Draw the following table in the work-book, and compute and fill in, to three decimal places, the omitted entries:

11. Weight of Sheet Steel. The weight of sheet steel is about' 487.7 lbs. per cubic foot.

Compute the weight per square foot, 1 inch thick.

12. Weight of Sheet Iron. Iron plates are estimated to weigh 480 lbs. to the cubic foot.

Compute the weight per square foot, 1 inch thick.

13. Formula for Weight per Square Foot. The weight of iron and steel plates per square foot, 1 inch thick, equals the weight per cubic foot divided by what?

Formulate this law, using the following notation:

Wweight per sq.ft.

Wc-weight per cu.ft.

If the plates were 2 inches thick, the weight per square foot would be how many times as much as when 1 inch thick?

If 5 inches thick, the weight per square foot would be how many times the weight per square foot, 1 inch thick?

If t = thickness of plate in inches, write a formula for the weight per square foot for any thickness.

14. By the formula compute and fill in, to three decimal places, the omitted entries in the following table:

for a boiler is commonly taken as the bursting pressure. When such is the case, 5 is called the factor of safety.

Po=bursting pressure in pounds per square inch;

T-tensile strength of the boiler plate in pounds per square

inch;

t=thickness of the boiler plate or shell in inches;
R=radius of boiler in inches.

C = a constant which has the following values:
.56 for single-riveted boilers;
.70 for double-riveted boilers;

.88 for triple-riveted boilers.

Compute the safe working pressure for single-, double-, and triple-riveted boilers 58 inches in diameter, when made of -inch steel plate, having a tensile strength of 55000 lbs. per square inch. 16. What is the bursting pressure Po, for each of the boilers in Problem 15?

17. Thickness of a Wrought-iron Tube. The actual inside diameter of a Briggs standard, wrought-iron, welded tube, is 0.623 inch; the actual outside diameter is 0.840 inch.

Compute the thickness of the metal to three decimal places.

18. Efficiency of a Motor. The efficiency of a motor, Eff, equals its output in horse-power HP。, divided by its input in horsepower HPi.

Formulate this law and compute Eff to two decimal places, when a motor, driven by 5 kilowatts, delivers 6 horse-power. (To reduce kilowatts to horse-power, multiply by 1.34.)

19. Time Required to Plane Metals. The time in minutes, in which a piece of work can be planed, equals the width of the work in inches, divided by the product of the number of strokes per minute and the feed per stroke (width of the cut) in inches.

inch,

Formulate this law and compute the time required to plane a piece of work 30 inches wide, when the feed per stroke is and the planer makes 8 strokes per minute.

CHAPTER II

POWERS AND ROOTS

SECTION 1. POWERS. SECTION 2. ROOTS. SECTION 3. SQUARE ROOT. SECTION 4. CUBE ROOT. SECTION 5. APPLIED PROBLEMS.

8.1. POWERS

30. Definition and Illustration. A power is the product obtained by multiplying a number one or more times by itself.

Thus

25=5X5
125=5X5X5

In the preceding, 25 is a power because it is the product obtained when 5 is multiplied once by itself; 125 is a power because it is the product obtained by multiplying 5 twice by itself.

When a number is multiplied, it is said to be used as a factor.

Thus in 5X4, both the 5 and the 4 are factors.

31. An Exponent. When a number is used more than once as a factor, it is denoted by a small figure at the right of and a little above the number, called an exponent.

Thus

32 denotes the square or second power of 3,

53 denotes the cube or third power of 5.

Therefore

32=3X3=9

53=5X5X5=125

32. Examples in Powers. Under the paragraph number and title, indicate and compute the following powers:

1. The eighth power of 2.
2. The sixth power of 4.
3. The fourth power of 8.
4. The fifth power of 7.
5. The third power of 12.
6. The second power of 225.
7. The third power of 134.

33. The Reciprocal of a Number. number is 1 divided by the number.

The reciprocal of a

Thus

is the reciprocal of 8

is the reciprocal of 12

is the reciprocal of 7

34. Examples in Reciprocals. Express and compute to five decimal places, the reciprocals of the following numbers:

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,

20, 21, 22, 23, 24, 25, 32, 36, 40, 42, 48, 50, 56, 125,
250, 275, 500.

35. A Negative Exponent. When an exponent has a minus sign, it is called a negative exponent; it denotes the reciprocal of the number having the same exponent with the sign omitted.