MATH PROBLEMSMATH PROBLEMSTOPIC ONETOPIC ONE

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

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

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

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

..

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

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

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

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

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

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

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.

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%

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

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%

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%

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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?

ANSWERANSWER

* ANSWER:* ANSWER:

100,000 tablets100,000 tablets

€

50.0kg( )1000g

1kg

⎛

⎝ ⎜

⎞

⎠ ⎟1000mg

1g

⎛

⎝ ⎜

⎞

⎠ ⎟

1tablet

500mgdrug

⎛

⎝ ⎜

⎞

⎠ ⎟=100,000tablets

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Dimensional AnalysisDimensional Analysis

AnswerAnswer

F = maF = ma

vv22 = 2ax = 2ax

F/v = m/tF/v = m/t

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

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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