Post on 21-Jan-2016
Chapter 2
Mathematics in Physics
Metric System
•A system of Measurements that
is based on the power of ten or multiples of ten
SI
International
System
•The system of measurements that has
been adopted by the scientific world based on the metric system
Basic Units
• Length meter m
• Mass kilogram kg
• Time second s
• Temp. kelvin K
• Matter mole mol
• Current amp A
• Lum. Int. candela cd
SI Prefixes
• Nano n 0.000000001 10-9
• micro 0.000001 10-6
• milli m 0.001 10-3
• centi c 0.01 10-2
• deci d 0.1 10-1
• kilok 1000 103
• mega M 1,000,000 106
• giga G 1,000,000,000 109
Scientific Notation
M x 10n
•1.00... M < 10
•n = an integer
M x 10n
•M is the coefficient
•n is the exponent
Convert each of the following to scientific
notation:620,000,000
0.000 000 000 045210,000
Addition & Subtraction in
Scientific Notation
• When adding w/o calculator– change all additives to the same power of
ten
– add coefficients
– power of ten remains constant
– 3 x 104 + 4 x 105 0.3 x 105 + 4 x 105
• When adding with calculator– all scientific notations must be within
parentheses
– 3 x 104 + 4 x 105 (3 x 104) + (4 x 105)
• When subtracting w/o a calculator–change all numbers to the same
exponent
–subtract coefficients
–keep exponents constant
• When subtracting with a calculator–place all scientific notations within
parentheses
Add:
4.10 x 1016 3.4 x 10-186
5.2 x 1015 6.20 x 10-185
Subtract:
4.10 x 1016 3.4 x 10-186
5.2 x 1015 6.20 x 10-185
Add: Subtract:
2.25 x 1016 3.40 x 10-18
7.7 x 1015 - 6.2 x 10-19
Multiplication & Division in Scientific Notation
• When multiplying w/o a calculator–multiply coefficients
–add exponents
• When multiplying with a calculator–place all scientific notations within
parentheses
• When dividing in w/o a calculator–divide coefficients
–subtract exponents
• When dividing in with a calculator–place all scientific notations within
parentheses
Multiply:
4.10 x 10126 2.0 x 10-186
3.0 x 1015 1.20 x 1018
divide:
4.40 x 1016 6.4 x 10186
2.2 x 1015 3.20 x 10-185
Compute:
4.40 x 10-6 6.4 x 10186
2.0 x 1015 3.20 x 1085x
Measurement Uncertainties
Accuracy
•How close the measurement is to
the correct measurement
Precision
•How well one can repeat the same
results in a measurement
Significant Digits
•The valid digits in a measurement
removing all digits that have too much uncertainty to count
Determine Sig Dig:• 215 21.5
• 21500 21.500
• 0.000 215 205
• 0.000 215 000 000
Conversion Factors
Ratios = 1
1 m
100 cm= 1
100 cm
1 m= 1
Conversion Factors• When you multiply any
number by a conversion factor, the number’s magnitude does not change
1 m
10-6 m= 1
1 nm
10-9 m= 1
1 cm
10-2 m= 1
1mm
10-3 m= 1
1 m
106 m= 1
1km
103 m= 1
109 m
1 Gm= 1
1Gm
109 m= 1
1 mm
10-3 m44 m x =
44 x 103 mm = 4.4 x 104 mm
Drill: Convert:1) 53 m to km2) 80 Gbytes to Mbytes3) 44 mg to ng
4) 62 cm to km
Parallax
•Differences in a measurement due
to the angle of observation
Common Units
•m = mass in (kg)
• t = time in (s)
•d = displacement in (m)
Common Units
•v = velocity in (m/s)
•a = acceleration in (m/s2)
•F = force in (N)
•N = Newton = kgm/s2
Common Units
•W = work in (J)
•J = Joules = kgm2/s2
•P = Power in (W)
•W = Watts = kgm2/s3
Graphing Data
Convert:1) 44 mm to km2) 21 s to Ms3) 64 cg to ng
Convert:1) 3.5 mm3 to m3
2) 3.6 km/hr to m/s
Density•A measure of mass
per unit volume
Density (D) ()
= m/V
Calculate the density of 750 g of a substance
occupying 12.5 mL of space.
Convert: 1) 23 cm/ms to km/ns 2) 56 g/nL to kg/ML
Convert:1800 km/hrto mm/ns
Convert: 47 g/nL to mg/L
Calculate the density in g/cm3 of a 0.62 Mg chunk
of metal that has dimensions of 12.5 mm by
4.0 m by 2.0 x 10-3 km.V = lwh = m/V
Convert: 144 km/hrto m/ns
Convert: 250 kg/m3 to
mg/cm3
Convert: 1)1800 miles/hr
to mm/ns2.54 cm = 1 inch
Drill: Convert:
4.6 g/nL to Mg/m3
1 mL = 1 cm3
Convert:2.5
xmiles/yearto m/ms
2.54 cm = 1.00 inch
Name & describe the seven basic
units
Name & give the multiple for: k, m,
M, , n, c, & G
Calculate the density in g/mL of 7.520 x 104 kg of
stuff occupying 2.5 x 103 m3 of space.
Calculate the volume in kL of an rectangular
prism with a length of 25 cm, width of 40.0 mm, & a height of
33500 mm.
Review LabDue
Monday