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Precision Precision MeasurementMeasurementFoundations of EngineeringFoundations of Engineering
Precision Measurement Precision Measurement When measured quantities are When measured quantities are
reported, the lastreported, the lastsignificant digit in a measurement significant digit in a measurement
is somewhatis somewhatuncertain. ( Park, 1996)uncertain. ( Park, 1996) “…“…the last significant digit is a carefully considered estimatethe last significant digit is a carefully considered estimateby the experimenter and represents the limit of his or herby the experimenter and represents the limit of his or herability to measure, given the measuring instrument being ability to measure, given the measuring instrument being
usedusedand the conditions under which the measurement is made.and the conditions under which the measurement is made.This uncertainty carries over into the result calculated fromThis uncertainty carries over into the result calculated fromthe measurements. Thus the number of significant figures in athe measurements. Thus the number of significant figures in aquantity is the number of trustworthy figures in it, the lastquantity is the number of trustworthy figures in it, the lasttrustworthy figure being somewhat in doubt (but still trustworthy figure being somewhat in doubt (but still useful), because it is based upon an estimation.” ( Park, 1996) useful), because it is based upon an estimation.” ( Park, 1996)
Precision Measurement Precision Measurement
Therefore Precision Measurement Therefore Precision Measurement must take into consideration:must take into consideration: Significant DigitsSignificant Digits UnitsUnits Measuring Power & EnergyMeasuring Power & Energy
Precision Measurement Precision Measurement
How many digits are significant?How many digits are significant? Addition and Subtraction:Addition and Subtraction:
Any answer can be no more accurate as the LEAST accurate number that was used to calculate it
Therefore: 2.200 kg + 1.2 kg = 3.4 kg 2.25 kg + 1.2 kg = *3.5 kg
* - see rules for rounding.
Precision Measurement Precision Measurement In multiplication and division you must count the digits.In multiplication and division you must count the digits. The answer can have only have as many significant The answer can have only have as many significant
figures as the LEAST of the numbers used to get it. figures as the LEAST of the numbers used to get it. Non-zero digits are always significant.
523.7 has ____ significant figures Any zeros between two significant digits are
significant. 23.07 has ____ significant figures
A final zero or trailing zeros in the decimal portion ONLYare significant. 3.200 has ____ significant figures 200 has ____ significant figures 2.00 x 10^2 ____ significant figures
Precision Measurement Precision Measurement
Does 1000 ml mean exactly 1000? Does 1000 ml mean exactly 1000? Not necessarily.Not necessarily.
100, 100, 10, and 1 all have one 100, 100, 10, and 1 all have one significant digit.significant digit.
If the engineer wanted to express If the engineer wanted to express exactly 1000, he/she would have to exactly 1000, he/she would have to write 1.00 x 10^3.write 1.00 x 10^3.
Precision Measurement Precision Measurement RoundingRounding Example: 3.141592653589 (What number is this?)*Example: 3.141592653589 (What number is this?)* Look at the number to the immediate right of the place you are Look at the number to the immediate right of the place you are
rounding to:rounding to: If it is greater than 5 (i.e., 6, 7, 8, or 9), round the place of interest If it is greater than 5 (i.e., 6, 7, 8, or 9), round the place of interest
up.up. So π to 4 decimal places is __________So π to 4 decimal places is __________
If it is less than 5 (i.e., 0, 1, 2, 3, 4), leave the place of interest If it is less than 5 (i.e., 0, 1, 2, 3, 4), leave the place of interest unchanged.unchanged.
So π to 2 decimal places is __________So π to 2 decimal places is __________
If it is 5 (use the round-to-even rule): round up by one if there are If it is 5 (use the round-to-even rule): round up by one if there are any non-zero digits following the 5any non-zero digits following the 5
If there are only zeros following the 5, round up by one if the place If there are only zeros following the 5, round up by one if the place of interest is odd, or else leave it unchanged if it is even.of interest is odd, or else leave it unchanged if it is even.
So π to 3 decimal places is __________So π to 3 decimal places is __________ So π to 7 decimal places is __________ So π to 7 decimal places is __________
Precision MeasurementPrecision Measurement
Units of MeasureUnits of Measure Base Units SI and EES (English Eng. Base Units SI and EES (English Eng.
System)System)QuantityQuantity SI SI EESEESLengthLength metermeter foot foot MassMass kilogramkilogram lb.lb.TimeTime secondsecond secondsecondElectric currentElectric current ampereampereThermd tempThermd temp kelvinkelvin fahrenheitfahrenheitAmount of SubstanceAmount of Substance molemoleLuminous intensityLuminous intensity candelacandela
Precision MeasurementPrecision Measurement
Units of MeasureUnits of Measure Supplemental Units SI and EES Supplemental Units SI and EES
(English Eng. System)(English Eng. System)QuantityQuantity SI SI EESEES
Plane AnglePlane Angle radianradian
Solid AngleSolid Angle steradiansteradian
Precision MeasurementPrecision Measurement
Units of MeasureUnits of Measure Derived Units and Common Derived UnitsDerived Units and Common Derived Units Unit ConversionsUnit Conversions
Several should be committed to memory.Several should be committed to memory. Fahrenheit to CelsiusFahrenheit to Celsius Millimeters to inchesMillimeters to inches Kilograms to poundsKilograms to pounds Gallons to litersGallons to liters
Online Conversion SourcesOnline Conversion Sources www.onlineconversions.comwww.onlineconversions.com or or www.efunda.comwww.efunda.com
Precision Measurement Precision Measurement
Using the Engineering Solution Using the Engineering Solution Layout Excel Spreadsheet, convert Layout Excel Spreadsheet, convert the following paying attention to the following paying attention to significant digits.significant digits.
Assignment 1: Conversion Assignment 1: Conversion WorksheetWorksheet
Precision MeasurementPrecision Measurement
Measuring Power & Measuring Power & Energy VocabularyEnergy Vocabulary
PowerPower Mechanical ConverterMechanical Converter TorqueTorque EfficiencyEfficiency HorsepowerHorsepower BTUBTU CalorieCalorie ForceForce GravityGravity Metric SystemMetric System PressurePressure SpeedSpeed TachometerTachometer WeightWeight WorkWork
Precision MeasurementPrecision Measurement
Energy DefinedEnergy Defined Most energy converters such as a diesel or gasoline engine Most energy converters such as a diesel or gasoline engine
are designed to accomplish one purpose: convert energy are designed to accomplish one purpose: convert energy into useful work.into useful work.
Energy: the ability to do workEnergy: the ability to do work.. How does this take place in a gasoline engine?How does this take place in a gasoline engine? ForceForce is any push or pull on an object.is any push or pull on an object. Gravity is a force that pulls down on every object on earthGravity is a force that pulls down on every object on earth.. To lift the object we must exert force greater than the To lift the object we must exert force greater than the
weight…weight…therefore weight is considered to be a force equal therefore weight is considered to be a force equal to the pull of gravity on an objectto the pull of gravity on an object..
Precision MeasurementPrecision Measurement
Work Defined:Work Defined: Work is defined as the result of applying a force to move a Work is defined as the result of applying a force to move a
mass a certain distance.mass a certain distance. This force is created by the combustion of a source of fuel, This force is created by the combustion of a source of fuel,
such as gasoline.such as gasoline. Work is produced when the force moves a certain mass a Work is produced when the force moves a certain mass a
certain distance.certain distance. WORK = FORCE X DISTANCEWORK = FORCE X DISTANCE Problem 1:Problem 1:
FORCE
50 FEET
20 LBS.
20 LBS. X 50 FT.=
1000 FT-LB.
Precision MeasurementPrecision Measurement
Torque Defined:Torque Defined: Torque is the twisting force on a shaft.Torque is the twisting force on a shaft. Torque wrench produces a twisting force, measured in ft.-lb.Torque wrench produces a twisting force, measured in ft.-lb. Torque = Force (lbs.) x radius (ft.) Torque = Force (lbs.) x radius (ft.) Torque is also produced on the output shaft of engines because Torque is also produced on the output shaft of engines because
of the combustion of fuel/pushes pistons downward/causing of the combustion of fuel/pushes pistons downward/causing crankshaft to spin.crankshaft to spin.
This force (torque) causes other objects to rotate, turning This force (torque) causes other objects to rotate, turning transmissions and wheels, boat props, lawn mower blades, etc.transmissions and wheels, boat props, lawn mower blades, etc.
Problem 2:Problem 2: A lug nut on a car tire is very tight. When repairingA lug nut on a car tire is very tight. When repairing a a
flat tire, Jenny has a choice between a 12 inch and 18 flat tire, Jenny has a choice between a 12 inch and 18 inch wrench. Which wrench will produce more torque?inch wrench. Which wrench will produce more torque?
Precision MeasurementPrecision Measurement
Power DefinedPower Defined:: A measure of the work being done in a given period of time:A measure of the work being done in a given period of time: P (Power) = W (Work) / t (time) or P=(d * m)/tP (Power) = W (Work) / t (time) or P=(d * m)/t Power is the final output of an engine after it has converted Power is the final output of an engine after it has converted
the energy in the fuel into work.the energy in the fuel into work. A common term used to describe output power is A common term used to describe output power is
horsepower.horsepower. Based on the premise of the amount of work that a horse Based on the premise of the amount of work that a horse
can do in one minute.can do in one minute. One One horsepowerhorsepower is equal to the energy needed to lift is equal to the energy needed to lift
33,000 pounds 1 foot in 1 minute. This is the same energy 33,000 pounds 1 foot in 1 minute. This is the same energy needed to lift 550 lbs. one foot in one second.needed to lift 550 lbs. one foot in one second.
Precision MeasurementPrecision Measurement
Horsepower is a measure of the work being done by a Horsepower is a measure of the work being done by a mechanical converter, such as a diesel engine.mechanical converter, such as a diesel engine.
Horsepower is described in many ways as it relates to the Horsepower is described in many ways as it relates to the mechanical converters.mechanical converters.
When comparing engines, brake horsepower is used.When comparing engines, brake horsepower is used. When discussing efficiency, frictional and indicated When discussing efficiency, frictional and indicated
horsepower are used.horsepower are used. When analyzing gasoline mileage, road horsepower is used.When analyzing gasoline mileage, road horsepower is used. POWER:POWER: Energy per unit of time or work accomplished in a Energy per unit of time or work accomplished in a
given period of time.given period of time. Example…I climb stairs, weight x height determines work Example…I climb stairs, weight x height determines work
done. Same work regardless if you walk or run up the done. Same work regardless if you walk or run up the stairs…but more power is used to run up the stairs.stairs…but more power is used to run up the stairs.
Precision MeasurementPrecision Measurement
A A watt(W)watt(W) is a unit used to measure electrical power. is a unit used to measure electrical power. It is equal to one joule of electrical energy per second.It is equal to one joule of electrical energy per second. A toaster may use 800 watts of power. This means the toaster A toaster may use 800 watts of power. This means the toaster
needs 800 joules per second to make the heating element red-needs 800 joules per second to make the heating element red-hot.hot.
The heating of the element is the work that is accomplished.The heating of the element is the work that is accomplished. Relationship to Power?Relationship to Power? Pwr = W Pwr = W ÷ ÷ ΔΔtt Horsepower Horsepower
1 hp = 550 ft lb/s = 746 W1 hp = 550 ft lb/s = 746 W 1 Watt = 1J/s (Joule per second)1 Watt = 1J/s (Joule per second) 1 kW = 1000 W1 kW = 1000 W
Problem 3: How much power is required for you to run Problem 3: How much power is required for you to run up a flight of stairs 10.54 ft higher than where you start up a flight of stairs 10.54 ft higher than where you start in 2.2 seconds, if your mass was 160.2 lbs? Be sure to in 2.2 seconds, if your mass was 160.2 lbs? Be sure to apply the rule for significant digits and indicate your apply the rule for significant digits and indicate your answer in Watts.answer in Watts.
Precision MeasurementPrecision Measurement
PressurePressure Pressure is another measurement of force. Pressure is another measurement of force. Pressure is determined by the area over which a force is Pressure is determined by the area over which a force is
applied. applied. Pressure is force per a unit of areaPressure is force per a unit of area.. Snow shoes example.Snow shoes example. Therefore is area = length x width and we apply 100 pounds Therefore is area = length x width and we apply 100 pounds
per square inch…less pressure is applied on a greater area.per square inch…less pressure is applied on a greater area. A confined fluid under pressure exerts equal force on all A confined fluid under pressure exerts equal force on all
enclosing surfaces. enclosing surfaces. The air in an inflated balloon pushes with a small amount of The air in an inflated balloon pushes with a small amount of
pressure in all directions…however it is an even amount all pressure in all directions…however it is an even amount all over the interior surface of the chamber.over the interior surface of the chamber.
Precision MeasurementPrecision Measurement
We can determine the force produced by a certain amount We can determine the force produced by a certain amount of pressure.of pressure.
We must multiply the pressure (force per unit area) by the We must multiply the pressure (force per unit area) by the total area.total area.
Inside surface area = 100 sq. in., Pressure is 1/4 psi.Inside surface area = 100 sq. in., Pressure is 1/4 psi. Force = Pressure x AreaForce = Pressure x Area Force = 1/4 psi x 100 sq. in.Force = 1/4 psi x 100 sq. in. Force = 25 poundsForce = 25 pounds The difference between pressure and force is important.The difference between pressure and force is important. We must remember that pressure is a special measurement We must remember that pressure is a special measurement
of force.of force. It is force per unit of area. It is force per unit of area. However, the total amount of force depends on the total However, the total amount of force depends on the total
amount of area.amount of area. Problem 4: Show Mathematical proof why a sharp knife Problem 4: Show Mathematical proof why a sharp knife
cuts better than a dull knife.cuts better than a dull knife.
Precision MeasurementPrecision Measurement
Two pistons, different sizes: 1 square inch area and a large Two pistons, different sizes: 1 square inch area and a large one, 10 square inch area.one, 10 square inch area.
The pressure above each is 50 pounds per sq.l in.The pressure above each is 50 pounds per sq.l in. Each provides different amounts of force.Each provides different amounts of force. The large piston produces ten times the force of the smaller The large piston produces ten times the force of the smaller
cylinder. cylinder. But if the same amount of air is applied to each, the larger But if the same amount of air is applied to each, the larger
only moves 1/10 the distance of the smaller.only moves 1/10 the distance of the smaller.
Precision MeasurementPrecision Measurement
Heat:Heat: Heat energy is measured in British Thermal Units (BTU’s).Heat energy is measured in British Thermal Units (BTU’s). One One BTUBTU is equal to the amount of heat energy needed to is equal to the amount of heat energy needed to
raise the temperature of one pound (about 1 pint) of water 1 raise the temperature of one pound (about 1 pint) of water 1 degree F.degree F.
BTU is a measurement of energy…not power.BTU is a measurement of energy…not power. Power requires the element of time.Power requires the element of time. But we can measure BTU’s per hour.But we can measure BTU’s per hour. We can also convert heat into power with engines.We can also convert heat into power with engines. When this happens we lose most of the heat.When this happens we lose most of the heat. It is absorbed in air and metal of the engines.It is absorbed in air and metal of the engines. In a typical gasoline engine only 1/5th of the available heat In a typical gasoline engine only 1/5th of the available heat
energy is converted into power.energy is converted into power.
Precision MeasurementPrecision Measurement
Another common unit of measurement for heat is called a Another common unit of measurement for heat is called a calorie.calorie.
Small calorie: amount of heat needed to raise the Small calorie: amount of heat needed to raise the temperature of 1 cubic cm of water 1 degree Celsius.temperature of 1 cubic cm of water 1 degree Celsius.
252 calories in a BTU.252 calories in a BTU. Large calorie: measures the amount of heat energy Large calorie: measures the amount of heat energy
available to us in the food we eat.available to us in the food we eat.
Precision MeasurementPrecision Measurement
Converter Efficiency:Converter Efficiency: Several types of efficiency are used for mechanical Several types of efficiency are used for mechanical
converters.converters. Efficiency generally refers to how well a particular job can Efficiency generally refers to how well a particular job can
be done.be done. Efficiency is expressed in a ratio of input to output.Efficiency is expressed in a ratio of input to output.
Efficiency
INPUT En. Con. OUTPUT
Precision MeasurementPrecision Measurement
Efficiencies are expressed as percentages, which are Efficiencies are expressed as percentages, which are always less than 100%.always less than 100%.
The difference between the percent efficiency and 100% is The difference between the percent efficiency and 100% is due to the percent loss incurred during the process of due to the percent loss incurred during the process of converting power.converting power.
Efficiency is important because it shows how much energy Efficiency is important because it shows how much energy is being wasted.is being wasted.
Mechanical Efficiency: relationship between the theoretical Mechanical Efficiency: relationship between the theoretical (mat calculated) amount of work to move the motorcycle, (mat calculated) amount of work to move the motorcycle, and the actual amount of work to move it.and the actual amount of work to move it.
Mech. Efficiency=(actual work/theoretical work) x 100.Mech. Efficiency=(actual work/theoretical work) x 100. Power Efficiency=(output power/input power) x 100Power Efficiency=(output power/input power) x 100 Problem 5a. The total mass of an elevator is 1200kg. An Problem 5a. The total mass of an elevator is 1200kg. An
electric motor raises the elevator three floors (1.5m) at a electric motor raises the elevator three floors (1.5m) at a constant speed in 12 seconds. Problem5b. What is the constant speed in 12 seconds. Problem5b. What is the power outage of the motor?power outage of the motor?
Precision Measurement Precision Measurement BJ Furman SJSU MAEBJ Furman SJSU MAEBeckwith, T. G., Marangoni, R. D., Lienhard, J. H., MechanicalBeckwith, T. G., Marangoni, R. D., Lienhard, J. H., Mechanical
Measurements, Addison-Wesley, Reading, MA, 1995.Measurements, Addison-Wesley, Reading, MA, 1995.Histand, M. B., Alciatore, D. G., Introduction to Mechatronics Histand, M. B., Alciatore, D. G., Introduction to Mechatronics
andandMeasurement Systems 2Measurement Systems 2ndnd ed., WCB/McGraw-Hill, Boston, ed., WCB/McGraw-Hill, Boston, 2003.2003.
Park, J. L., Rules for Rounding Off [Online]. Available atPark, J. L., Rules for Rounding Off [Online]. Available athttp://dbhs.wvusd.k12.ca.us/webdocs/SigFigs/SigFigs.html, http://dbhs.wvusd.k12.ca.us/webdocs/SigFigs/SigFigs.html, 1996.1996.
NIST Guide to SI Units –Appendix B [Online]. Available atNIST Guide to SI Units –Appendix B [Online]. Available athttp://physics.nist.gov/Pubs/SP811/appenB.html#B.7http://physics.nist.gov/Pubs/SP811/appenB.html#B.7
““See, I have a rhyme assisting my little brain its tasks See, I have a rhyme assisting my little brain its tasks sometimesometimeresisting” (the number of letters in each word gives pi to resisting” (the number of letters in each word gives pi to 12 decimal places) 12 decimal places)