in. 81. Short Rule for Plates.-A flat wrought-iron plate thick and 1 ft. square will weigh 5 lb., since 12 X 12 X = 18 cu. in., and 18 X .278 5 lb. The rule obtained from this is very easy to remember and is very useful for plates the dimensions of which are in exact feet. = = Rule. Weight of flat iron plates area in square feet X number of eighths of an inch in thickness X 5. This rule can also be used for steel plates by adding 2% to the result calculated from the above rule. Example: Find the weight of a steel plate 30 in. × 96 in. × 3 in. 2 1/2 × 8 × 3 × 5 2% of 300 300 + 6 = = 6 lb. 306 lb.; weight of steel plate, Answer. If this weight is calculated by first getting the cubic inches of steel, we get: 30 × 96 × 3 = 1080 cu. in. 1080 X .283 = 305.64 lb., weight of steel plate, Answer. We see that the results check as closely as could be expected and, in fact, different plates of supposedly the same size would differ as much as this because of differences in rolling. 82. Weight of Casting from Pattern.-In foundry work, it is often desired to get the approximate weight of a casting in order to calculate the amount of metal needed to make it. The probable weight of the casting can be obtained closely enough by weighing the pattern and multiplying this weight by the proper number from the following table. In case the pattern contains core prints, the weight of these prints should be calculated and subtracted from the pattern weight before multiplying; or the total pattern weight can be multiplied first and then the weight of metal which would occupy the same volume as the core print be subtracted from the product. PROPORTIONATE WEIGHT OF CASTINGS TO WEIGHT OF WOOD PATTERNS 83. Finding Dimensions from Weights or Volumes.-Sometimes we have the weight or volume of a body, but not all of the dimensions are known, and it is desired to find the unknown dimensions. By a method of working backward we can find the volume from the total weight by dividing by the weight per unit volume. Then, if the length is known, we can find the area of the end by dividing the volume by the length; or if the area is known, the length can be found by dividing the volume by the area. The rest of the calculation can be performed as explained in previous paragraphs of this chapter. Example: The superintendent of a small factory desires to store 100 tons of coal in addition to its usual supply. The only available space in which to put it is a small shed 20 ft. wide by 40 ft. long. As the roof is rather low it is necessary to find out how high the coal will be in the shed, assuming that it is piled level. (The weight of 1 cu. ft. of coal is about 43 lb.) 139. The diameter of a 31-in. bolt at the bottom of the threads is 3.1 in. What is the cross-sectional area of the bolt at the bottom of the threads? (Use tables.) 140. How many square feet of roofing paper will be required to cover a flat roof 40 ft. wide and 70 ft. long, allowing 10% extra for lap and waste? 141. In the design of a hot air heating system it was determined that the air pipes (or leaders) from the furnace to the second floor risers should have a cross-sectional area of about 50 sq. in. What should be the diameter of the pipes used? 142. The riser pipes in the above problem are rectangular in shape and have the same cross-sectional area as the leaders. The short dimension or depth of the riser is limited by the wall space and in this case is 3 in. How wide must the risers be made? 143. The piston of a steam engine is 8 in. in diameter. If the steam pressure in the cylinder is 100 lb. per square inch at the beginning of the stroke, what is the total pressure acting on the piston at that time? 144. A 6-in. pipe and an 8-in. pipe both discharge into a single header. Find the diameter of the header so that it will have an area equal to that of both pipes. 145. How many cubic feet of water will be contained in a cistern 6 ft. deep, 8 ft. wide, and 10 ft. long? 146. What is the weight of a steel shaft 6 in. in diameter and 20 ft. long? 147. A foundry is to cast 10 hollow, round, cast-iron columns, each 15 ft. long, 12 in. outside diameter, and 9 in. inside diameter. How many pounds of iron will be required to cast all the columns allowing 15% extra for waste? 148. A paint shop wants a tank 4 ft. deep with a square bottom built to hold, when full, 400 gal. of varnish. What will be the dimensions of the tank? (There are 231 cu. in. in a gallon.) 149. A copper billet 2 in. by 8 in. by 24 in. is rolled out into a plate of No. 10 B & S. gage. The thickness of this gage is .1019 in. What would be the probable area of this plate in square feet? CHAPTER XII LEVERS 84. Types of Machines.-All machines consist of one or more of the three fundamental types of machines-the Lever, the Cord, and the Inclined Plane or Wedge. Any piece of mechanism can be proved to be of one or more of these types. Pulleys, gears, and cranks will be shown to be forms of levers; belts and chains come under the type called the cord; while screws, worms, and cams are forms of inclined planes. They are all used to transmit power from one place to another and to modify it, as desired. 85. The Lever.-The lever is probably the most used and the simplest type of machine. We are all familiar with it in its W FIG. 42. Simple lever. simplest forms, such as crowbars, shears, pliers, tongs, and the numerous simple levers found on machine tools. A lever is a rigid rod or bar so arranged as to be capable of turning about a fixed point. This fixed point about which the lever turns is called the Fulcrum. In Fig. 42 the fulcrum is represented by the small triangular block F. The position of this fulcrum determines the effect which the force P applied at one end has toward lifting the weight W at the other end. If F is close to W, a comparatively small force P may be able to raise the weight W, but if F is moved away from W and placed close to P, then a greater force will be required at P. If F is in the middle, P and W will be just equal. In every lever there are two opposing tendencies: first, that of the load or weight W tending to descend; and second, that of the force P tending to raise W. The ability of W to descend or to resist being lifted depends upon two things-its weight and its distance from the fulcrum F. The product of these two is the |