Angular Velocity-Effective Force-D'Alembert's Principle-Pres- Work accumulated in a Rotating Body-Smeaton's Machine-At- Impulsive Action-Impact of Smooth Balls-Impulse on Axis of Ro- PAGE 282 PRACTICAL MECHANICS. CHAPTER I. ON SOME OF THE PHYSICAL PROPERTIES OF MATERIALS. 1. Properties of Materials. The present chapter is intended to serve as an introduction to those that follow. It contains examples illustrative of the more obvious physical properties of the materials commonly used in construction and machinery. These physical properties are (1) Weight; (2) Expansion or Contraction, produced by change of temperature; (3) Elongation and Compression, produced by Strain or Pressure; (4) Resistance offered to Rupture by Strain; (5) Resistance offered to Rupture by Compression. 2. Weight. For estimating the weight of masses with sufficient accuracy it may be assumed that the weight of a cubic foot of water is 1000 oz. This number is easily remembered, and is within a very little of the truth. In every example contained in the following pages wherein the weight of masses is concerned, it will be assumed that the weight of a cubic foot of water is 1000 oz., unless the contrary is specified. As a matter of fact, a cubic foot of pure water at 39° F. (when its density is greatest) weighs 998.8 oz. It may also be convenient for the reader to B remember that a gallon contains 277-274 cubic inches, and that a gallon of water at the standard temperature (62° F.) weighs 10 lbs. Ex. 1. A reservoir is internally 12 ft. long, 5 ft. wide, and 3 ft. deep: determine the weight of the water it contains when full, and the least error produced by considering that each cubic foot weighs 1000 oz. Ans. Weight, 5 tons, 0 cwt. 50 lbs. Ex. 2.-A cylindrical boiler terminated by plane ends, is internally 15 ft. long and 4 ft. in diameter; through the lower half pass lengthwise 50 fire tubes, 3 in. in external diameter: determine the volume and weight of the water contained in it when the surface of the water passes through the centres of the ends. Ans. Vol. 57.43 cubic ft. Weight, 1 ton, 12 cwts. 0 qr. 5.5 lbs. Ex. 3. The surface of a pond measures 10 acres; in the course of a period of dry weather the surface falls 11⁄2 in. by evaporation: what is the weight of the water that has been withdrawn ? Ans. 1520 tons, nearly. 3. Specific Gravity. The specific gravity of a solid or liquid substance is the proportion which the weight of a certain volume of that substance bears to the weight of an equal volume of water; thus when it is stated that the specific gravity of cast iron is 7.2070, it means that a cubic foot, or a cubic inch, &c., of cast iron weighs 7.2070 times as much as a cubic foot, cubic inch, &c., of water; consequently a cubic foot of cast iron will weigh 7207 oz., and in general, if s is the specific gravity of a substance, a cubic foot of it will weigh 1000-s oz., at least with sufficient accuracy in almost all cases. The following table gives the specific gravities of some common materials : Copper (cast) 8-7880 1 foot length of Hempen rope weighs in lbs. 0.045 × (circ. in inches)". NOTE. The above numbers, where printed to four places of decimals, are taken from Dr. Young's Lectures on Natural Philosophy, vol. ii. p. 503; where printed to three places of decimals, from Mr. Moseley's Mechanics of Engineering, 1st ed. p. 622. A definite specific gravity is assigned to each substance to prevent ambiguity in working the following examples. It will be remarked, however, that different specimens of the same substance have different specific gravities: thus, of 16 specimens of cast iron the specific gravities have been found to vary from 7.295 to 6.963. The reader must, therefore, bear in mind that the numbers in the text give mean values from which the specific gravity of any specimen of a given substance will not largely vary though the limits of variation are greater with some substances than with others. A similar remark applies to all quantities determined by experiment. Ex. 4.-What is the weight of a rectangular block of marble 63 ft. long, and in section 12 ft. square? Ans. Weight, 667 tons, 14 cwts. 3 qrs. Ex. 5. The girth of a tree is 3 ft. at top, 3 ft. 9 in. at bottom, it is 14 ft. long. Determine its weight according as it is larch, oak, or mahogany. Also, its value at the following prices: larch, 2s. 6d.; oak, 7s.; mahogany, 19s. per cubic foot rough. [The volume to be determined as the frustum of a cone.] Ex. 6. Find the weight of a rectangular mass of oak, 12 ft. long, 4 ft. broad, and 2 feet thick. What would be the weight of a mass of granite of the same dimensions? Ans. Oak, 62 cwts. 2 qrs. 5 lbs. Granite, 175 cwts. 3 qrs. 3 lbs. |