FUNDAMENTAL DIMENSIONS AND UNITS CHAPTER 6. UNITS Used to measure physical dimensions Appropriate divisions of physical dimensions to keep numbers manageable

FUNDAMENTAL DIMENSIONS AND UNITS

CHAPTER 6

UNITSUsed to measure physical dimensionsAppropriate divisions of physical dimensions

to keep numbers manageable19 years old instead of

612,000,000 seconds old

Common systems of unitsInternational System (SI) of Units

British Gravitational (BG) System of Units

U.S. Customary Units

Engineering Fundamentals, By Saeed Moaveni, Third Edition, Copyrighted 2007 6-3

Units – SIMost common system of units used in the

world

Examples of SI units are: kg, N, m, cm,

Approved by the General Conference on Weights and Measures (CGPM)

Series of prefixes & symbols of decimal multiples (adapted by CGPM, 1960)

British Gravitation (BG) System

KTRTCTFT5

9 32

5

9


Primary units arefoot (ft) for length (1 ft = 0.3048 m)second for time pound (lb) for force (1 lb = 4.448 N)Fahrenheit (oF) for temperature

Slug is unit of mass which is derived from Newton’s second law1 lb = (1 slug)(1 ft/s2)


U.S. Customary System of Units

Primary units areFoot (ft) for length (1 ft = 0.3048 m)second for time pound mass (lbm) for mass (1 lbm = 0.453592

kg, 1slug = 32.2 lbm)

Pound force (lbf) is defined as the weight of an object having a mass of 1 lbm at sea level and at a latitude of 45o, where acceleration due to gravity is 32.2 ft/s2 (1lbf = 4.448 N)


Fundamental Unit of Length

meter (m) – length of the path traveled by light in a vacuum during a time interval of 1/299,792,458 of a second


kilogram (kg) – a unit of mass; it is equal to the mass of the international prototype of the kilogram


second (s) – duration of 9,192,631,770 periods of the radiation corresponding to the transition between the 2 hyperfine levels of the ground state of cesium 133 atom


ampere (A) – constant current which, if maintained in 2 straight parallel conductors of infinite length, of negligible circular cross section, and placed 1 meter apart in a vacuum, would produce between these conductors a force equal to 2x10-7N/m length


kelvin (K) – unit of thermodynamic temperature, is the fraction 1/273.16 of thermodynamic temperature of the triple point of water


mole (mol) – the amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12


candela (cd) – in a given direction, of a source that emits monochromatic radiation of frequency 540x1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian


Unit ConversionIn engineering analysis and design, there may be

a need to convert from one system of units to another

When communicate with engineers outside of U.S.

Important to learn to convert information from one system of units to another correctly

Always show the appropriate units that go with your calculations

See front & back cover pages for conversion factors

SEPTEMBER 23, 1999Mars Climate Orbiter Believed To Be LostMars Climate Orbiter is believed to be lost due to a suspected navigation error.

CASE STUDY: THE IMPORTANCE OF UNIT CONVERSIONS

The engine burn began as planned five minutes before the spacecraft passed behind the planet as seen from Earth.

Flight controllers did not detect a signal when the spacecraft

was expected to come out from behind the planet.

"We had planned to approach the planet at an altitude of

about 150 kilometers (93 miles).

We thought we were doing that, but upon review of the

last six to eight hours of data leading up to arrival, we

saw indications that the actual approach altitude had

been much lower. It appears that the actual altitude

was about 60 kilometers (37 miles). We are still trying

to figure out why that happened," said Richard Cook,

project manager for the Mars Surveyor Operations

Project at NASA's Jet Propulsion Laboratory.

SEPTEMBER 30, 1999Likely Cause Of Orbiter Loss FoundThe peer review preliminary findings indicate that one team used English units (e.g., inches, feet and pounds) while the other used metric units for a key spacecraft operation.

Significant Digits:By accuracy of a measurement, we mean the number of digits, called significant digits, that it contains.

These are the units we are reasonably certain of having counted and of being able to rely on in measurement.

The greater the number of significant digits, of a measurement, the greater the accuracy of the measurement, and vice versa.


Significant Digits (Figures)Engineers make measurements and carry out

calculations

Engineers record the results of measurements and calculations using numbers.

Significant digits (figures) represent (convey) the extend to which recorded or computed data is dependable.

1) All nonzero digits are significant. 1432 has 4 significant

digits.

2) All zeros between significant digits are significant.

40050 m has 4 significant digits.

3) A zero in a whole-number measurement that is specially tagged, such as by a bar above it, is significant.

SIGNIFICANT DIGITS

40,000 ft has 2 significant digits.

Significant Digits (continued)3) All zeros to the right of a significant digit and

a decimal point are significant. 6.100 L has 4 significant digits.

4) The number of significant digits for the number 1500

is not clear. 1.5 x 103 has 2 significant digits. 1.50 x 103 has 3 significant digits.3) Zeros to the left in a decimal measurement

that is less than 1 are not significant. 0.00870 has 3 significant digits.


Significant Digits – How to Record a Measurement

Least count – one half of the smallest scale division

What should we record for this temperature measurement?

71 ± 1oF



What should we record for the length?

3.35 ± 0.05 in.


What should we record for this pressure?

7.5 ± 0.5 in.



Significant Digits175, 25.5, 1.85, and 0.00125 each has

three significant digits.

The number of significant digits for the number 1500 is not clear.

It could be 2, 3, or 4

If recorded as 1.5 x 103 or 15 x 102, then 2 significant digits

6-26

Significant Digits – Addition And Subtraction RulesWhen adding or subtracting numbers, the result of the calculation should be recorded with the last significant digit in the result determined by the position of the last column of digits common to all of the numbers being added or subtracted.

For example, 152.47 or 132. 853 + 3.9 - 5

156.37 127.853 (your calculator will display) 156.3 127 (however, the results should be recorded this way)

6-27

When multiplying or dividing numbers, the result of the calculation should be recorded with the least number of significant digits given by any of the numbers used in the calculation.

For example,

152.47 or 152.47 × 3.9 ÷ 3.9 594.633 39.0948717949 (your calculator will display)

5.9 x 102 39 (however, the result should be recorded this way)

Significant Digits – Multiplication and Division Rules


Significant Digits – Examples 276.34 + 12.782

289.12

2955 x 326

9.63 x 105


Rounding NumbersIn many engineering calculations, it may be sufficient to record the results of a calculation to a fewer number of significant digits than obtained from the rules we just explained

56.341 to 56.34 12852 to 1.285 x 104

UNIT CONVERSION:

A person who is 5 feet 9 inches tall and weighs 173 pound force (lbf ) is driving a car at a speed of 62 miles per hour over a distance of 25 miles. The outside temperature is 80℉ and the air has a density of .0735 pounds per cubic foot (lbm/ft3). Convert all of the values given in this example from U.S. Customary to SI units.

A) Height: in meters

15 (9 )

12

ftH ft in

in

0.3048

1

m

ft

1.7526m

Height: in centimeters (1.753 )H m

100

1

cm

m

=175.3cm

Weight in Newtons:

4.448(173 )

1ff

NW lb

lb

769.50N

Speed of car: 67

mileS

h5280 ft

mile

0.3048

1

m

ft

107826 m/h

107,826m

Or Sh

How do we convert to km/h?

1

1000

km

m

107.826

km

h

Distance traveled:

25D miles 5280

1

ft

mile

0.3048

1

m

ft

1

1000

km

m

40.233km

, :Density of air

3

0.4530.0735

1m

m

lb kg

ft lb

31

0.3048

ft

m

31.176 /kg m

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FUNDAMENTAL DIMENSIONS AND UNITS CHAPTER 6. UNITS Used to measure physical dimensions Appropriate divisions of physical dimensions to keep numbers manageable