math problems
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MATH PROBLEMS. TOPIC ONE. Measurement, Uncertainty, Significant Figures. The age of the universe is thought to be about 14 billion years. Assuming 2 significant figures, write this in powers of ten in a) Years b) Seconds. ANSWER. A) 14 Billion years = 14,000,000,000 years - PowerPoint PPT PresentationTRANSCRIPT
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MATH PROBLEMSMATH PROBLEMSTOPIC ONETOPIC ONE
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Measurement, Measurement, Uncertainty, Significant Uncertainty, Significant
FiguresFigures The age of the universe is thought to be The age of the universe is thought to be
about 14 billion years. Assuming 2 about 14 billion years. Assuming 2 significant figures, write this in powers significant figures, write this in powers of ten inof ten in
a) Yearsa) Years
b) Secondsb) Seconds
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ANSWERANSWER
A) 14 Billion years = 14,000,000,000 A) 14 Billion years = 14,000,000,000 years years
1.4 x 101.4 x 101010 years years
B)B)
€
1.4x1010years( )365days
1year
⎛
⎝ ⎜
⎞
⎠ ⎟24hours
1day
⎛
⎝ ⎜
⎞
⎠ ⎟60min
1hour
⎛
⎝ ⎜
⎞
⎠ ⎟60sec
1min
⎛
⎝ ⎜
⎞
⎠ ⎟= 4.4x1017 sec
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QUESTIONQUESTION
How many significant figures do each of How many significant figures do each of the following numbers have:the following numbers have:
A.A. 214214 E. E. 0.00860.0086
B.B. 81.6081.60 F.F. 32363236
C.C. 7.037.03 G.G. 87008700
D.D. 0.030.03
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ANSWERANSWER
A.A. 214214 3 Significant Figures3 Significant Figures
B.B. 81.6081.60 4 Significant Figures4 Significant Figures
C.C. 7.037.03 3 Significant Figures3 Significant Figures
D.D. 0.030.03 1 Significant Figure1 Significant Figure
E.E. 0.00860.0086 2 Significant 2 Significant FiguresFigures
F.F. 32363236 4 Significant Figures4 Significant Figures
G.G. 87008700 2 Significant Figures2 Significant Figures
..
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QUESTIONQUESTION
Write the following numbers in powers Write the following numbers in powers of ten notation (Scientific Notation):of ten notation (Scientific Notation):
A.A. 1.1561.156 F.F. 444444
B.B. 21.821.8
C.C. 0.00680.0068
D.D. 27.63527.635
E.E. 0.2190.219
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ANSWERANSWER
A.A. 1.1561.156 1.1.56 x 10 1.1.56 x 1000
B.B. 21.821.8 2.18 x 10 2.18 x 1011
C.C. 0.00680.0068 6.8 x 10 6.8 x 10-3-3
D.D. 27.63527.635 2.7635 x 10 2.7635 x 1011
E.E. 0.2190.219 2.19 x 10 2.19 x 10-1-1
F.F. 444444 4.44 x 10 4.44 x 1022
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QUESTIONQUESTION
An electron can tunnel through an An electron can tunnel through an energy barrier with probability energy barrier with probability 0.0000000000375. (This is a concept 0.0000000000375. (This is a concept used in quantum mechanics.) Express used in quantum mechanics.) Express this probability in scientific notation.this probability in scientific notation.
* Answer:* Answer:
3.75 x 103.75 x 10−11−11
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QUESTIONQUESTION
Sara has lived 18.0 years. How many Sara has lived 18.0 years. How many seconds has she lived? Express the seconds has she lived? Express the answer in scientific notation. Use 365.24 answer in scientific notation. Use 365.24 days per year for your calculations.days per year for your calculations.
* Answer:* Answer:
5.68 x 105.68 x 1088 s s
€
18years( )365.24days
1year
⎛
⎝ ⎜
⎞
⎠ ⎟24hours
1day
⎛
⎝ ⎜
⎞
⎠ ⎟60min
1hour
⎛
⎝ ⎜
⎞
⎠ ⎟60sec
1min
⎛
⎝ ⎜
⎞
⎠ ⎟= 5.68x108 sec
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QUESTIONQUESTION
Write out the following numbers in full Write out the following numbers in full with the correct number of zeros:with the correct number of zeros:
A. A. 8.69 x 108.69 x 1044
B.B. 9.1 x 109.1 x 1033
C.C. 8.8 x 108.8 x 10-1-1
D.D. 4.76 x 104.76 x 1022
E.E. 3.62 x 103.62 x 10-5-5
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ANSWERANSWER
A. A. 8.69 x 108.69 x 1044 86,90086,900
B.B. 9.1 x 109.1 x 1033 9,1009,100
C.C. 8.8 x 108.8 x 10-1-1 0.880.88
D.D. 4.76 x 104.76 x 1022 476476
E.E. 3.62 x 103.62 x 10-5-5 0.00003620.0000362
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QUESTIONQUESTION
Express the following sum with the correct number of Express the following sum with the correct number of significant figures:significant figures:
1.80 m + 142.5 cm + 5.34 x 101.80 m + 142.5 cm + 5.34 x 1055 μμmm
* To add values with significant figures, adjust all * To add values with significant figures, adjust all values to be added so that their units are all the samevalues to be added so that their units are all the same
1.80 m + 142.5 cm + 5.35 x 101.80 m + 142.5 cm + 5.35 x 105 5 μμm = m =
1.80 m + 1.425 m + 0.534 m = 3.759 m 1.80 m + 1.425 m + 0.534 m = 3.759 m 3.76 m 3.76 m
** When adding, the final result is to be no more When adding, the final result is to be no more accurate than the least accurate number used. In this accurate than the least accurate number used. In this case, that is the first measurement, which is accurate case, that is the first measurement, which is accurate to the hundredths place.to the hundredths place.
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QUESTIONQUESTION
What is the percent uncertainty in the What is the percent uncertainty in the measurement 3.76 +/- 0.25 m?measurement 3.76 +/- 0.25 m?
PERCENT UNCERTAINTY:PERCENT UNCERTAINTY:
Percent Uncertainty = Uncertainty /Measurement x Percent Uncertainty = Uncertainty /Measurement x 100%100%
* Measurement = 3.76 m* Measurement = 3.76 m
* Uncertainty = 0.25 m* Uncertainty = 0.25 m
€
0.25 m
3.76 m
⎡ ⎣ ⎢
⎤ ⎦ ⎥x100% = 6.6%
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QUESTIONQUESTION
Time intervals measured with a Time intervals measured with a stopwatch typically have an uncertainty stopwatch typically have an uncertainty of about 0.2s, due to human reaction of about 0.2s, due to human reaction time at the start and stop moments. time at the start and stop moments. What is the percent uncertainty of a What is the percent uncertainty of a handtimed measurement of handtimed measurement of
A)A) 5 s5 s
B)B) 50 s50 s
C)C) 5 min5 min
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ANSWERANSWER
Percent uncertainty = Uncertainty / Measurement x Percent uncertainty = Uncertainty / Measurement x 100%100%
A)A)
% Uncertainty =% Uncertainty =
B) B)
% Uncertainty = % Uncertainty =
€
0.2 sec
5 sec
⎡ ⎣ ⎢
⎤ ⎦ ⎥x100% = 4%
€
0.2 sec
50 sec
⎡ ⎣ ⎢
⎤ ⎦ ⎥x100% = 0.4%
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ANSWERANSWER
Percent uncertainty = Uncertainty / Measurement x Percent uncertainty = Uncertainty / Measurement x 100%100%
C)C)
% Uncertainty =% Uncertainty =
€
0.2 sec
300 sec
⎡ ⎣ ⎢
⎤ ⎦ ⎥x100% = 0.07%
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QUESTIONQUESTION
Express each of the following numbers to Express each of the following numbers to only three significant figures:only three significant figures:
A. A. 10.072 m10.072 m
B.B. 775.4 km775.4 km
C.C. 0.002549 kg0.002549 kg
D.D. 93,000,000 mi93,000,000 mi
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ANSWERANSWER
Express each of the following numbers to Express each of the following numbers to only three significant figures:only three significant figures:
A. A. 10.072 m10.072 m 10.1 m10.1 m
B.B. 775.4 km775.4 km 775 km775 km
C.C. 0.002549 kg0.002549 kg 2.55 x 102.55 x 10-3-3 kgkg
D.D. 93,000,000 mi93,000,000 mi 9.30 x 109.30 x 1077 mi mi
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QUESTIONQUESTION
* Multiplying Numbers in Scientific Notation* Multiplying Numbers in Scientific Notation
Multiply 3.65×10Multiply 3.65×102323 by 4.12×10 by 4.12×10154154 by 1.11×10 by 1.11×10−11 −11 and and express the answer in scientific notation.express the answer in scientific notation.
*ANSWER: 1.67 x 10*ANSWER: 1.67 x 10167167
11stst:: Add together exponents Add together exponents
(23+154+(-11)) = 166(23+154+(-11)) = 166
22ndnd:: Multiply (3.65)(4.12)(1.11) = 16.7Multiply (3.65)(4.12)(1.11) = 16.7
16.7 16.7 1.67 x 10 1.67 x 101 1 1+166 = 167 1+166 = 167
**ANSWER **ANSWER 1.67 x 10 1.67 x 10167167
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QUESTIONQUESTION
*Dividing Numbers in Scientific *Dividing Numbers in Scientific NotationNotation
Newton's second law states that the net Newton's second law states that the net force equals the product of mass and force equals the product of mass and acceleration. A boat's mass of is 9.6×10acceleration. A boat's mass of is 9.6×1055 kg and it experiences a net force of kg and it experiences a net force of 1.5×101.5×1044 kg∙m/s kg∙m/s22. State its acceleration.. State its acceleration.
* GIVEN * GIVEN F = ma F = ma
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ANSWERANSWER
*Dividing Numbers in Scientific *Dividing Numbers in Scientific NotationNotation
Boat's mass = 9.6×10Boat's mass = 9.6×1055 kg kg
Net force = 1.5×10Net force = 1.5×1044 kg∙m/s kg∙m/s22
* GIVEN * GIVEN F = ma F = ma
* Acceleration = ?* Acceleration = ?
ANSWER:ANSWER: 1.6 x 10 1.6 x 10−2 −2 m/sm/s22
€
1.5x104 kgxm
sec2
⎛
⎝ ⎜
⎞
⎠ ⎟/(9.6x105kg) =1.6x10−2m /s2
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ANSWERANSWER
*Dividing Numbers in Scientific Notation*Dividing Numbers in Scientific Notation
Boat's mass = 9.6×10Boat's mass = 9.6×1055 kg kg Net force = 1.5×10Net force = 1.5×1044 kg∙m/skg∙m/s22
1.5×101.5×1044 kg∙m/s kg∙m/s2 2 / 9.6×10/ 9.6×1055 kg kg
11stst: Subtract the exponents: Subtract the exponents
4 – 5 = -14 – 5 = -1
22ndnd: Divide 1.5/9.6 = 0.16 : Divide 1.5/9.6 = 0.16 1.6 x 10 1.6 x 10-1-1
33rdrd: Add together the exponents : Add together the exponents
(-1) + (-1) = -2(-1) + (-1) = -2
** ANSWER: 1.6 x 10** ANSWER: 1.6 x 10-2 -2 m/sm/s22
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QUESTIONQUESTION
* Adding and Subtracting Numbers in * Adding and Subtracting Numbers in Scientific Notation:Scientific Notation:
A 3.70×10A 3.70×1066 kg piece splits off an iceberg of mass kg piece splits off an iceberg of mass of 5.96×10of 5.96×1077 kg. Calculate the mass of the kg. Calculate the mass of the remaining iceberg and express the answer in remaining iceberg and express the answer in scientific notation.scientific notation.
(5.96 × 10(5.96 × 1077 kg) – (3.70 x 10 kg) – (3.70 x 1066 kg) = kg) =
(5.96 × 10(5.96 × 1077 kg) – (0.370 x 10 kg) – (0.370 x 1077 kg)= kg)=
(5.96 – 0.370) × 10(5.96 – 0.370) × 1077 kg = kg =
5.59 x 105.59 x 1077 kg kg
* ANSWER:* ANSWER: 5.59 x 105.59 x 1077 kg kg
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QUESTIONQUESTION
* Adding and Subtracting Numbers in Scientific * Adding and Subtracting Numbers in Scientific Notation:Notation:
A small metal chamber contains 5.632×10A small metal chamber contains 5.632×10−9−9 mol of mol of oxygen gas at very low pressure. An additional oxygen gas at very low pressure. An additional 4.379×104.379×10−8−8 mol of oxygen gas are added. Find the total mol of oxygen gas are added. Find the total amount of gas in the chamber.amount of gas in the chamber.
(5.632 × 10(5.632 × 10−9−9 mol) + (4.379 × 10 mol) + (4.379 × 10−8−8 mol) = mol) =
(5.632 × 10(5.632 × 10−9−9 mol) + (4.379 × 10 mol) + (4.379 × 10−8−8 mol) = mol) =
(0.5632 × 10(0.5632 × 10−8−8 mol) + (4.379 × 10 mol) + (4.379 × 10−8−8 mol) = mol) =
(0.5632 + 4.379) × 10(0.5632 + 4.379) × 10−8−8 mol = mol =
* ANSWER:* ANSWER: 4.942 x 10 4.942 x 10−8−8 mol mol
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Standard Units, Standard Units, Converting UnitsConverting Units
Which of the following is not an SI base Which of the following is not an SI base quantity?quantity?
A)A) LengthLength
B)B) MassMass
C)C) WeightWeight
D)D) TimeTime
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Standard Units, Standard Units, Converting UnitsConverting Units
Which of the following is not an SI base Which of the following is not an SI base quantity?quantity?
A)A) LengthLength
B)B) MassMass
C)C) WeightWeight
D)D) TimeTime
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QUESTIONQUESTION
Which of the following is the SI unit of Which of the following is the SI unit of mass?mass?
a)a) poundpound
b)b) gramgram
c)c) kilogramkilogram
d)d) tonton
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ANSWERANSWER
Which of the following is the SI unit of Which of the following is the SI unit of mass?mass?
a)a) poundpound
b)b) gramgram
c)c) kilogramkilogram
d)d) tonton
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QUESTIONQUESTION
How many centimeters are there in a How many centimeters are there in a kilometer?kilometer?
*Answer:*Answer:
100,000 cm100,000 cm
€
1km( )1000m
1km
⎛
⎝ ⎜
⎞
⎠ ⎟100cm
1m
⎛
⎝ ⎜
⎞
⎠ ⎟=100,000cm
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QUESTIONQUESTION
Write the following as full (decimal) Write the following as full (decimal) numbers with standard units:numbers with standard units:
a)a) 286.6 mm286.6 mm
b)b) 85 85 μμVV
c)c) 760 mg760 mg
d)d) 60.0 ps60.0 ps
e)e) 2.50 gigavolts2.50 gigavolts
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ANSWERANSWER
a)a) 286.6 mm 286.6 mm Standard Unit = Meter Standard Unit = Meter
1000 mm = 1 m1000 mm = 1 m
b)b) 85 85 μμV V Standard Unit = Volt Standard Unit = Volt
1000 microvolt (1000 microvolt (μμV) = 1 millivoltV) = 1 millivolt
1000 millivolt = 1 volt1000 millivolt = 1 volt
€
286.6mm( )1m
1000mm
⎛
⎝ ⎜
⎞
⎠ ⎟= 0.2866m
€
85μm( )1mV
1000μm
⎛
⎝ ⎜
⎞
⎠ ⎟
1V
1000mV
⎛
⎝ ⎜
⎞
⎠ ⎟= 0.000085V
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ANSWERANSWER
c)c) 760 mg 760 mg Standard unit = kg Standard unit = kg
1000 mg = 1 g1000 mg = 1 g
1000 g = 1 kg1000 g = 1 kg
€
760mg( )1g
1000mg
⎛
⎝ ⎜
⎞
⎠ ⎟
1kg
1000g
⎛
⎝ ⎜
⎞
⎠ ⎟= 0.000760kg
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ANSWERANSWER
d)d) 60.0 picoseconds 60.0 picoseconds Standard unit Standard unit = Second= Second
1 x 101 x 10-12-12 s = 1 ps or 1 x 10 s = 1 ps or 1 x 101212 ps = 1 ps = 1 s s
€
60.0ps( )1s
1x1012 ps
⎛
⎝ ⎜
⎞
⎠ ⎟= 0.0000000000600s
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ANSWERANSWER
e)e) 2.50 gigavolts 2.50 gigavolts Standard unit = Standard unit = VoltsVolts
1 x 101 x 1099 volts = 1 gigavolt volts = 1 gigavolt
€
2.50gigavolts( )1x109V
1gigavolt
⎛
⎝ ⎜
⎞
⎠ ⎟= 2,500,000,000V
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QUESTIONQUESTION
A drug company has just manufactured A drug company has just manufactured 50.0 kg of acetylsalicylic acid for use in 50.0 kg of acetylsalicylic acid for use in aspirin tablets. If a single tablet aspirin tablets. If a single tablet contains 500 mg of the drug, how many contains 500 mg of the drug, how many tablets can the company make out of tablets can the company make out of this batch?this batch?
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ANSWERANSWER
* ANSWER:* ANSWER:
100,000 tablets100,000 tablets
€
50.0kg( )1000g
1kg
⎛
⎝ ⎜
⎞
⎠ ⎟1000mg
1g
⎛
⎝ ⎜
⎞
⎠ ⎟
1tablet
500mgdrug
⎛
⎝ ⎜
⎞
⎠ ⎟=100,000tablets
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QUESTIONQUESTION
Determine your own height in meters, Determine your own height in meters, and your mass in kilograms.and your mass in kilograms.
* Example- Height = 5’8” (5 feet 8 * Example- Height = 5’8” (5 feet 8 inches)inches)
* Given: 1 meter = 39.37 inches* Given: 1 meter = 39.37 inches
€
68inches( )1meter
39.37inches
⎛
⎝ ⎜
⎞
⎠ ⎟=1.7meters
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QUESTIONQUESTION
Determine your own height in meters, and Determine your own height in meters, and your mass in kilograms.your mass in kilograms.
* Example- Weight = 165 lbs* Example- Weight = 165 lbs
* Given: 0.456 kg = 1 lb* Given: 0.456 kg = 1 lb
* Technically, pounds and mass measure 2 separate * Technically, pounds and mass measure 2 separate properties. To make this conversion, we have to assume properties. To make this conversion, we have to assume that we are at a location where the acceleration due to that we are at a location where the acceleration due to gravity is 9.8 m/sgravity is 9.8 m/s22
€
165lbs( )0.456kg
1lb
⎛
⎝ ⎜
⎞
⎠ ⎟= 75.2kg
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QUESTIONQUESTION
The Sun, on average, is 93 million miles The Sun, on average, is 93 million miles from Earth. How many meters is this? from Earth. How many meters is this? ExpressExpress
a) Powers of ten notation a) Powers of ten notation (Scientific Notation)(Scientific Notation)
b) Using a metric prefixb) Using a metric prefix
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ANSWERANSWER
a) Express using powers of ten…a) Express using powers of ten…
1 mile = 1610 meters1 mile = 1610 meters
93 million miles = (93 x 1093 million miles = (93 x 1066 miles) miles)
€
93x106miles( )1610meters
1mile
⎛
⎝ ⎜
⎞
⎠ ⎟=1.5x1011meters
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ANSWERANSWER
b) Express using a metric prefix…b) Express using a metric prefix…
1.5 x 101.5 x 101111 m m 150 x 10 150 x 1099 m = 150 gigameters m = 150 gigameters
OROR
1.5 x 101.5 x 101111 m m 0.15 x 10 0.15 x 101212 m = 0.15 m = 0.15 terameters terameters
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QUESTIONQUESTION
What is the conversion factor between…What is the conversion factor between…
a)a)ftft22 and yd and yd22
1 yard = 3 feet1 yard = 3 feet
b) mb) m2 2 and ftand ft22
1 meter = 3.28 feet1 meter = 3.28 feet€
1 ft 2( )1yd
3 ft
⎛
⎝ ⎜
⎞
⎠ ⎟
2
= 0.111yd2
€
1m2( )
3.28 ft
1m
⎛
⎝ ⎜
⎞
⎠ ⎟2
=10.8 ft 2
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QUESTIONQUESTION
An airplane travels at 950 km/h. How long An airplane travels at 950 km/h. How long does it take to travel 1.00 km?does it take to travel 1.00 km?
* Use the speed if the airplane to convert * Use the speed if the airplane to convert the travel distance into a time.the travel distance into a time.
€
1.00km( )1hour
950km
⎛
⎝ ⎜
⎞
⎠ ⎟60min
1hour
⎛
⎝ ⎜
⎞
⎠ ⎟60sec
1min
⎛
⎝ ⎜
⎞
⎠ ⎟= 3.8sec
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QUESTIONQUESTION
A typical atom has a diameter of about 1.0 A typical atom has a diameter of about 1.0 x 10x 10-10 -10 m.m.
A) What is this in inches?A) What is this in inches?
Given: 1 m = 3.28 ftGiven: 1 m = 3.28 ft
€
1.0x10−10m( )3.28 ft
1m
⎛
⎝ ⎜
⎞
⎠ ⎟12inches
1 ft
⎛
⎝ ⎜
⎞
⎠ ⎟= 3.9x10−9 in
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QUESTIONQUESTION
A typical atom has a diameter of about 1.0 A typical atom has a diameter of about 1.0 x 10x 10-10 -10 m.m.
B) Approximately how many atoms are B) Approximately how many atoms are there along a 1.0-cm line?there along a 1.0-cm line?
€
1.0cm( )1m
100cm
⎛
⎝ ⎜
⎞
⎠ ⎟
1atom
1x10−10m
⎛
⎝ ⎜
⎞
⎠ ⎟=1.0x108atoms
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QUESTIONQUESTION
11.2 meters per second is how many 11.2 meters per second is how many miles per hour?miles per hour?
* ANSWER:* ANSWER:
25.0 mi/h25.0 mi/h
€
11.2meters
1sec
⎛
⎝ ⎜
⎞
⎠ ⎟60sec
1hour
⎛
⎝ ⎜
⎞
⎠ ⎟3.28 feet
1meter
⎛
⎝ ⎜
⎞
⎠ ⎟
1mile
5280 feet
⎛
⎝ ⎜
⎞
⎠ ⎟= 25mi /h
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QUESTIONQUESTION
A A light-year light-year is the distance light travels is the distance light travels in one year (at speed = 2.998 x 10in one year (at speed = 2.998 x 1088 m/s). m/s).
A)A) How many meters are there in one How many meters are there in one light year?light year?
Know Know 1 light year = 2.998 x 10 1 light year = 2.998 x 1088 m/s m/s
* How many seconds are in one year?* How many seconds are in one year?
€
365days
1year
⎛
⎝ ⎜
⎞
⎠ ⎟24hours
1day
⎛
⎝ ⎜
⎞
⎠ ⎟60min
1hour
⎛
⎝ ⎜
⎞
⎠ ⎟60sec
1min
⎛
⎝ ⎜
⎞
⎠ ⎟= 3.156x107 sec/ year
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ANSWERANSWER
A A light-year light-year is the distance light travels in is the distance light travels in one year (at speed = 2.998 x 10one year (at speed = 2.998 x 1088 m/s). m/s).
A)A) How many meters are there in one How many meters are there in one light year?light year?
Know Know 1 light year = 2.998 x 10 1 light year = 2.998 x 1088 m/s m/s
€
3.156x107 sec
1year
⎛
⎝ ⎜
⎞
⎠ ⎟2.998x108meters
1sec
⎛
⎝ ⎜
⎞
⎠ ⎟= 9.46x1015meters / year
*Answer = 9.46 x 1015 meters
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QUESTIONQUESTION
A A light-year light-year is the distance light travels in is the distance light travels in one year (at speed = 2.998 x 10one year (at speed = 2.998 x 1088 m/s). m/s).
B)B) An astronomical unit (AU) is the An astronomical unit (AU) is the average distance from the Sun to Earth, average distance from the Sun to Earth, 1.50 x 101.50 x 1088 km. How many AU are there in km. How many AU are there in 1.00 light-year?1.00 light-year?
Know Know 1 light year = 9.46 x 101 light year = 9.46 x 101515 meters meters
1 AU = 1.50 x 101 AU = 1.50 x 1088 km km
€
9.46x1015meters
1lightyear
⎛
⎝ ⎜
⎞
⎠ ⎟
1AU
1.50x1011meters
⎛
⎝ ⎜
⎞
⎠ ⎟= 6.31x104 AU / lightyear
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QUESTIONQUESTION
A A light-year light-year is the distance light travels in is the distance light travels in one year (at speed = 2.998 x 10one year (at speed = 2.998 x 1088 m/s). m/s).
C)C) What is the speed of light in AU/h?What is the speed of light in AU/h?
Know Know 1 light year = 6.31 x 101 light year = 6.31 x 1044 AU AU
1 AU = 1.50 x 101 AU = 1.50 x 1011 11 mm
1 light year = 2.998 x 101 light year = 2.998 x 1088 m/s m/s
€
2.998x108meters
1sec
⎛
⎝ ⎜
⎞
⎠ ⎟
1AU
1.50x1011meters
⎛
⎝ ⎜
⎞
⎠ ⎟3600sec
1hr
⎛
⎝ ⎜
⎞
⎠ ⎟= 7.20AU /hr
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Dimensional AnalysisDimensional Analysis
The following variables are commonly seen in The following variables are commonly seen in equations. The name of the quantity represented equations. The name of the quantity represented by each variable, and its dimension(s), are also by each variable, and its dimension(s), are also shown.shown.
x distance (L)x distance (L) a acceleration (L/Ta acceleration (L/T22))
t time (T)t time (T) v speed (L/T)v speed (L/T)
m mass (M)m mass (M) F force (ML/TF force (ML/T22))
Using the information above, select the equations that are Using the information above, select the equations that are dimensionally correct.dimensionally correct.
F = maF = ma vv2 2 = 2ax= 2ax v = atv = at22
F/v = m/tF/v = m/t
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Dimensional AnalysisDimensional Analysis
AnswerAnswer
F = maF = ma
vv22 = 2ax = 2ax
F/v = m/tF/v = m/t
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QUESTIONQUESTION
The dimensions for force are the product of The dimensions for force are the product of mass and length divided by time squared. mass and length divided by time squared. Newton's second law states that force Newton's second law states that force equals the product of mass and acceleration. equals the product of mass and acceleration. What are the dimensions of acceleration?What are the dimensions of acceleration?
A)A) TT22
B)B) TT22/L/L
C)C) L/TL/T22
D)D) L/TL/T
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QUESTIONQUESTION
The dimensions for force are the product of The dimensions for force are the product of mass and length divided by time squared. mass and length divided by time squared. Newton's second law states that force Newton's second law states that force equals the product of mass and acceleration. equals the product of mass and acceleration. What are the dimensions of acceleration?What are the dimensions of acceleration?
A)A) TT22
B)B) TT22/L/L
C)C) L/TL/T22
D)D) L/TL/T
* Disclaimer: This powerpoint presentation is a compilation of various works.