55. (a) Will more or less than 1 effective horse-power be required to lift 1 ton, 10 ft. high, in 1 minute? (b) To lift 1 ton, 20 ft. high, in 1 minute? (c) To lift 2 tons, 10 ft. high, in 1 minute? (d) To lift 2 tons, 20 ft. high, in 2 minutes ? (e) To lift 50 gallons of water, 100 feet high, in 1 minute? (f) To lift 8 cubic feet of water, 60 feet high, in 1 minute? 56. How many effective horse-power required to lift 5000 gallons of water, 100 feet, in 1 hour ? 57. How many indicated horse-power required to do the work described in Problem 56, provided 30 % of the force is lost by friction and imperfections of machinery? 58. How many indicated horse-power required to raise 2000 cubic feet of water, 80 feet, in 1 hour, provided 30 % of the power is lost by friction of machinery and of water in the pipes ? 59. If a horse pushes into the collar continuously with a force of 150 lb. and travels at the rate of 27 miles an hour, (a) how many foot-pounds per minute does his work represent? * (b) Is this more or less than 1 horse-power? 60. If 30 % of the force of an engine is lost in friction and in the imperfections of the machinery, how many gallons of water per hour can be raised 150 feet by a 20 horse-power engine? 61. What is the effective horse-power of an engine that can raise 1500 pounds 2376 feet in 6 minutes ? 62. What is the effective horse-power of an engine that can raise 150 cubic feet of water per minute from a mine 264 feet deep? * Pushing continuously into the collar with a force of 150 lb. and moving 24 miles an hour while doing this, is equivalent to lifting 150 lb. as many feet in an hour, as there are feet in 2} miles. NOTE. — The remaining pages of this book are devoted to problems that are distinctively agricultural. They may be omitted by pupils and teachers who are in no way interested in such work. The efforts that are being made in many states to introduce the elements of agricultural science into the rural schools, the thousands of boys in the public schools who will soon be, either directly or indirectly, interested in such problems as are here presented, the great and increasing interest in the rural school problem, and the fact that the teachers for the rural schools are, for the most part, educated in the city schools, is the apology, if one is needed, for introducing this topic in the pages of a common school arithmetic. The problems in nutritive ratio on pages 316 and 317, are as thoroughly “practical" as any in the book. The proper “balancing” of. foods with reference to their muscle-forming and their fat-forming elements, is receiving much attention in the Agricultural Colleges and Experiment Stations as well as among the more intelligent stock feeders everywhere. Enterprising young farmers in all sections of the United States, are asking for information in regard to the method of computing the “ balanced ration.” Hence a few simple problems under this head are introduced, and the author confidently believes that the skillful teacher will so use these pages as to make them of great value in aiding a large class of boys to see the relation of their school work to their prospective life work. The Comparative Value of Land for Agricultural Purposes. 1. If a certain piece of land, with an average annual expenditure of $17 per acre, gives an average annual return of $20 per acre, and is therefore considered worth $40 an acre as an investment, what is that piece of land worth that, with the same average expenditure, will give an average annual return of $29 per acre? 2. One piece of land produces 40 bushels of corn to the acre; another piece produces 60 bushels. If the cost of producing and marketing is $8 per acre in each case, and if the average price of corn is 25 cents a bushel, and if the difference in yield is due to the nature of the soils and not to differences in methods of cultivation, what is the relative value of the two pieces of land as an investment ? Shrinkage of Corn. At the Agricultural Experiment Station, Ames, Iowa, in the autumn of 1898, a corn-crib was built upon the platform of a set of farm scales. On Oct. 19, 7000 lb. of corn was husked and stored in the crib. The corn was weighed once a week for a year with the following results : Oct. 19, 7000 Feb. 15, 6290 June 14, 5860 June 28, 5840 July 19, 5760 Aug. 2, 5730 Aug. 9, 5800 Aug. 16, 5740 Aug. 30, 5700 Sept. 6, 5670 Sept. 13, 5640 Sept. 20, 5610 Sept. 27, 5630 Oct. 4, 5570 1. Find the per cent of shrinkage from Oct. 19 to Oct. 19 of the next year. 2. Using 7000 lb. as the base, find the per cent of shrinkage for each monthly period, - Oct. 19 to Nov. 2; Nov. 2 to Dec. 7; Dec. 7 to Jan. 4; Jan. 4 to Feb. 1, etc. 3. Find the sum of the thirteen answers to Problem 2 and compare this with the answer to Problem 1. Shrinkage of Corn and Hay. 1. Making no allowance for loss by rats and mice, for risk of destruction by fire or tornado, or for extra labor in handling, what per cent above the Oct. 19th price, should a farmer receive for corn on Jan. 4th to make up for the loss by shrinkage as shown in the table on the preceding page? 2. What per cent above the Jan. 4th price, should a farmer receive for corn on the following Sept. 6th to make up for loss by shrinkage as shown in the table? 3. If new corn is +0 cents per bushel of 75 lb., Nov. 2nd, what should be the price per bushel of 70 lb., on the following Aug. 2nd to make up for shrinkage as shown on the preceding page ? 4. Which is the better for the seller, corn at 50 cents per cwt. from the field Oct. 19th, or corn at 41 cents a bushel from the crib on the following June 7th ? 5. Which is the better for the buyer, new corn at 371 cents for 75 lb. on Nov. 2nd, or the same corn on the following May 3rd at 371 cents for 70 lb ? 6. Making proper allowance for the use of money, for risk of loss by vermin, fire, and tornado, for extra labor, and for shrinkage, what, in your judgment,* should the farmer receive for corn 70 lb. to the bushel, on July 5th, to be equivalent to 75 lb. for 30 cents, drawn directly from the field Oct. 19th ? 7. If clover hay shrinks in weight 30% from June to October, what should be the price in October to correspond with $6.00 per ton in June ? 8. If timothy hay shrinks in weight 20% from July to October, what should be the price in October to correspond with $7 per ton in July ? * The author very well knows that many pupils will be confronted with this problem who can have no “judgment" regarding it. Such may omit it. For those who can understand the conditions, the problem may prove the most valuable of any on the page. At the Slaughter-House. Shrinkage in dressing. Beeves shrink from 43 to 55 % in dressing. This means that a carcass of dressed beef weighs from 43 to 55 % less than the live weight of the animal. Hogs shrink from 15 to 22 %. BEEVES. (a) Find the per cent of shrinkage in each of the above cases ? (b) If the tongue, liver, heart, and offal are worth enough to pay for slaughtering, and the hide is worth 7 cents per pound, what is the cost per cwt. of each carcass of beef ? (c) Find the per cent of shrinkage on the entire lot of ten head. (d) Find the average cost of the dressed beef per cwt. Hogs. 11. Live weight, 450 lb. ; dressed weight, 370 lb. 12. Live weight, 650 lb.; dressed weight, 540 lb. 13. Live weight, 260 lb.; dressed weight, 220 lb. 14. Live weight, 350 lb.; dressed weight, 290 lb. 15. Live weight, 340 lb. ; dressed weight, 270 lb. (e) Find the per cent of shrinkage in each of the above cases. (f) If live hogs are worth $4.80 per cwt., and the cost of slaughtering is 50 cents per head, what is the cost per cwt. of each of the above carcasses of pork? |