Precision Measurement Foundations of Engineering

Precision Measurement When measured quantities are reported, the last significant digit in a measurement is somewhat uncertain. ( Park, 1996) “…the last significant digit is a carefully considered estimate by the experimenter and represents the limit of his or her ability to measure, given the measuring instrument being used and the conditions under which the measurement is made. This uncertainty carries over into the result calculated from the measurements. Thus the number of significant figures in a quantity is the number of trustworthy figures in it, the last trustworthy figure being somewhat in doubt (but still useful), because it is based upon an estimation.” ( Park, 1996)

Precision Measurement Therefore Precision Measurement must take into consideration: Therefore Precision Measurement must take into consideration: Significant Digits Significant Digits Units Units Measuring Power & Energy Measuring Power & Energy

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: kg kg = 3.4 kg 2.25 kg kg = *3.5 kg * - see rules for rounding.

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 figures as the LEAST of the numbers used to get it. The answer can have only have as many significant figures as the LEAST of the numbers used to get it. Non-zero digits are always significant has ____ significant figures Any zeros between two significant digits are significant has ____ significant figures A final zero or trailing zeros in the decimal portion ONLY are significant has ____ significant figures 200 has ____ significant figures 2.00 x 10^2 ____ significant figures

Precision Measurement Does 1000 ml mean exactly 1000? Not necessarily. Does 1000 ml mean exactly 1000? Not necessarily. 100, 100, 10, and 1 all have one significant digit. 100, 100, 10, and 1 all have one significant digit. If the engineer wanted to express exactly 1000, he/she would have to write 1.00 x 10^3. If the engineer wanted to express exactly 1000, he/she would have to write 1.00 x 10^3.

Precision Measurement Rounding Rounding Example: (What number is this?)* Example: (What number is this?)* Look at the number to the immediate right of the place you are rounding to: Look at the number to the immediate right of the place you are rounding to: If it is greater than 5 (i.e., 6, 7, 8, or 9), round the place of interest up. If it is greater than 5 (i.e., 6, 7, 8, or 9), round the place of interest 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 unchanged. If it is less than 5 (i.e., 0, 1, 2, 3, 4), leave the place of interest 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 any non- zero digits following the 5 If it is 5 (use the round-to-even rule): round up by one if there are any non- zero digits following the 5 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. 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. 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 Measurement Units of Measure Units of Measure Base Units SI and EES (English Eng. System) Base Units SI and EES (English Eng. System) QuantitySI EES Lengthmeterfoot Masskilogramlb. Timesecondsecond Electric currentampere Thermd tempkelvinfahrenheit Amount of Substancemole

Precision Measurement Units of Measure Units of Measure Derived Units and Common Derived Units Derived Units and Common Derived Units Unit Conversions Unit Conversions Several could be committed to memory. Several could be committed to memory. Fahrenheit to Celsius Fahrenheit to Celsius Millimeters to inches Millimeters to inches Kilograms to pounds Kilograms to pounds Gallons to liters Gallons to liters Online Conversion Sources Online Conversion Sources or or

Precision Measurement Using the Engineering Solution Layout Excel Spreadsheet, convert the following paying attention to significant digits. Using the Engineering Solution Layout Excel Spreadsheet, convert the following paying attention to significant digits. Assignment 1: Conversion Worksheet Assignment 1: Conversion Worksheet

Precision Measurement Precision Measurement Measuring Power & Energy Vocabulary Measuring Power & Energy Vocabulary Power Power Mechanical Converter Mechanical Converter Torque Torque Efficiency Efficiency Horsepower Horsepower BTU BTU Calorie Calorie Force Force Gravity Gravity Metric System Metric System Pressure Pressure Speed Speed Tachometer Tachometer Weight Weight Work Work

Precision Measurement Precision Measurement Energy Defined Energy Defined Most energy converters such as a diesel or gasoline engine are designed to accomplish one purpose: convert energy into useful work. Most energy converters such as a diesel or gasoline engine are designed to accomplish one purpose: convert energy into useful work. Energy: the ability to do work. Energy: the ability to do work. How does this take place in a gasoline engine? How does this take place in a gasoline engine? Force is any push or pull on an object. Force is any push or pull on an object. Gravity is a force that pulls down on every object on earth. Gravity is a force that pulls down on every object on earth. To lift the object we must exert force greater than the weight…therefore weight is considered to be a force equal to the pull of gravity on an object. To lift the object we must exert force greater than the weight…therefore weight is considered to be a force equal to the pull of gravity on an object.

Precision Measurement Precision Measurement Work Defined: Work Defined: Work is defined as the result of applying a force to move a mass a certain distance. Work is defined as the result of applying a force to move a mass a certain distance. This force is created by the combustion of a source of fuel, such as gasoline. This force is created by the combustion of a source of fuel, such as gasoline. Work is produced when the force moves a certain mass a certain distance. Work is produced when the force moves a certain mass a certain distance. WORK = FORCE X DISTANCE WORK = FORCE X DISTANCE Problem 1: Problem 1: FORCE 50 FEET 20 LBS. 20 LBS. X 50 FT.= 1000 FT-LB.

Precision Measurement Precision 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 of the combustion of fuel/pushes pistons downward/causing crankshaft to spin. Torque is also produced on the output shaft of engines because of the combustion of fuel/pushes pistons downward/causing crankshaft to spin. This force (torque) causes other objects to rotate, turning transmissions and wheels, boat props, lawn mower blades, etc. This force (torque) causes other objects to rotate, turning transmissions and wheels, boat props, lawn mower blades, etc. Problem 2: Problem 2: A lug nut on a car tire is very tight. When repairing a flat tire, Jenny has a choice between a 12 inch and 18 inch wrench. Which wrench will produce more torque? A lug nut on a car tire is very tight. When repairing a flat tire, Jenny has a choice between a 12 inch and 18 inch wrench. Which wrench will produce more torque?

Precision Measurement Precision Measurement Power Defined: Power 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)/t P (Power) = W (Work) / t (time) or P=(d * m)/t Power is the final output of an engine after it has converted the energy in the fuel into work. Power is the final output of an engine after it has converted the energy in the fuel into work. A common term used to describe output power is horsepower. A common term used to describe output power is horsepower. Based on the premise of the amount of work that a horse can do in one minute. Based on the premise of the amount of work that a horse can do in one minute. One horsepower is equal to the energy needed to lift 33,000 pounds 1 foot in 1 minute. This is the same energy needed to lift 550 lbs. one foot in one second. One horsepower is equal to the energy needed to lift 33,000 pounds 1 foot in 1 minute. This is the same energy needed to lift 550 lbs. one foot in one second.