Physics Unit Measurements and Quantitative Analysis Review

A set of 100 question-and-answer flashcards based on high school physics lessons on measurement, unit conversions, thermal expansion, data organization, scaled models, scientific notation, and CER framework.

What is thermal expansion in concrete?

The tendency of concrete to increase in size (expand) when its temperature rises and decrease in size (contract) when its temperature falls.

How does thermal expansion happen in concrete at the molecular level when heated?

Molecules within the concrete move faster and spread farther apart, forcing the material to expand and take up more physical space.

What is the typical coefficient of thermal expansion for concrete?

About $5\text{ to }10 \times 10^{-6}\text{/}^\circ\text{C}$.

How much does $1\,\text{meter}$ of concrete expand for every $1^\circ\text{C}$ ($1.8^\circ\text{F}$) increase in temperature?

About $0.005$ to $0.010\,\text{mm}$.

What percentage change in volume due to thermal conditions can concrete withstand before cracking?

$$\pm 5\%$$

For a square concrete slab measuring $0.52\,\text{m}$ on all sides at its coldest temperature, what is its maximum length at its hottest temperature before cracking?

Approximately $0.533\,\text{meters}$ (or $0.5328\,\text{m}$).

By what factor does the side length of a square slab increase when its volume increases by $5\%$ with constant thickness?

$$\sqrt{1.05} \approx 1.0247$$

In the Park Avenue skyscraper case study, what caused drying shrinkage across the lower columns?

Hurried construction schedules and a compromised concrete mix that was heavy on water but light on aggregate.

What design failure caused the luxury skyscraper on Park Avenue to crush its own skin and crack?

The structural facade was poured as a continuous rigid shell lacking necessary allowance for thermal expansion during seasonal temperature swings from $0^\circ\text{F}$ to $100^\circ\text{F}$ ($-18^\circ\text{C}$ to $38^\circ\text{C}$).

What is the formula to convert temperature from Fahrenheit ($F$) to Celsius ($C$)?

$$C = (F - 32) \times \frac{5}{9}$$

Convert an average temperature of $56^\circ\text{F}$ to Celsius, rounded to the nearest tenth.

$$13.3^\circ\text{C}$$

Convert a temperature drop of $14^\circ\text{F}$ to Celsius.

$$-10^\circ\text{C}$$

What are key structural design features used to accommodate thermal movement in building facades?

Expansion joints, slip/sliding connections, flexible sealants with backer rods, isolated supports, decoupled layers, and compatible materials.

What catastrophic event occurred to the Mars Climate Orbiter in September 1999?

The $\$125\,\text{million}$ spacecraft plunged to within $57\,\text{km}$ of Mars' surface instead of its safe $140\,\text{km}$ altitude and was destroyed by atmospheric friction and pressure.

What unit conversion mistake destroyed the Mars Climate Orbiter?

Lockheed Martin calculated thruster performance data in Imperial units (pound-force seconds), whereas NASA navigation expected SI metric units (Newton-seconds).

By what factor was thruster force miscalculated in the Mars Climate Orbiter mission because $1\,\text{pound of force} \approx 4.45\,\text{Newtons}$?

A factor of more than four.

What was the safe orbital height planned for the Mars Climate Orbiter in kilometers and in meters?

$350\,\text{km}$, which equals $350{,}000\,\text{meters}$.

Convert a safe orbital height of $350\,\text{km}$ to miles using dimensional analysis.

Approximately $217.67\,\text{miles}$ (or $218\,\text{miles}$ using 3 significant figures).

What conversion error led to Air Canada Flight 143 (the Gimli Glider) running out of fuel at $41{,}000\,\text{feet}$ in 1983?

The ground crew used fuel density in pounds per liter ($1.77\,\text{lb/L}$) instead of kilograms per liter ($0.80\,\text{kg/L}$) when calculating required fuel weight for a Boeing 767.

Who was the captain who successfully glided the powerless Boeing 767 to safety in Gimli, Manitoba?

Captain Robert Pearson.

Why is a raw number without a unit considered meaningless in physics and engineering?

A unit provides physical meaning, context, and scale; without it, measurements cannot be accurately communicated, compared, or calculated.

What is the formula for initial velocity $v_i$ when isolated from $v_f^2 = v_i^2 + 2ad$?

$$v_i = \pm \sqrt{v_f^2 - 2ad}$$

How do you isolate acceleration $a$ in Newton's second law equation $F = ma$?

$$a = \frac{F}{m}$$

How do you isolate distance $d$ in the average speed formula $v = \frac{d}{t}$?

$$d = vt$$

What is the golden rule when manipulating algebraic equations?

Whatever you do to one side of an equation, do the exact same thing to the other side to keep it balanced.

What are the four steps of the dimensional analysis method?

1. Write the given value with units; 2. Choose conversion factor(s) as fractions; 3. Multiply and cancel units diagonally; 4. Compute and write answer with correct units.

How many feet are in one mile, and how many yards are in one mile?

$1\,\text{mile} = 5{,}280\,\text{feet} = 1{,}760\,\text{yards}$.

Which distance is longer, 1 mile or 1 kilometer?

A mile (since $1\,\text{mile} \approx 1.609\,\text{km}$ and $1\,\text{km} \approx 0.621\,\text{miles}$).

What is proportional analysis?

A method used to solve problems when two quantities change together at a constant ratio ($y = kx$).

What does the constant of proportionality $k$ represent on a graph of two proportional quantities?

The slope of the straight line passing through the origin $(0,0)$, where $k = \frac{y}{x}$.

Using proportional analysis, convert $3{,}000\,\text{feet}$ to miles ($1\,\text{mile} = 5{,}280\,\text{feet}$).

$$0.568\,\text{miles}$$

Using proportional analysis, convert $7.2\,\text{atm}$ to kilopascals ($101.3\,\text{kPa} = 1\,\text{atm}$).

$$729.4\,\text{kPa}$$

Using proportional analysis, convert $1.6 \times 10^{-17}\,\text{C}$ to electronvolts ($1\,\text{eV} = 1.60 \times 10^{-19}\,\text{C}$).

$$100\,\text{eV}$$

Using dimensional analysis, convert $5.5\,\text{miles}$ to feet ($1\,\text{mile} = 5{,}280\,\text{feet}$).

$$29{,}040\,\text{feet}$$

Using dimensional analysis, convert $14.3\,\text{kPa}$ to atmospheres ($101.3\,\text{kPa} = 1\,\text{atm}$).

$$0.141\,\text{atm}$$

Using dimensional analysis, convert $1.6 \times 10^{21}\,\text{eV}$ to coulombs ($1\,\text{eV} = 1.60 \times 10^{-19}\,\text{C}$).

$$256\,\text{C}$$

Convert $500\,\text{grams}$ to kilograms ($\text{kg}$).

$$0.500\,\text{kg}$$

Convert $500\,\text{grams}$ to milligrams ($\text{mg}$).

$500{,}000\,\text{mg}$ (or $5.00 \times 10^5\,\text{mg}$)

Convert $67\,\text{MW}$ (megawatts) to watts ($\text{W}$).

$6.7 \times 10^7\,\text{W}$ (or $67 \times 10^6\,\text{W}$)

How did Eratosthenes calculate the circumference of Earth around 240 BC?

He measured the Sun's shadow angle at Alexandria ($7.2^\circ$) while the Sun was directly overhead at Syene during summer solstice, then used the $5{,}000\,\text{stadia}$ distance to solve a proportion for $360^\circ$.

What proportion did Eratosthenes set up to find Earth's circumference $C$?

$$\frac{7.2^\circ}{360^\circ} = \frac{5{,}000\,\text{stadia}}{C}$$

What was Eratosthenes' estimate of Earth's circumference in stadia and in kilometers?

$\approx 250{,}000\,\text{stadia}$, which equals $\approx 39{,}375\,\text{kilometers}$ ($1\,\text{stadium} \approx 157.5\,\text{m}$).

What is the trigonometric ratio for sine (SOH)?

$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$grid

What is the trigonometric ratio for cosine (CAH)?

$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$grid

What is the trigonometric ratio for tangent (TOA)?

$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$grid

Given vector components $A_x = 5.4\,\text{meters}$ and $A_y = 3.7\,\text{meters}$, find angle $\theta$.

$\theta \approx 34.4^\circ$ (since $\tan(\theta) = \frac{3.7}{5.4} \approx 0.6852$)

Given vector components $A_x = 5.4\,\text{meters}$ and $A_y = 3.7\,\text{meters}$, find length $A$.

$A \approx 6.55\,\text{meters}$ (using $A = \sqrt{5.4^2 + 3.7^2}$)

What mapping technique was used in the 1700s by the Cassini family to map France?

Triangulation, measuring baseline distances and angles in a network of connected triangles using trigonometry.

On a distance vs. time graph, what does a horizontal line with a slope of zero represent?

The object is stationary/at rest (it is not moving).

On a distance (km) vs. time (hours) graph, what are the units of the line's slope?

Kilometers per hour ($\text{km/h}$).

If a line on a distance vs. time graph passes through $(0,0)$ and $(10,10)$, what is its slope?

$$1\,\text{km/h}$$

In the exam scores frequency table for 34 physics students, which score interval had the highest frequency?

The $80\text{--}89$ range, with 11 students.

How many total students were included in the physics exam scores dataset?

34 students.

In Sarah's bike ride experiment, during what time interval was she at rest?

From $40\,\text{seconds}$ to $60\,\text{seconds}$ (position stayed at $160\,\text{m}$).

What was Sarah's total displacement at the end of her 90-second ride?

$$430\,\text{meters}$$

On a position vs. time graph, what does a straight diagonal line indicate?

The object is moving at a constant speed.

How did Sarah's speed during her final sprint ($60\text{--}90\,\text{s}$) compare to her initial pace ($0\text{--}40\,\text{s}$)?

The final sprint was faster ($270\,\text{m}$ in $30\,\text{s}$) and had a steeper slope than the initial pace ($160\,\text{m}$ in $40\,\text{s}$).

What power of ten (characteristic length in meters) represents the diameter of an atom?

$$10^{-10}\,\text{m}$$

What power of ten (characteristic length in meters) represents the size of a bacterium (E. coli)?

$$10^{-6}\,\text{m}$$

What power of ten (characteristic length in meters) represents the width of a human hair?

$$10^{-5}\,\text{m}$$

What power of ten (characteristic length in meters) represents the height of Mount Everest?

$$10^4\,\text{m}$$

What power of ten (characteristic length in meters) represents the diameter of Earth?

$$10^6\,\text{m}$$

What power of ten (characteristic length in meters) represents the distance from Earth to the Sun?

$$10^{11}\,\text{m}$$

What power of ten (characteristic length in meters) represents the diameter of the Milky Way?

$$10^{21}\,\text{m}$$

Convert a lab track length of $2.5\,\text{meters}$ into centimeters ($\text{cm}$).

$$250\,\text{cm}$$

Convert a physics textbook mass of $1{,}450\,\text{grams}$ to kilograms ($\text{kg}$).

$$1.45\,\text{kg}$$

Convert a current pulse time of $0.0085\,\text{seconds}$ to milliseconds ($\text{ms}$).

$$8.5\,\text{ms}$$

Express a radio frequency of $4.2 \times 10^6\,\text{Hertz}$ in Mega Hertz ($\text{MHz}$).

$$4.2\,\text{MHz}$$

Convert a processor wire measurement of $450\,\mu\text{m}$ (micrometers) into millimeters ($\text{mm}$).

$$0.45\,\text{mm}$$

Convert an optical fiber distance of $0.075\,\text{kilometers}$ into centimeters ($\text{cm}$).

$$7{,}500\,\text{cm}$$

Convert a powder sample measurement of $320\,\text{milligrams}$ into kilograms ($\text{kg}$).

$3.2 \times 10^{-4}\,\text{kg}$ (or $0.00032\,\text{kg}$)

If sound travels through air at $343\,\text{m/s}$, how many kilometers does it travel in 1 second?

$$0.343\,\text{km}$$

Convert green pointer light wavelength of $0.000000532\,\text{meters}$ into micrometers ($\mu\text{m}$).

$$0.532\,\mu\text{m}$$

Convert a file backup size of $8{,}300\,\text{Megabytes}$ ($\text{MB}$) into Gigabytes ($\text{GB}$).

$$8.3\,\text{GB}$$

What is a scaled model?

A smaller (or larger) representation of a real object that keeps the exact same proportions as the original using a scale factor.

If a person's height is $1.6\,\text{meters}$ ($160\,\text{cm}$) and their model is $10\,\text{cm}$ tall, what is the scale ratio?

$$1:16$$

In a Play-Doh scale model with scale $1:16$, if actual leg length is $80\,\text{cm}$, what is the model leg length?

$$5.0\,\text{cm}$$

What three common forms are used to express map scales?

1. Graphic Scale (scale bar); 2. Verbal Scale; 3. Representative Fraction (RF ratio).

What does a Representative Fraction (RF) map scale of $1:50{,}000$ represent?

1 unit of length on the map equals $50{,}000$ of those same units in the real world.

If a map scale is $1\,\text{cm} = 2\,\text{km}$ and two towns are $4.5\,\text{cm}$ apart on the map, what is the actual distance?

$$9\,\text{km}$$

If a map scale is $1:100{,}000$ and a river measures $3.2\,\text{cm}$ on the map, what is its actual length in kilometers?

$3.2\,\text{km}$ (since $320{,}000\,\text{cm} = 3.2\,\text{km}$)

Using a verbal scale factor of $1\,\text{cm}\text{ on paper} = 2\,\text{meters}\text{ in real life}$, what real distance corresponds to $5.5\,\text{cm}$ on paper?

$$11\,\text{meters}$$

For a classroom measuring $24\,\text{ft}$ long, $15\,\text{ft}$ wide, and $10\,\text{ft}$ high, what is the gross surface area of the four walls combined?

$780.0\,\text{sq ft}$ (or $780.0\,\text{ft}^2$)

If four classroom walls have a gross area of $780.0\,\text{sq ft}$ and contain one door ($20\,\text{sq ft}$) and two windows ($15\,\text{sq ft}$ each), what is the net paintable area?

$$730.0\,\text{sq ft}$$

If 1 gallon of paint covers $350\,\text{sq ft}$, how many whole gallons are needed to apply two coats of paint to a net area of $730.0\,\text{sq ft}$?

$5\,\text{gallons}$ (total coverage $1{,}460\,\text{sq ft}$; $1460/350 = 4.17$, which rounds up to 5 gallons)

What percentage of the total four-wall surface area ($780.0\,\text{sq ft}$) is made up of unpainted doors and windows ($50\,\text{sq ft}$)?

$$6.4\%$$

What is the standard format for writing a number in scientific notation?

$a \times 10^n$ where $1 \le a < 10$ and $n$ is an integer.

Convert $452{,}000$ into scientific notation.

$$4.52 \times 10^5$$

Convert $0.00073$ into scientific notation.

$$7.3 \times 10^{-4}$$

Convert $560{,}000{,}000$ into scientific notation.

$$5.6 \times 10^8$$

Convert $0.000032$ into scientific notation.

$$3.2 \times 10^{-5}$$

Convert $7.5 \times 10^4$ from scientific notation to standard notation.

$$75{,}000$$

Convert $1.9 \times 10^{-5}$ from scientific notation to standard notation.

$$0.000019$$

What rule must be followed before adding or subtracting two numbers written in scientific notation?

The exponents (powers of 10) must be made the same before adding or subtracting the coefficients.

Calculate $(3.2 \times 10^5) + (5.6 \times 10^5)$ in scientific notation.

$$8.8 \times 10^5$$

Calculate $(9.1 \times 10^6) - (3.7 \times 10^6)$ in scientific notation.

$$5.4 \times 10^6$$

What rule is used when multiplying two numbers in scientific notation: $(a \times 10^m)(b \times 10^n)$?

Multiply the coefficients ($a \times b$) and add the exponents ($m + n$).

Calculate $(3.0 \times 10^4) \times (2.5 \times 10^3)$ in scientific notation.

$$7.5 \times 10^7$$

What rule is used when dividing two numbers in scientific notation: $(a \times 10^m) \div (b \times 10^n)$?

Divide the coefficients ($a \div b$) and subtract the exponents ($m - n$).

What are the three components of the CER framework used in scientific arguments?

Claim (concise answer to hypothesis), Evidence (verifiable objective data/proof), and Reasoning (scientific logic tying evidence to claim).