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38. Observe a piece of ice floating in water. Estimate (a) its specific gravity and (b) its weight per cubic foot.
39. Estimate the weight of a cake of ice 2 feet square and 18 inches thick.
40. Estimate the weight of ice (tons) that can be stored in an ice-house 20 feet square inside measurement, provided the depth of the ice is 12 feet and one foot of space next to the walls is filled with sawdust.
41. How many tons in an acre of ice that is 10 inches thick?
WEIGHT OF LUMBER.
42. Observe a piece of partly seasoned pine scantling floating in water. Estimate (a) its specific gravity and (b) its weight per cubic foot.
43. Estimate the weight of a load of 12-foot pine fencing, the load being 3 feet wide and five feet high and the lumber "half-seasoned."
44. Estimate the weight of a pine log 16 feet long, 17 inches in diameter at one end and 19 inches at the other, the probable specific gravity being .8.*
WEIGHT Of Wood.
45. Observe a piece of oak or maple stove-wood floating in water. (a) Estimate its specific gravity; (b) estimate the weight of a cubic foot of it; and (c), on the supposition that a cord is equal to 100 solid feet of wood, estimate the weight of a cord of it.
46. The specific gravity of green hickory is almost 1. Estimate the weight of a round stick of it, 6 inches in diameter and 5 feet long.
*Although using the "average diameter," 18 in., will not give the exact solid content, it is sufficiently accurate for a practical estimate of weight. The fraction may be used as the approximate ratio of a circle to its circumscribed square.
NOTE.-A foot-pound is the amount of work required to lift one pound one foot.
47. How many foot-pounds of work must be done to raise 30 pounds 20 feet?
48. How many foot-pounds of work required to raise a man weighing 195 lb., to the third story of a building,27 feet?
49. How many foot-pounds of work must a boy weighing 90 lb. do to raise himself to the second story of the schoolhouse,-15 feet?
50. How many foot-pounds of work required, adding 25 % for friction and weight of ropes, chains, etc., to raise a stone weighing 340 lb. to the top of a monument 125 feet high?
51. How many foot-pounds of work required, adding 25 % for friction, etc., to raise a stone 2 ft. by 3 ft. by 18 in., specific gravity, 21, to the top of a wall 42 feet high?
52. How many foot-pounds of work required, adding 20 % for friction of machinery and of water in the pipes, to raise 5000 gallons of water 150 feet?
53. How many foot-pounds of work must a man do to carry himself, weight 150 lb., 18 bricks, weight 75 lb., and a hod, weight 12 lb., from the first floor to the third floor of a building,-22 feet?
54. How many foot-pounds of work required, adding 20% for friction, weight of carrier, etc., to lift 18 bricks weighing 75 lb., 22 feet?
NOTE.-A horse-power is the force required to do 33000 foot-pounds of work per minute. The indicated horse-power is that exhibited at the engine doing the work. The effective or net horse-power is the indicated horse-power less losses by friction and imperfections of machinery. The effective horse-power is computed from the work actually done.
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 2 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
Oct. 26, 6835
Nov. 2, 6715
Dec. 7, 6410
Dec. 21, 6380
Jan. 4, 6375
Feb. 1, 6330
Oct. 4, 5570
June 7, 5860
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.