words.” (c) Very few candidates attempted this division of the question, and though most of them were able to describe fairly satisfactorily some form of brake or dynamometer for obtaining the power developed by the waterwheel, or turbine wheel, very few appeared to have anything but the most hazy idea as to the method of determining the actual energy supplied to the motor. Q. 3. In connection with a contract for the supply of cast-iron pipes, certain bending tests were specified on bars (cast at the same time) 40 inches long, 2 inches deep, and 1 inch thick. The following results were obtained when one of these bars was tested on edge on a 36-inch span : Plot on squared paper a curve to show the relation between the load at the centre of the beam and the deflection at the centre of the beam. From your curve determine the load which will be required at the centre of the beam in order to give a deflection of } inch. The plotting was on the whole satisfactory, but some of the candidates went out of their way to choose inconvenient scales, such as 1 inch = 0·06 inch, and a number of candidates were unable to express inch as a decimal, candidates writing ! 102, or 0125, and so on. Q. 4. In a direct-acting steam-engine mechanism the stroke of the piston is 2 feet and the crank shaft makes 150 revolutions per minute. What is the speed of the crank shaft in radians per second ? What is the speed of the crank pin in feet per second ? What is the mean speed of the piston in feet per minute? Usually well answered. The most common mistake was to multiply by 60, instead of dividing by 60, in order to convert the speed per minute into speed per second. Very few candidates had the slightest idea that any connection exists between angular and linear velocity, and therefore the bulk of the candidates wasted time in unnecessary arithmetic. Q. 5. In a shale mine in order to drain one of the pits a treble ram pump, driven by an electric motor, is employed. The rams are 99 inches minute. minute. (c) The useful horse-power when the pumps are running steadily. This question was attempted by a very large number of candidates, and arithmetical blunders were extremely common. Actual mistakes in units were not very frequent, most of the blunders being purely arithmetical. A considerable number of candidates, however, are still uncertain as to the proper formula for the determination of the area of the circle. Q. 6. Hemp ropes are employed to transmit power from the engine shaft to the driving pulleys on the different floors in a spinning factory. The maximum tension in a rope is twice the minimum tension, the breaking strength of one rope is 5,700 lbs., and it is desired to have a factor of safety of 30. Find the maximum horse-power which can be safely transmitted by one of these hemp ropes at a speed of 70 feet per second. The maximum allowable tension in the rope in this question was generally correctly found, but a common mistake was then to work out the horsepower transmitted, using the maximum tension, instead of the difference between the maximum and the minimum tensions. A common error was to write 70 feet per second = of a foot per minute. Q. 7. A cycle track is approximately elliptical in shape, the maximum radius of curvature being 150 yards and the minimum 50 yards. Find at each of these two places, the ratio which the centrifugal force bears to the weight, if the speed of the racing cyclist is 25 miles per hour. What would be the two inclinations of the track to the horizontal if the track is laid so as to be perpendicular to the resultant force in each case ? Comparatively few candidates attempted this question; as a rule the answers showed a sound knowledge of the formula for centrifugal force, but mistakes were made in units, such as obtaining the velocity in miles per hour, and measuring the radius in yards. Q. 8. The floor of a room, which is 12 feet square, is supported by timber joists 9 inches deep by 3 inches thick. It is found by testing a piece of timber of the same quality as that of the joists that a beam 2 inches deep by 1 inch thick on a span of 24 inches is broken by a load at the centre of 1,000 lbs. What load, uniformly spread over its length, will each joist carry, the factor of safety being 9? If the joists are spaced 15 inches apart, centre to centre, what load per square foot will the floor carry? The factors which govern the strength of a beam seemed to be quite well understood by a large proportion of the candidates, but there are a few here and there who think that the strength depends simply upon the cross sectional area. The question of the factor of safety was not at all satisfactorily dealt with by the bulk of the candidates; such an extremely nonsensical answer as the following shows this :-"Breaking load = 9,000 lbs.; factor of safety 9; therefore safe load=9,009 lbs.” Q. 9. A tie-bar in a roof is made of steel angle bar; the section of the steel angle is 4 inches by 4 inches by inch, and the tie-bar when finished in the workshop is 20 feet in length. When in position in the roof the tie-bar may during a gale have to resist a total pull of 22 tons; what is the tensile stress per square inch in the metal of the tie-bar under these conditions, and how much would the tie-bar lengthen under this load ? Young's modulus of elasticity is 12,500 tons per square inch. Very few of the candidates were able to calculate correctly the area of the cross section of an angle bar. The most common answer was that the 2 x 4 x 5 square inches. The rest of the work of the question was satisfactory. Q. 10. To do the cutting work in a small screw cutting lathe it is found that 0:47 H.P. is required, and that the frictional losses in the gearing, bearings, &c., absorb another 0:21 H.P. How many foot-pounds of work per minute is the driving belt giving to the lathe? The countershaft is driven by an electric motor, and the countershaft and belts absorb 0:17 H.P. How many watts must the motor give off in order to keep the lathe running ? If the voltage is 220, how many ampères will the motor require, assuming that its own efficiency is 89 per cent. ? 1 H.P. = 746 watts, and ampères multiplied by volts = watts. A favourite question, and usually very well answered. area = Q. 11. A railway truck weighing 10 tons starts from rest down an incline a mile long of 1 in 250. If the frictional and other resistances are equivalent to 8 lbs. per ton weight of the truck, with what velocity will the truck be moving when it gets to the end of the incline? How far would it then run along a level stretch of the line before coming to rest ? Attempted by only a few candidates, most of whom made serious blunders. The idea of friction as a resisting force seemed quite unfamiliar to most of the candidates, and absurd answers were, as a result, frequently obtained. For example, one candidate stated that the velocity of the truck at the foot of the incline would be 500,000,000 feet per second. Q. 12. The right-angled bell crank lever, centred at A, shown in the sketch, is attached to a spring by one of its arms, and to another If the spring requires a direct pull of 20 lbs. in order to stretch а 1 A favourite question, and the answers as a rule were satisfactory. Q. 13. Two adjacent positions G1, G2 of the centre of mass G of a balance weight were obtained by geometrical construction from The displacement G, G, took place in 1/50 second. Find the x and y components of the mean velocity of G for this interval. Plot the points G1, G2, on squared paper. This question was attempted by only a few candidates, and usually with poor results. Instead of plotting the values of x and y, the candidates, as a rule, plotted G, against Gz. STAGE 2 Results : 1st Class, 176; 2nd Class, 744; Failed, 349 ; Total, 1,269. (c), or (d):- a shaft or spindle, say about 2 inches diameter and 17 feet long. (6) An hydraulic accumulator. (c) A circular saw and saw bench. (d) The preparation of a sand mould for the casting of a pulley or the like. Most of the candidates selected division (a) of this question, and showed a good practical knowledge of the operations required in the piece of work they had to describe. The other sections of the question were not so satisfactorily answered. Q. 22. Answer only one of the following, (a), (6) or (c) : (a) Describe how you would determine experimentally the coefficient of sliding friction between two pieces of metal of any convenient size when the speed of rubbing is low. (6) Describe how you would determine experimentally the modulus of rigidity of either a block of india-rubber or a steel rod. (c) Describe how you would determine the mechanical efficiency of either a Pelton waterwheel, or a small turbine; state fully what measurements you would make, and what calculations would be needed. Nearly all the candidates selected division (a) of this question also, and the answers were good, though very few of the candidates made any reference to making a series of observations in order to obtain the mean value of the coefficient of friction. In division (6) the answers were fairly satisfactory, most of the candidates described a direct experiment in torsion in order to obtain the modulus of rigidity, but a few explained the method of torsional oscillations. In division (c) the answers were not at all satisfactory; the descriptions of the various measurements that were required were vague and unsatisfactory, and appeared to show that the candidates had never themselves taken part in the carrying out of such an experiment. Q. 23. In connection with a contract for the supply of cast-iron pipes, certain bending tests were specified on bars (cast at the same time) 40 inches long, 2 inches deep, and 1 inch thick. The following results were obtained when one of these bars was tested on edge on a 36-inch span : a Plot on squared paper a curve to show the relation between the load at the centre of the beam and the deflection at the centre of the beam. |