FUNDAMENTAL DIMENSIONS AND UNITS CHAPTER 6

UNITS Used to measure physical dimensions Appropriate divisions of physical dimensions to keep numbers manageable 19 years old instead of 612,000,000 seconds old Common systems of units International System (SI) of Units British Gravitational (BG) System of Units U.S. Customary Units

Engineering Fundamentals, By Saeed Moaveni, Third Edition, Copyrighted Units – SI Most 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 Engineering Fundamentals, By Saeed Moaveni, Third Edition, Copyrighted Primary units are foot (ft) for length (1 ft = m) second for time pound (lb) for force (1 lb = N) Fahrenheit ( o F) for temperature Slug is unit of mass which is derived from Newton’s second law 1 lb = (1 slug)(1 ft/s 2 )

Engineering Fundamentals, By Saeed Moaveni, Third Edition, Copyrighted U.S. Customary System of Units Primary units are Foot (ft) for length (1 ft = m) second for time pound mass (lb m ) for mass (1 lb m = kg, 1slug = 32.2 lb m ) Pound force (lb f ) is defined as the weight of an object having a mass of 1 lb m at sea level and at a latitude of 45 o, where acceleration due to gravity is 32.2 ft/s 2 (1lb f = N)

Engineering Fundamentals, By Saeed Moaveni, Third Edition, Copyrighted 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

Engineering Fundamentals, By Saeed Moaveni, Third Edition, Copyrighted kilogram (kg) – a unit of mass; it is equal to the mass of the international prototype of the kilogram Fundamental Unit of Mass

Engineering Fundamentals, By Saeed Moaveni, Third Edition, Copyrighted Fundamental Unit of Time 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

Engineering Fundamentals, By Saeed Moaveni, Third Edition, Copyrighted 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 -7 N/m length Fundamental Unit of Electric Current

Engineering Fundamentals, By Saeed Moaveni, Third Edition, Copyrighted kelvin (K) – unit of thermodynamic temperature, is the fraction 1/ of thermodynamic temperature of the triple point of water Fundamental Unit of Temperature

Engineering Fundamentals, By Saeed Moaveni, Third Edition, Copyrighted mole (mol) – the amount of substance of a system that contains as many elementary entities as there are atoms in kilogram of carbon 12 Fundamental Unit of Amount of Substance

Engineering Fundamentals, By Saeed Moaveni, Third Edition, Copyrighted Fundamental Unit of Luminous Intensity candela (cd) – in a given direction, of a source that emits monochromatic radiation of frequency 540x10 12 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian

Engineering Fundamentals, By Saeed Moaveni, Third Edition, Copyrighted Unit Conversion In 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, 1999 Mars Climate Orbiter Believed To Be Lost Mars 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, 1999 Likely Cause Of Orbiter Loss Found The 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.

Engineering Fundamentals, By Saeed Moaveni, Third Edition, Copyrighted 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 has 4 significant digits. 2) All zeros between significant digits are significant 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

Significant Digits (continued) 3) All zeros to the right of a significant digit and a decimal point are significant L has 4 significant digits. 4) The number of significant digits for the number 1500 is not clear. 1.5 x 10 3 has 2 significant digits x 10 3 has 3 significant digits. 3) Zeros to the left in a decimal measurement that is less than 1 are not significant has 3 significant digits.

Engineering Fundamentals, By Saeed Moaveni, Third Edition, Copyrighted 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 ± 1 o F

Engineering Fundamentals, By Saeed Moaveni, Third Edition, Copyrighted Significant Digits – How to Record a Measurement What should we record for the length? 3.35 ± 0.05 in.

Engineering Fundamentals, By Saeed Moaveni, Third Edition, Copyrighted What should we record for this pressure? 7.5 ± 0.5 in. Significant Digits – How to Record a Measurement

Engineering Fundamentals, By Saeed Moaveni, Third Edition, Copyrighted Significant Digits 175, 25.5, 1.85, and 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 10 3 or 15 x 10 2, then 2 significant digits

6-26 Significant Digits – Addition And Subtraction Rules When 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, or ( your calculator will display) ( 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, or × 3.9 ÷ ( your calculator will display) 5.9 x ( however, the result should be recorded this way) Significant Digits – Multiplication and Division Rules

Engineering Fundamentals, By Saeed Moaveni, Third Edition, Copyrighted Significant Digits – Examples x x 10 5

Engineering Fundamentals, By Saeed Moaveni, Third Edition, Copyrighted Rounding Numbers In 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 to to x 10 4

UNIT CONVERSION: A person who is 5 feet 9 inches tall and weighs 173 pound force (lb f ) 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 (lb m /ft 3 ). Convert all of the values given in this example from U.S. Customary to SI units. A)Height: in meters m Height: in centimeters =175.3cm

Weight in Newtons : Speed of car:m/h How do we convert to km/h?

Distance traveled: