# 2.11: Untitled Page 23

## Chapter 2

11

a

11

b

12

a

12

b

......

1

a n

1

b n

a b

a

b

......

a

b

21

21

22

22

2 n

2 n

A  B

 

(2‐48)

....

....

......

....

a

 1

m

b 1

m

m

a 2

m

b 2 ......

mn

a

mn

b

When working with large matrices, addition and subtraction is best carried out using computers and the appropriate software.

2.7 Problems

Section 2.1

2‐1. The following prefixes are officially approved for various multiples of ten: 10  deca  D ,

100  hecto  H ,

1000  kilo  K

6

9

12

10  mega  M ,

10  giga  G ,

10

tera  T

Indicate how to express the following quantities in terms of a prefix and a symbol using the appropriate SI units.

(a) 100, 000 watt,

(b) 100 meter,

(c) 300,000 meter

(d) 100,000 hertz,

(e) 200,000 kg,

(f) 2,000 ampere

2‐2. If a 1‐inch nail has a mass of 2.2 g, what will be the mass of one mole of 1‐inch nails?

Section 2.2

2‐3. Convert the following quantities as indicated:

a) 5000 cal to Btu

b) 5000 cal to watt‐s

c) 5000 cal to N‐m

2‐4. At a certain temperature, the viscosity of a lubricating oil is

3

0.136  10 lb s / ft2 . What is the kinematic viscosity in 2

m /s if the density of the

f

oil is

3

  0.936 g/cm .

Units

33

2‐5. The density of a gas mixture is

3

  1.3 kg/m . Calculate the density of the

gas mixture in the following list of units:

(a) lbm/ft3

(b) g/cm3

(c) g/L

(d) lbm/in3

2‐6. Write an expression for the volume per unit mass, ˆ

V , as a function of the molar

volume, V , (that is the volume per mole) and the molecular mass, MW. Write an expression for the molar volume, V , as a function of the density of the component,  , and its molecular mass, MW.

2‐7. The CGS system of units was once commonly used in science. What is the unit of force in the CGS system? Find the conversion factor between this unit and a Newton. Find the conversion factor between this unit and lb .

f

2‐8. In rotating systems one uses angular velocity in radians per second. How do you convert revolutions per minute, rev/min, to rad/s?

2‐9. Platinum is used as a catalyst in many chemical processes and in automobile catalytic converters. If a troy ounce of platinum costs \$100 and a catalytic converter has 5 grams of platinum, what is the value in dollars of the platinum in a catalytic converter? To solve this problem one needs to determine the relation between a troy ounce and a gram, and this conversion factor is not listed in Table 2‐4. While the troy ounce originated in sixteenth century Britain, it has largely been replaced by the measures of mass indicated in Table 2‐4. However, it is still retained today for the measure of precious stones and metals such as platinum, gold, etc.

2‐10. In the textile industry, filament and yarn sizes are reported in denier which is defined as the mass in grams of a length of 9000 meters. If a synthetic fiber has an average specific gravity of 1.32 and a filament of this material has a denier of 5.0, what is the mass per unit length in pounds‐mass per yard? What is the cross sectional area of this fiber in square inches? The specific gravity is defined as density

specific gravity =

density of water

34