Solution

Report
Chapter 2: Measurement and Problem Solving
The SI System
• All units in the SI system are related to the standard unit by a power of 10
• The power of 10 is indicated by a prefix
• The prefixes are always the same, regardless of the standard unit
Common Prefixes in the SI System
Prefix
Symbol
Decimal
Equivalent
Power of 10
1,000,000
Base x 106
1,000
Base x 103
mega-
M
kilo-
k
deci-
d
0.1
Base x 10-1
centi-
c
0.01
Base x 10-2
milli-
m
0.001
Base x 10-3
micro-
m or mc
0.000 001
Base x 10-6
nano-
n
0.000 000 001
Base x 10-9
Length
• = Measure of the two-dimensional distance an object covers
• SI unit = meter
 About 3½ inches longer than a yard
• 1 meter = one ten-millionth the distance from the North Pole to the
Equator = distance between marks on standard metal rod in a Paris
vault = distance covered by a certain number of wavelengths of a
special color of light
• Commonly use centimeters (cm)
 1 m = 100 cm
 1 cm = 0.01 m = 10 mm
 1 inch = 2.54 cm (exactly)
Mass
• = Measure of the amount of matter present in an object
• SI unit = kilogram (kg)
 about 2 lbs. 3 oz.
• Commonly measure mass in grams (g) or milligrams
(mg)
 1 kg = 2.2046 pounds, 1 lbs. = 453.59 g
 1 kg = 1000 g = 103 g,
 1 g = 1000 mg = 103 mg
 1 g = 0.001 kg = 10-3 kg,
 1 mg = 0.001 g = 10-3 g
Volume
• = Measure of the amount of three-dimensional space occupied
• SI unit = cubic meter (m3)
 a Derived Unit
• Commonly measure solid volume in cubic centimeters (cm3)
 1 m3 = 106 cm3
 1 cm3 = 10-6 m3 = 0.000001 m3
• Commonly measure liquid or gas volume in milliliters (mL)
 1 L is slightly larger than 1 quart
 1 L = 1 dL3 = 1000 mL = 103 mL
 1 mL = 0.001 L = 10-3 L
 1 mL = 1 cm3
Common Units and Their Equivalents
Length
1 kilometer (km)
=
0.6214 mile (mi)
1 meter (m)
=
39.37 inches (in.)
1 meter (m)
=
1.094 yards (yd)
1 foot (ft)
=
30.48 centimeters (cm)
1 inch (in.)
=
2.54 centimeters (cm) exactly
1 kilogram (kg)
=
2.205 pounds (lb)
1 pound (lb)
=
453.59 grams (g)
1 ounce (oz)
=
28.35 (g)
Mass
Common Units and Their Equivalents
Volume
1 liter (L)
=
1000 milliliters (mL)
1 liter (L)
=
1000 cubic centimeters (cm3)
1 liter (L)
=
1.057 quarts (qt)
1 U.S. gallon (gal)
=
3.785 liters (L)
Problem Solving and Dimensional Analysis
• Arrange conversion factors so starting unit cancels
 Arrange conversion factor so starting unit is on the bottom of
the conversion factor
• May string conversion factors
 So we do not need to know every relationship, as long as we
can find something else the beginning and ending units are
related to
unit 1
x
unit 2
unit 1
=
unit 2
Dimensional Analysis Exercise 1: Convert 7.8 km to miles
1.
Write down the Given
quantity and its unit
2.
Write down the quantity you
want to Find and unit
3.
Write down the appropriate
Conversion Factors
4.
Write a Solution Map
Given:
7.8 km
Find:
? miles
Conversion
Factors:
Solution
Map:
Solution:
1 km = 0.6214 mi
km
mi
0.6214 mi
1 km
5.
Follow the Solution Map to
Solve the problem
6.
Sig. Figs. and Round
Round:
7.
Check
Check: Units & Magnitude are
correct
7.8 km 
0.6214 mi
 4.84692 mi
1 km
4.84692 mi = 4.8 mi
Dimensional Analysis Exercise 2: Convert 20.0 lbs to kg
1.
Write down the Given
quantity and its unit
2.
Write down the quantity you
want to Find and unit
3.
Write down the appropriate
Conversion Factors
4.
Write a Solution Map
Given:
20.0 lbs
Find:
? kg
Conversion
Factors:
Solution
Map:
Solution:
1 kg = 2.205 pounds
lbs
kg
2.205 lb
1 kg
5.
Follow the Solution Map to
Solve the problem
6.
Sig. Figs. and Round
Round:
7.
Check
Check: Units & Magnitude are
correct
20 lbs 
1 kg
 9.07029 kg
2.205 lbs
9.07029 kg = 9.1 kg
Dimensional Analysis Exercise 3: How many cups of cream is 0.75 L?
1.
Write down the Given
quantity and its unit
2.
Write down the quantity you
want to Find and unit
3.
Write down the appropriate
Conversion Factors
4.
Write a Solution Map
Given:
0.75 L
Find:
? cu
Conversio
n Factors:
Solution
Map:
Solution:
1 L = 1.057 qt
1 qt = 4 cu
L
qt
1.057 qt
1L
cu
4 cu
1 qt
5.
Follow the Solution Map to
Solve the problem
6.
Sig. Figs. and Round
Round:
3.171 cu = 3.2 cu
7.
Check
Check:
Units & Magnitude are
correct
0.75 L 
1.057 qt 4 cu

 3.171 cu
1L
1 qt
Converting Quantities Involving Units Raised
to a Power
Convert Cubic Inches into Cubic Centimeters
1) Find Relationship Equivalence: 1 in = 2.54 cm
2) Write Solution Map
in3
cm3
3) Change Equivalence into Conversion Factors with Starting
Units on the Bottom
3
2.543 cm3 16.4 cm3
 2.54 cm 


 
3
3
1 in
1 in 3
 1 in 
Convert 2,659 cm2 into square meters
1.
Write down the Given
quantity and its unit
2.
Write down the quantity you
want to Find and unit
3.
Write down the appropriate
Conversion Factors
4.
Write a Solution Map
5.
Follow the Solution Map to
Solve the problem
Given:
2,659 cm2
? m2
Find:
Conversion
Factors:
Solution
Map:
Solution:
1 cm = 0.01 m
cm2
m2
 0.01 m 


 1 cm 
2,659 cm 2 
2
1 10 4 m 2
1 cm
2
 0.2659 m 2
6.
Sig. Figs. and Round
Round:
0.2659 m2
7.
Check
Check:
Units & Magnitude are
correct
Volume vs Mass of Brass
y = 8.38x
160
140
120
Mass, g
100
80
60
40
20
0
0.0
2.0
4.0
6.0
8.0
10.0
Volume, cm3
12.0
14.0
16.0
18.0
Density
Ratio of mass:volume
Solids = g/cm3
1 cm3 = 1 mL
Liquids = g/mL
Gases = g/L
Mass
Density 
Volume
Volume of a solid can be determined by water displacement – Archimedes
Principle
Density : solids > liquids >>> gases
except ice is less dense than liquid water!
Density
• For equal volumes, denser object has larger mass
• For equal masses, denser object has smaller volume
• Heating objects causes objects to expand
 does not effect their mass!!
 How would heating an object effect its density?
• In a heterogeneous mixture, the denser object sinks
 Why do hot air balloons rise?
Density
Solution Maps:
Volume
Density 
Mass
m, V
D
Density
Volume 
Mass
m, D
V
V, D
m
Mass  Density  Volume
Density as a Conversion Factor
• The gasoline in an automobile gas tank has a mass of 60.0 kg and a
density of 0.752 g/cm3. What is the volume?
• Given: 60.0 kg
• Find: Volume in L
• Conversion Factors:
 0.752 grams/cm3
 1000 grams = 1 kg
Density as a Conversion Factor
Exercise:
• A 55.9 kg person displaces 57.2 L of water when submerged
in a water tank. What is the density of the person in g/cm3?

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