1. Precision Measurement Foundations of Engineering

2. 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)

3. 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

4. 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.

5. 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. 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 ONLY are significant. 3.200 has ____ significant figures 200 has ____ significant figures 2.00 x 10^2 ____ significant figures

6. 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.

7. Precision Measurement Rounding Rounding 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 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 __________

8. 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 Luminous intensitycandela

9. Precision Measurement Units of Measure Units of Measure Supplemental Units SI and EES (English Eng. System) Supplemental Units SI and EES (English Eng. System) QuantitySI EES Plane Angleradian Solid Anglesteradian

10. 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 should be committed to memory. Several should 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 www.onlineconversions.com or www.efunda.com www.onlineconversions.com or www.efunda.com www.onlineconversions.comwww.efunda.com www.onlineconversions.comwww.efunda.com

11. 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

12. 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

13. 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.

14. 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.

15. 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?

16. 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.

17. Precision Measurement Precision Measurement Horsepower is a measure of the work being done by a mechanical converter, such as a diesel engine. Horsepower is a measure of the work being done by a mechanical converter, such as a diesel engine. Horsepower is described in many ways as it relates to the mechanical converters. Horsepower is described in many ways as it relates to the mechanical converters. When comparing engines, brake horsepower is used. When comparing engines, brake horsepower is used. When discussing efficiency, frictional and indicated horsepower are used. When discussing efficiency, frictional and indicated horsepower are used. When analyzing gasoline mileage, road horsepower is used. When analyzing gasoline mileage, road horsepower is used. POWER: Energy per unit of time or work accomplished in a given period of time. POWER: Energy per unit of time or work accomplished in a given period of time. Example…I climb stairs, weight x height determines work done. Same work regardless if you walk or run up the stairs…but more power is used to run up the stairs. Example…I climb stairs, weight x height determines work done. Same work regardless if you walk or run up the stairs…but more power is used to run up the stairs.

18. Precision Measurement Precision Measurement A watt(W) is a unit used to measure electrical power. A watt(W) 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 needs 800 joules per second to make the heating element red-hot. A toaster may use 800 watts of power. This means the toaster needs 800 joules per second to make the heating element red-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 ÷ Δ t Pwr = W ÷ Δ t Horsepower Horsepower 1 hp = 550 ft lb/s = 746 W 1 hp = 550 ft lb/s = 746 W 1 Watt = 1J/s (Joule per second) 1 Watt = 1J/s (Joule per second) 1 kW = 1000 W 1 kW = 1000 W Problem 3: How much power is required for you to run 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 apply the rule for significant digits and indicate your answer in Watts. Problem 3: How much power is required for you to run 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 apply the rule for significant digits and indicate your answer in Watts.

19. Precision Measurement Precision Measurement Pressure Pressure Pressure is another measurement of force. Pressure is another measurement of force. Pressure is determined by the area over which a force is applied. Pressure is determined by the area over which a force is applied. Pressure is force per a unit of area. Pressure is force per a unit of area. Snow shoes example. Snow shoes example. Therefore is area = length x width and we apply 100 pounds per square inch…less pressure is applied on a greater area. Therefore is area = length x width and we apply 100 pounds per square inch…less pressure is applied on a greater area. A confined fluid under pressure exerts equal force on all enclosing surfaces. A confined fluid under pressure exerts equal force on all enclosing surfaces. The air in an inflated balloon pushes with a small amount of pressure in all directions…however it is an even amount all over the interior surface of the chamber. The air in an inflated balloon pushes with a small amount of pressure in all directions…however it is an even amount all over the interior surface of the chamber.

20. Precision Measurement Precision Measurement We can determine the force produced by a certain amount of pressure. We can determine the force produced by a certain amount of pressure. We must multiply the pressure (force per unit area) by the total area. We must multiply the pressure (force per unit area) by the 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 Area Force = Pressure x Area Force = 1/4 psi x 100 sq. in. Force = 1/4 psi x 100 sq. in. Force = 25 pounds Force = 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 of force. We must remember that pressure is a special measurement 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 amount of area. However, the total amount of force depends on the total amount of area. Problem 4: Show Mathematical proof why a sharp knife cuts better than a dull knife. Problem 4: Show Mathematical proof why a sharp knife cuts better than a dull knife.

21. Precision Measurement Precision Measurement Two pistons, different sizes: 1 square inch area and a large one, 10 square inch area. Two pistons, different sizes: 1 square inch area and a large 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 cylinder. The large piston produces ten times the force of the smaller cylinder. But if the same amount of air is applied to each, the larger only moves 1/10 the distance of the smaller. But if the same amount of air is applied to each, the larger only moves 1/10 the distance of the smaller.

22. Precision Measurement Precision Measurement Heat: Heat: Heat energy is measured in British Thermal Units (BTU’s). Heat energy is measured in British Thermal Units (BTU’s). One BTU is equal to the amount of heat energy needed to raise the temperature of one pound (about 1 pint) of water 1 degree F. One BTU is equal to the amount of heat energy needed to raise the temperature of one pound (about 1 pint) of water 1 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 energy is converted into power. In a typical gasoline engine only 1/5th of the available heat energy is converted into power.

23. Precision Measurement Precision Measurement Another common unit of measurement for heat is called a calorie. Another common unit of measurement for heat is called a calorie. Small calorie: amount of heat needed to raise the temperature of 1 cubic cm of water 1 degree Celsius. Small calorie: amount of heat needed to raise the 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 available to us in the food we eat. Large calorie: measures the amount of heat energy available to us in the food we eat.

24. Precision Measurement Precision Measurement Converter Efficiency: Converter Efficiency: Several types of efficiency are used for mechanical converters. Several types of efficiency are used for mechanical converters. Efficiency generally refers to how well a particular job can be done. Efficiency generally refers to how well a particular job can be done. Efficiency is expressed in a ratio of input to output. Efficiency is expressed in a ratio of input to output. Efficiency INPUTEn. Con. OUTPUT

25. Precision Measurement Precision Measurement Efficiencies are expressed as percentages, which are always less than 100%. Efficiencies are expressed as percentages, which are always less than 100%. The difference between the percent efficiency and 100% is due to the percent loss incurred during the process of converting power. The difference between the percent efficiency and 100% is due to the percent loss incurred during the process of converting power. Efficiency is important because it shows how much energy is being wasted. Efficiency is important because it shows how much energy is being wasted. Mechanical Efficiency: relationship between the theoretical (mat calculated) amount of work to move the motorcycle, and the actual amount of work to move it. Mechanical Efficiency: relationship between the theoretical (mat calculated) amount of work to move the motorcycle, 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 100 Power Efficiency=(output power/input power) x 100 Problem 5a. The total mass of an elevator is 1200kg. An electric motor raises the elevator three floors (1.5m) at a constant speed in 12 seconds. Problem5b. What is the power outage of the motor? Problem 5a. The total mass of an elevator is 1200kg. An electric motor raises the elevator three floors (1.5m) at a constant speed in 12 seconds. Problem5b. What is the power outage of the motor?

26. Precision Measurement BJ Furman SJSU MAE Beckwith, T. G., Marangoni, R. D., Lienhard, J. H., Mechanical Measurements, Addison-Wesley, Reading, MA, 1995. Histand, M. B., Alciatore, D. G., Introduction to Mechatronics and Measurement Systems 2 nd ed., WCB/McGraw-Hill, Boston, 2003. Park, J. L., Rules for Rounding Off [Online]. Available at http://dbhs.wvusd.k12.ca.us/webdocs/SigFigs/SigFigs.html, 1996. NIST Guide to SI Units –Appendix B [Online]. Available at http://physics.nist.gov/Pubs/SP811/appenB.html#B.7 “See, I have a rhyme assisting my little brain its tasks sometime resisting” (the number of letters in each word gives pi to 12 decimal places)