CHAPTER XIV

MECHANICAL PROBLEMS

1. In a 10-lb. sample of solder composed of 5 parts zinc, 2 parts tin, and 1 part lead, how many pounds of each metal are there?

2. Find the cost at 8 cents a pound of a concrete tank 3 ft. long, 2 ft. wide, and 2 ft. high, the sides and bottom of the tank to be 2 in. thick.

3. What will the tank of Ex. 2 cost if made of cast iron, at the same price per

pound?

4. How many tanks 3 ft. 4 in. long, 2 ft. 4 in. wide, and 2 ft. 2 in. high can be made from 1000 cu. yd. of concrete if the sides and bottom of the tank are 2 in. thick?

5. Find the cost at 8 cents per pound of 1000

HOLLOW PRISM

concrete receptacles in the form of the frustum of a pyramid 3 ft. square at the top, 2 ft. 8 in. at the bottom, outside measurements, 2 ft. 2 in. high, the sides and bottom of the boxes to be 2 in. thick. Find the cost at 25 cents per cubic yard of sufficient earth to fill them all.

6. If an engine pumps 24 gallons of water per stroke and makes 46 strokes per minute, how many gallons will it deliver in an hour?

A convenient formula for finding capacity of cylindrical tanks standing on end is the following:

CIRCULAR CYLINDER

where

V = .0034 d2h

7. Find the capacity in gallons of an upright cylindrical tank 24 in. in diameter, 30 in. high.

8. Find the capacity of an upright cylindrical tank 4 ft. in diameter and 6 ft. high.

9. What is the capacity in gallons of a cylindrical can 15 in. in diameter and 23 in. high? What weight of materials weighing 50 lb. per cubic foot will it hold?

10. What is the height of a can of the same diameter as the can of Ex. 9 which will hold about 100 lb. of the same material?

11. What are the dimensions of a cylindrical tank whose height and diameter are equal, if the capacity of the tank is 75,000 gallons?

12. Find the cost of lumber and nails to inclose a corral 120 ft. by 200 ft. with a 4-rail fence 5 ft. high, according to the following specifications: posts to be 4 in. by 4 in., 8 ft. apart, and set 2 ft. in the ground; rails to be 1 in. by 6 in., fastened with 8-penny nails, 2 in each rail at each post; cost of lumber $36 per M; nails 35 cents per pound. (There are about 106 8-penny nails to the pound.)

13. Determine the cost of materials and labor to inclose a 10-acre field in the form of a square with a 3-rail fence 4 ft. high, post holes to cost 10 cents apiece, and labor $3 a day, assuming one man can build 200 ft. of fence per day; other specifications as in Ex. 12.

14. With lumber at $ 35.50 per M find the cost of materials for a coal bin with sides and bottom, no top, 6 ft. square and 3 ft. deep; corner posts 4 in. by 4 in.; floor to be laid on stringers 2 in. by 6 in., placed 3 ft. apart.

15. If a stick of timber is 16 in. square, what distance must be laid off from each corner to line for a chamfer, if the stick is to be octagonal?

16. If steel expands 0.000007 of its length for each degree increase in temperature (Fahrenheit), how much will a 30-ft. steel rail increase in length when heated from 32° to 120° ?

17. A cornucopia has a circular top 23 inches across. It is 9 inches deep. How many cubic inches will it contain?

18. A ball 9 inches in diameter is placed in a cubical box 10 inches on an edge, inside measurement. How many cubic inches of the box are not occupied by the ball?

19. How many loads of earth will have to be excavated to make a cut for a flume of rectangular section 300 feet long, 16 feet wide, and 8 feet deep?

20. Find the volume of a sphere 1 foot in diameter; of a cylinder of the same diameter and altitude; and of a cone of the same diameter and altitude. The volume of the sphere is how many times the volume of the cone? The volume of the cylinder is how many times the volume of the cone ?

SPHERE

21. If the cost of operating a motorcycle is $0.00 per mile, how far can one ride for a cent? for $.75? What is the cost per thousand miles?

22. The driving pulley on a shaft is 42 in. in diameter and makes 200 revolutions per minute. How many revolutions per minute will the driven pulley make if its diameter is 3 ft.?

23. The diameter of the driving pulley is 9 in. and its speed is 1000 revolutions per minute. At what speed will the driven pulley run if its diameter is 4 in. ?

24. If a locomotive driving wheel is 6 ft. in diameter and makes 110 revolutions per minute, find the speed of the locomotive in miles per hour.

The horse power of a 4-cycle gas engine is given by the formula:

HP

=

(Diam. of Cylinder)2 × (Length of Stroke) × (No. of Rev. per Min.) 18000 x (No. of Cylinders)

25. Find the horse power of a cycle-car gas engine with 2 cylinders, 31-in. bore, 3g-in. stroke, running at 2500 revolutions per minute.

26. Find the horse power of a single-cylinder engine with 3-in. bore, 31-in. stroke, running at 800 revolutions per minute.

27. Brass contains 65 per cent copper and 35 per cent zinc. When copper is worth 40 cents a pound and zinc 8 cents, what ought brass castings to cost if 2 cents a pound is allowed for casting the brass?

28. If 400 cubic feet of stacked hay weighs one ton, find the weight of a stack 22 ft. by 40 ft. by 24 ft.

29. The material excavated from a cellar 52 ft. long by 34 ft. wide and 6 ft. deep was evenly distributed over a lot 30 ft. by 1371⁄2 ft. To what depth was the lot covered?

30. Find the cost at 30 cents per load to excavate the ground for a cellar 24 ft. wide and 42 ft. long, the ground being excavated to a depth of 7 ft. 6 in. at one end and 2 ft. 6 in. at the other.

31. A rectangular piece of tin 16 in. by 20 in. has four equal squares cut out at the corners, and the sides and ends are then

turned up so as to form a rectangular tray. What is the capacity in pints of the tray if the sides of the square are 1 in.? if 11⁄2 in.? if 2 in.? if 21⁄2 in.? if 3 in.? if 31⁄2 in.? if 4 Tabulate your results. What depth gives the maximum

in. ? capacity?

32. If the piece of tin is 14 in. by 24 in. and other conditions as in the preceding example, determine the capacity of the tray if the sides of the squares are 1 in., 2 in., 3 in., 4 in.

33. A concrete swimming-tank is 40 ft. long and 22 ft. wide. Its depth is 10 ft. at one end and 4 ft. at the other. How many gallons of water are in it when it is filled to within 1 ft. of the top? (One cubic foot is equivalent to about 7.5 gallons.)

34. Cast iron disks are to be designed for a dumb-bell whose weight can be varied. The disks are to be 4 in. in diameter with a 13-in. hole through the center, and are to weigh 3 lb., 4 lb., and 5 lb. What must be the thickness of each?

Exercise

1. Given the following Paving Material data:

A Paving Mixture consists of:

1 part of cement,

3 parts of sand,

6 parts of crushed rock.

A sack of cement is equivalent to about 1.3 cubic feet,

A wheelbarrow load of sand to about 4 cubic feet,

A wheelbarrow load of rock to about 4 cubic feet.

If all the materials necessary for the mixture are to be dumped every 30 feet, how much of each material should be dumped at each place if the street is 40 feet wide, and the paving mixture is to be laid 5 inches deep?

2. How much of each material at each place if the street is 50 feet wide?

3. How much if the street is 30 feet wide?