Unit Conversions & Dimensional Analysis

•What are units?•Why are they important?•Famous Conversion Errors•Dangers of not using units?•An Assignment

WARNING: Avoid Dimensional Analysis if

1) You enjoy making mistakes.2) You have a phobia of correct answers3) You enjoy solving problems in a convoluted manner.4) You take pleasure in “re-inventing the wheel.”5) You are a bad human being.

Metric Mania

• How many feet long is the room?

• Who tells a ruler how long to be?

• The Royal Foot vs Standard Foot

• We need a standardized system.

What Ruler Measures Rulers?

1ft = 12in

1ft = 12in

m-k-s systemA Meter is defined by the speed of light. A meter is defined as the length light will travel in 1/299792458 of a second.

A kilogram measures mass and it is equal to an international prototype. Meaning there is an object in a museum that was arbitrarily chosen to have a mass of 1kg. All other masses (including pounds, grams, etc.) and weight are based upon this object.

A second is defined as the duration of 9,192,631,770 periods of the radiation of a cesium atom between two hyperfine levels of the ground state cesium-133 atom.

Img via BIPM

7 BASE SI UnitsUnit Name and

Symbol Dimension Symbol What does it measure?

Meter (m) L Length

Kilogram (kg) M Mass

Second (s) T Time

Ampere (A) I Electric Current

Kelvin (K) Θ Temperature

Mole (mol) N Amount of substance

Candela (cd) J Luminous Intensity

Other units are DERIVED units

Some Units Get Special NamesScientists are Lazy!

• A NEWTON is the force required to accelerate a one kilogram object at a rate of one meter per second squared.

Instead of writing (kg)(m)/(s2) physicists just use Newton (N) instead.

• Thus 1N = 1(kg)(m)/(s2)

Pressure = Force/Area

• Force = (kg)(m)/(s2) • Area = m2

• Units for pressure

= 1 Pascal=

Units on One side of an Equation must equal the units on the other in order to

be dimensionally correct!

• This formula is saying a measure of length divided by some measure of time is equal to half of a mass squared. Is this valid?

• Speed in miles/hour = a distance (miles) divided by a time (hours). This is valid.

What are units? Why are they important?

• Units give us some idea of the magnitude of the thing we are describing.

Weight = 160

SI vs English UnitsUnit Name and

Symbol Murica What does it measure?

Meter| Kilometer Feet | Miles Length

Gram | Kilogram Ounce | Pound Mass

Second Seconds Time

Kelvin or Celsius Fahrenheit Temperature

Converting Units is ImportantCountries in Red have not adopted the SI system of measurement.

Collaboration

Major Conversion Errors

• NASA Mars Climate Orbiter• Gimli Glider -- 747• Space Mountain in Tokyo• Escaping 250kg Tortoise• Korean Air-MD Crash• Expensive Rice• Medical Overdose Errors

Mars Climate Orbiter: Pounds vs Newtons

Gimli Glider: fuel in lbs vs kgs

Rollercoaster Derailment: Metric Conversion

250lb Tortoise …..err 250kg Tortoise (=550lbs)!

Wild Rice: $0.39 per pound or kilogram???

Medication Overdose Errors!!!

• The FDA has estimated that medication errors cause a death a day and injure over a million people a year.

• These are preventable medical injuries.

• Unit conversion errors are a big part of this.

What happens when we don’t use units?

Medication: A typical adult prescription of the painkiller acetaminophen with codeinein it is 500 _______?

(a) tablets (b) grams (c) milligrams (d) ounces (e) milliliters

Consequences of Being Incorrect: symptoms of overdose may include cold and clammy skin, extreme sleepiness, progression to stupor or coma, general bodily discomfort, heart attack, kidney failure, liver failure, low blood pressure, muscle weakness, nausea, slow heartbeat, sweating, and vomiting.

What happens when we don’t use units?

Speed Limit: The speed limit in a school zone in Canada is 30 _______?

(a) miles/hour, (b) kilometers/hour, (c) feet/second, (d) meters/second , (e) yards/second

Consequences of Being Incorrect: speeding in a school zone may result in an accident, loss of life or a significant fine.

What happens when we don’t use units?

Bicycle Tire Pressure: The recommended air pressure in many mountain bike tires is 60 _______?

(a) Pascals (b) kilopascals (c) pounds per square inch (d) torr (e) millimeters of mercury

Consequences of Being Incorrect: underinflated tires may puncture more easily, wear out faster, are more difficult to pedal, and don’t stop as efficiently. Overinflated tires may blow out. Improperly inflated tires increase the chances of a serious injury or loss of life.

What happens when we don’t use units?

Dietetics: Many physicians recommend that pregnant women take no more than 10,000_______ of vitamin A per day?

(a) grams (b) milligrams (c) ounces (d) international units (e) microliters

Consequences of Being Incorrect: Excess vitamin A may give rise to birth defects, dry skin, scaly skin, headaches, fatigue, painful bones and loss of appetite.

What happens when we don’t use units?

Food Storage: Food scientists recommend that produce companies store apples, cherries, apricots, and most berries at 2 _______?

(a) Degrees Fahrenheit (b) Kelvin (c) degrees Celsius (d) degrees Rankine (e) degrees Reaumur

Consequences of Being Incorrect: Storing these fruits at too high a temperature will result in ethylene production and early ripening. Storing them at too low a temperature will damage the integrity of the fruit.

Resources and Thanks

• Sourcebook for Teaching Science by Norman Herr

• Metric Mixups by Colorado State University USMA

• Google Images

Your Assignment

CONCEPT CHECK: Why is it essential that all measurements be accompanied by units?

1. Individuals who travel to regions of the world with poor sanitation are warned to filter water before drinking it to remove deadly water-born pathogens that cause diseases such as cholera or typhoid. If you were traveling in a region known to have a polluted water supply, would you drink water that your host said said had been heated to 100 degrees for five minutes? Explain.

2. We saw five examples of what happens when we don’t use units, now its your turn to create a scenario. Develop a hypothetical problem that may arise when units are omitted in a field such as sports-casting, international trade, or an area of your choice. Include a “consequences of being incorrect” section.