chapter 2 mathematics in physics. metric system a system of measurements that is based on the power...
TRANSCRIPT
![Page 1: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/1.jpg)
Chapter 2
Mathematics in Physics
![Page 2: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/2.jpg)
Metric System
![Page 3: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/3.jpg)
•A system of Measurements that
is based on the power of ten or multiples of ten
![Page 4: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/4.jpg)
SI
International
System
![Page 5: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/5.jpg)
•The system of measurements that has
been adopted by the scientific world based on the metric system
![Page 6: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/6.jpg)
Basic Units
![Page 7: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/7.jpg)
• Length meter m
• Mass kilogram kg
• Time second s
• Temp. kelvin K
• Matter mole mol
• Current amp A
• Lum. Int. candela cd
![Page 8: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/8.jpg)
SI Prefixes
![Page 9: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/9.jpg)
• 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
![Page 10: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/10.jpg)
Scientific Notation
![Page 11: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/11.jpg)
M x 10n
•1.00... M < 10
•n = an integer
![Page 12: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/12.jpg)
M x 10n
•M is the coefficient
•n is the exponent
![Page 13: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/13.jpg)
Convert each of the following to scientific
notation:620,000,000
0.000 000 000 045210,000
![Page 14: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/14.jpg)
Addition & Subtraction in
Scientific Notation
![Page 15: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/15.jpg)
• 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)
![Page 16: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/16.jpg)
• 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
![Page 17: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/17.jpg)
Add:
4.10 x 1016 3.4 x 10-186
5.2 x 1015 6.20 x 10-185
![Page 18: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/18.jpg)
Subtract:
4.10 x 1016 3.4 x 10-186
5.2 x 1015 6.20 x 10-185
![Page 19: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/19.jpg)
Add: Subtract:
2.25 x 1016 3.40 x 10-18
7.7 x 1015 - 6.2 x 10-19
![Page 20: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/20.jpg)
Multiplication & Division in Scientific Notation
![Page 21: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/21.jpg)
• When multiplying w/o a calculator–multiply coefficients
–add exponents
• When multiplying with a calculator–place all scientific notations within
parentheses
![Page 22: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/22.jpg)
• When dividing in w/o a calculator–divide coefficients
–subtract exponents
• When dividing in with a calculator–place all scientific notations within
parentheses
![Page 23: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/23.jpg)
Multiply:
4.10 x 10126 2.0 x 10-186
3.0 x 1015 1.20 x 1018
![Page 24: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/24.jpg)
divide:
4.40 x 1016 6.4 x 10186
2.2 x 1015 3.20 x 10-185
![Page 25: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/25.jpg)
Compute:
4.40 x 10-6 6.4 x 10186
2.0 x 1015 3.20 x 1085x
![Page 26: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/26.jpg)
Measurement Uncertainties
![Page 27: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/27.jpg)
Accuracy
![Page 28: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/28.jpg)
•How close the measurement is to
the correct measurement
![Page 29: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/29.jpg)
Precision
![Page 30: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/30.jpg)
•How well one can repeat the same
results in a measurement
![Page 31: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/31.jpg)
Significant Digits
![Page 32: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/32.jpg)
•The valid digits in a measurement
removing all digits that have too much uncertainty to count
![Page 33: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/33.jpg)
Determine Sig Dig:• 215 21.5
• 21500 21.500
• 0.000 215 205
• 0.000 215 000 000
![Page 34: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/34.jpg)
Conversion Factors
Ratios = 1
![Page 35: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/35.jpg)
1 m
100 cm= 1
100 cm
1 m= 1
![Page 36: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/36.jpg)
Conversion Factors• When you multiply any
number by a conversion factor, the number’s magnitude does not change
![Page 37: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/37.jpg)
1 m
10-6 m= 1
1 nm
10-9 m= 1
![Page 38: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/38.jpg)
1 cm
10-2 m= 1
1mm
10-3 m= 1
![Page 39: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/39.jpg)
1 m
106 m= 1
1km
103 m= 1
![Page 40: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/40.jpg)
109 m
1 Gm= 1
1Gm
109 m= 1
![Page 41: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/41.jpg)
1 mm
10-3 m44 m x =
44 x 103 mm = 4.4 x 104 mm
![Page 42: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/42.jpg)
Drill: Convert:1) 53 m to km2) 80 Gbytes to Mbytes3) 44 mg to ng
4) 62 cm to km
![Page 43: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/43.jpg)
Parallax
![Page 44: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/44.jpg)
•Differences in a measurement due
to the angle of observation
![Page 45: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/45.jpg)
Common Units
•m = mass in (kg)
• t = time in (s)
•d = displacement in (m)
![Page 46: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/46.jpg)
Common Units
•v = velocity in (m/s)
•a = acceleration in (m/s2)
•F = force in (N)
•N = Newton = kgm/s2
![Page 47: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/47.jpg)
Common Units
•W = work in (J)
•J = Joules = kgm2/s2
•P = Power in (W)
•W = Watts = kgm2/s3
![Page 48: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/48.jpg)
Graphing Data
![Page 49: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/49.jpg)
![Page 50: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/50.jpg)
Convert:1) 44 mm to km2) 21 s to Ms3) 64 cg to ng
![Page 51: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/51.jpg)
Convert:1) 3.5 mm3 to m3
2) 3.6 km/hr to m/s
![Page 52: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/52.jpg)
Density•A measure of mass
per unit volume
![Page 53: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/53.jpg)
Density (D) ()
= m/V
![Page 54: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/54.jpg)
Calculate the density of 750 g of a substance
occupying 12.5 mL of space.
![Page 55: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/55.jpg)
Convert: 1) 23 cm/ms to km/ns 2) 56 g/nL to kg/ML
![Page 56: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/56.jpg)
Convert:1800 km/hrto mm/ns
![Page 57: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/57.jpg)
Convert: 47 g/nL to mg/L
![Page 58: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/58.jpg)
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
![Page 59: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/59.jpg)
Convert: 144 km/hrto m/ns
![Page 60: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/60.jpg)
Convert: 250 kg/m3 to
mg/cm3
![Page 61: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/61.jpg)
Convert: 1)1800 miles/hr
to mm/ns2.54 cm = 1 inch
![Page 62: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/62.jpg)
Drill: Convert:
4.6 g/nL to Mg/m3
1 mL = 1 cm3
![Page 63: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/63.jpg)
Convert:2.5
xmiles/yearto m/ms
2.54 cm = 1.00 inch
![Page 64: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/64.jpg)
Name & describe the seven basic
units
![Page 65: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/65.jpg)
Name & give the multiple for: k, m,
M, , n, c, & G
![Page 66: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/66.jpg)
Calculate the density in g/mL of 7.520 x 104 kg of
stuff occupying 2.5 x 103 m3 of space.
![Page 67: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/67.jpg)
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.
![Page 68: Chapter 2 Mathematics in Physics. Metric System A system of Measurements that is based on the power of ten or multiples of ten](https://reader035.vdocuments.site/reader035/viewer/2022062217/5697bfd01a28abf838caac3b/html5/thumbnails/68.jpg)
Review LabDue
Monday