International System of UnitsUnit Conversion

Gary AndersonEDTC 3123Spring 2010

Metric System & Unit Conversion

Real world problem!

John needs to change out two battery cells on critical equipment where he works. The battery manual says to torque the 8mm connection bolts to 20 N-m (Newton meters). He has a torque wrench that only measures in foot-lbs. At what value (ft-lbs) should he tighten the connector bolts?

Facts about the Metric System:

• Developed by the French chemist Lavoisier in the 18th century to promote the standardization of measurement units commonly used in scientific inquiry and experimentation.

• In 1960, an international conference was called to standardize the metric system. The International System of Units (SI) was the result!

• There are seven “fundamental” or “base” units: meter (distance), kilogram (mass), second (time), ampere (electrical current), Kelvin (temperature), mole (quantity), and candela (luminous intensity).

• There are other “derived” units that are built around the “base units”. An example of this is density which is mass/unit volume.

• An accurate and consistent system of measurement is the foundation of a healthy economy!

METERKILOGRAMSECONDAMPEREKELVINMOLECANDELA

Click for more details!

Lavoisier – developed the metric system of units to replace the disparate systems of measures with a unified, natural and universal system. Multiples of metric units are related by powers of ten and named by prefixes. The first fundamental or base units included:

• metre for length• gram for weight• litre for capacity.

:Hecto – one hundredKilo – one thousandMega – one million

Or

Deci – one tenthCenti – one hundredthMilli – one

thousandth

Consider the importance of units in your life. We use units everyday, usually without even realizing it! Imagine the following statements being made without their appropriate units!

• America’s tallest building, the Sears tower in Chicago is 110 ______ high!

• The Nile is the world’s longest river. It is 4180 ____________ long.

• The Amazon River in South America is 6296 ____________ long.

• The largest recorded “hailstone” landed in Aurora, Nebraska in 2003, and had a circumference of 47.6 _________.

“Derived Units”Units that are build upon the use of one or more of the

fundamental units! Here are only a few! Click on any of these for additional detail.

Pressure

Density

BTU

Foot-pounds

Newton-meter

Bar

Horsepower

Hertz

watts

VelocityKilowatt hour

ATM

How do we convert from one type of units to another?

Remember John’s Problem with the torque wrench?

John needs to change out two battery cells on critical equipment where he works. The battery manual says to torque the 8mm connection bolts to 20 N-m (Newton meters). He has a torque wrench that only measures in foot-lbs. At what value (ft-lbs) should he tighten the connector bolts?

We need to use a conversion factor and some simple math!

• Use an equivalent value to convert units! • While this chart doesn’t show the equalities for the derived units of ft-lbs and N-m, it will be useful for many other conversions!

• Here is the conversion factor for ft-lbs and Newton meters. Both are units for “force”.

1 ft-lb = 1.3558 N-m- or -

1 N-m = .73756 ft-lbs

John’s Torque setting Problem:

If we use the equivalent factors for these “derived” units, we can easily convert a value of N-m to ft-lbs or ft-lbs to N-m!

Using: 1 ft-lb = 1.3558 N-m or 1 N-m = .73756 ft-lbs

Set the problem up like this, using the factor-label method which will factor-out unwanted units and leave desired units.

Unknown: How many ft-lbs?Known: 20 Nm is needed!Equiv units: 1 ft-lb = 1.3558 Nm or 1 Nm = .73756 ft-lbs

John’s Torque setting Problem:

• Doesn’t really matter which equivalent factor is used – as long as it has the starting units and the desired units!

• The Nm units divide out and you are left with whatever units are on the dividend or top side of our equation! In this case “ft-lbs”!

• Either conversion factor would have worked!

• Remember to always have your desired units in the dividend portion of the equation – that is what will remain after solving!

Here’s the equation steps showing how the different units factor out!

Using: 1 ft# = 1.3558 Nm

- Or –

Using: 1 Nm = .73756 ft#

Here are two examples showing multiple steps used in converting a value from one type of units to the type of units we need!

1. How many millimeters (mm) is 2 inches?

2. An artificial heart is capable of pumping 17 million pints of blood before failure. If a average heart rate is 72 beats/min and average stroke volume is 70 milliliter (ml) then how many years could we expect this artificial heart to last?

⁼

or

Multiply the factors, while the un-desired units cancel out!

http://physics.nist.gov/cuu/units

http://physics.nist.gov/Document/sp811.pdf

http://eu.wikipedia.org

www.animoto.com

This ends our lesson on SI units and the Unit-Factor method of conversion. Below are additional resources for further exploration into this important topic!