...MEASUREMENT AND UNITS & DIMENSIONS Synopsis : 1. Every measurement has two parts. The first is a number (n) and the next is a unit (u). Q = nu. Eg : Length of an object = 40 cm. 2. The number expressing the magnitude of a physical quantity is inversely proportional to the unit selected. 3. If n1 and n2 are the numerical values of a physical quantity corresponding to the units u1 and u2, then n1u1 = n2u2. Eg : 2.8 m = 280 cm; 6.2 kg = 6200 g 4. The quantities that are independent of other quantities are called fundamental quantities. The units that are used to measure these fundamental quantities are called fundamental units. 5. There are four systems of units namely C.G.S, M.K.S, F.P.S and SI 6. The quantities that are derived using the fundamental quantities are called derived quantities. The units that are used to measure these derived quantities are called derived units. 7. The early systems of units : Fundamental Quantity System of units C.G.S. M.K.S. F.P.S. Length centimetre Metre foot Mass Gram Kilogra m pound Time second Second second 8. Fundamental and supplementary physical quantities in SI system (Systeme Internationale d’units) : Physical quantity Unit Symbol Length Metre m Mass kilogram kg Time second s Electric current ampere A Thermodynamic temperature kelvin K Intensity of light candela cd Quantity of substance mole mol Supplementary...
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...Metrology Laboratory MECN3003 - Aeronautical Laboratory Deepa Daya Student number: 473706 Supervisor: Mr. R. Paton A project report submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in partial fulfilment of the requirements for the degree of Bachelor of Science in Engineering. Johannesburg, March 2014 University of the Witwatersrand, Johannesburg School of Mechanical, Industrial & Aeronautical Engineering INDIVIDUAL DECLARATION WITH TASK SUBMITTED FOR ASSESSMENT I, the undersigned, am registered for the course MECN3003 - Aeronautical Laboratory in the year 2014. I herewith submit the following task ”Metrology Laboratory” in partial fulfilment of the requirements of the above course. I hereby declare the following: • I am aware that plagiarism (the use of someone else’s work without their permission and / or without acknowledging the original source) is wrong; • I confirm that the work submitted herewith for assessment in the above course is my own unaided work except where I have explicitly stated otherwise; • This task has not been submitted before. either individually or jointly, for any course requirement, examination or degree at this or any other tertiary educational institution; • I has followed the required conventions in referencing the thoughts and ideas of others; • I understand that the University of the Witwatersrand may take disciplinary action against me if it can be shown...
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...After completing Lab 4 Acceleration Due To Gravity I can conclude that using a direct method (free falling activity) in obtaining acceleration is more precise than compared to the indirect method (pendulum swing activity). Thusly when I compared my results of each experiment, the free falling measurements were not so great, but closer to the earth’s acceleration. For example, my last measurement of the free falling activity was approximately 985.11 cm/s^2, which was very close to the earth’s acceleration. On the other hand my last measurement on the pendulum swing activity my last measurement was 2196.14 cm/s^2, which was very off from the earth’s acceleration. It is possible to assume errors in my calculations may had alter any of my measurements. Also possible errors in the experiment could have also altered my results. I can honestly say it is not that simple to obtain multiple measure close to the earth’s average. This experiment was overall simple to conduct, but obtaining really good results compared to the earth’s average is the challenge. I really enjoyed conducting this experiment using two different methods to obtain acceleration. My favorite activity was the free falling activity, because I actually obtain one very good measure. These experiments were pretty simple once I got the hang of using the equipment. I thought this experiment was quite interesting looking at my results and comparing them to the average. I had no dislikes on these experiments. Overall this...
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...SIMILITUDE AND DIMENSION ANALYSIS DEFINITION AND USES OF SIMILITUDE • Similitude means similarity • it impossible to determine all the essential facts for a given fluid flow by pure theory alone • we must often depend on experimental investigations. • we can greatly reduce the number of tests needed by systematically using dimensional analysis and the laws of similitude or similarity. • For these enable us to apply test data to other cases than those observed. • we can obtain valuable results at a minimum cost from tests made with small-scale models of the full-size apparatus. The laws of similitude enable us to predict the performance of the prototype, which means the full-size device, from tests made with the model. for example, we might study the flow in a carburetor in a very large model. • A few examples of where we have used models are – ships in towing basins, – airplanes in wind tunnels, – hydraulic turbines, – centrifugal pumps, – spillways of dams, – river channels and the study of such phenomena as the action of waves and tides on beaches, – soil erosion and – transport of sediment. GEOMETRIC SIMILARITY • geometric similarity means that the model and its prototype have identical shapes but differ only in size. • the flow patterns must be geometrically similar. If subscripts p and m denote prototype and model, respectively, we define the length scale ratios as the ratio of the linear dimensions of the prototype to the corresponding dimensions in the model. = ...
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...natural processes. Answer 1: One such laws is the Newton’s gravitation law, According to this law everybody in this nature are attracts with other body with a force of attraction which is directly proportional to the product of their masses and inversely proportionally to the square of the distance between them. Question 2: Among which type of elementary particles does the electromagnetic force act? Answer 2: Electromagnetic force acts between on all electrically charged particles. Question 3: Name the forces having the longest and shortest range of operation. Answer 3: Longest range force is gravitational force and nuclear force is shortest range force. Question 4: If ‘slap’ times speed equals power, what will be the dimensional equation for ‘slap’? Answer 4: Slap × speed = power Or slap = power/speed = [MLT-2] Question 5: If the units of force and length each are doubled, then how many times the unit of energy would be affected? Answer 5: Energy = Work done = Force x length So when the units are doubled, then the unit of energy will increase four times. www.tiwariacademy.in A free web Support in education 1 Physics (www.tiwariacademy.com) (Chapter 1 and 2)(Physical World, Units and Measurements) (Class 11) Question 6: Can a quantity has dimensions but still has no units? Answer 6: No, a quantity having dimension must have some units of its measurement. Question 7: Justify L + L = L and L – L = L. Answer 7: When we add or subtract...
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...Job Description: Quality Control / Inspector Principal Duties and Responsibilities: Performs complete layout inspection by measuring dimensions, such as length, height, and distance, between reference points, using precision instruments such as micrometers, calipers, dial indicator, and CMM, to ensure product meets specifications. Able to locate reference point(s) on part and measure dimension such as angle, arc, and radii, using combinations of aids, such as surface plate parallel bars, angle plates, gauge blocks, plug pins, V blocks, sine bars, and precision measuring instruments such as height gage. Performs verification on Incoming, In-Process, and Outgoing products. Visually compares work pieces against one another to assess/detect manufacturing variations in processes. Assists and/or trains operators on part visual acceptability, and measurement and process procedures as required. Reports quality problems or findings to Quality Control Manager and follows up to ensure that corrective action has/will take place. Maintains record of inspections and prepares list of defects, interacts with other departments to ensure compliance with specification and to facilitate the acceptance of parts. Knowledge, Skills and Abilities Required: The ideal candidate will have: Ability to interpret blueprints. Basic Math & Geometry/Trigonometry. Ability to work independently with limited supervision. Flexibility based on plant production schedules. A minimum of one-year...
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...ci3.1 BLOCK DIAGRAM Fig 3.1 block diagram of the vibration measurement system The above figure shows the block diagram of the vibration measurement system. The different blocks of the block diagram are the sensor which is used to measure the vibrations. The sensor we are using in this project is MMA8451Q accelerometer, which is able to measure the vibrations. The vibration data need to be measured from the acceleration data of the accelerometer by setting different thresholds. Then the data from the accelerometer need to be transferred to the microcontroller which is used to process the data. The microcontroller which we have selected to do the processing of the data is MKL25Z32VFM4 which is ARM® Cortex™-M0+ processor. This is best suited for the processing of the accelerometer data. There are different types of protocols that can be used to communicate with this controller. It supports SPI, I2C etc, the communication between the accelerometer and the microcontroller uses I2C protocol to transfer the data between two. For development we used MKL25Z128VLK4 controller. Even this is also ARM® Cortex™-M0+ processor. The reason for using this processor is this processor will be available on a FRDM KL25Z board from freescale and this board also has MMA8451Q accelerometer populated on the board. So till the completion of designing the PCB this board can be used for development. The processor which will be used in the final product and the processor which we are using now for development...
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...Tobi Gonzalez 2/25/13 Motion is Relative 1. The two units of measurement are distance and time. 2. The kind of speed is registered by an automobile speedometer is instantaneous speed. 3. Average speed is the speed averaged over duration of time. Usually the total distance covered divided by the total time. Instantaneous speed is the speed given at that instant within that span of time, measured with a real time speedometer. 4. The average speed in kilometers per hour for a horse that gallops a distance of 15 km in a time of 30 min is: Average speed = 15 km/30 min = 15 km/0.5 h = 30 km/h 5. Speed is the distance covered per unit of time. Acceleration is the rate in which an object changes its velocity. 6. If a car is moving at 90 km/h and it rounds a corner, also at 90 km/h, it does maintain a constant speed but not a constant velocity. The velocity never changed, only the direction it’s traveling. 7. Velocity is change in displacement, change in position over a period of time, while Acceleration is change in velocity over a time period. 8. The acceleration of a car that increases its velocity from 0, to 100 km/h in 10s is 10km/h*s 9. The acceleration of a car that maintains a constant velocity of 100 km/h for 10s is 0 km/h*s. Some of my classmates get this question wrong but the last question right because they fail to read the question. In the last question there was a change in velocity. However in this question there was no change in...
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...Procedure of Creating Dimensionless Groups 1. List all Variables that are included in the problem 2. Express each variable in terms of basic dimension 3. Determine the required number of pi terms 4. Select a number of repeating variables 5. Form a pi term by multiplying one of the non repeating variable by the product of repeating variables each raised to an exponent that will make the combination dimensionless 6. Repeat step 5 7. Check all the resulting pi terms 8. Express the final form as a relationship among the pi terms and think about what it means Recapitulation 1. A base quantity is a property that is defined in physical terms by two operations: a comparison operation, and an addition operation. The comparison operation is a physical procedure for establishing whether two samples of the quantity are equal or unequal; the addition operation defines what is meant by the sum of two samples of that property. 2. Base quantities are properties for which the following concepts are defined in terms of physical operations: equality, addition, subtraction, multiplication by a pure number, and division by a pure number. Not defined in terms of physical operations are: product, ratio, power, and logarithmic, exponential, trigonometric and other special functions of physical quantities. 3. A base quantity can be measured in terms of an arbitrarily chosen unit of its own kind and a numerical value. 4. A derived quantity of the first...
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...Chapter 1 student learning objectives (SLOs) Goal/Benchmark A: Students will be able to use dimensional analysis using appropriate SI and non SI units and apply their understanding of significant figures * Knowledge Focus A.1: Essential concepts Objectives-Students will be able to: * [Retrieval] * Define chemistry * Define and list each of the steps of the scientific method * Define physical and chemical properties * Define extensive and intensive properties * Define density * [Comprehension] * Explain in their own words or represent symbolically the meaning of: * Chemistry * Steps of the scientific method * Physical and chemical properties * Extensive and intensive properties * Density * [Analysis] * Identify and explain similarities and differences between the different steps of the scientific method * Analyze errors with the application of the steps of the scientific method * Identify and explain the similarities and differences between physical and chemical properties * Identify and explain the similarities and differences between extensive and intensive properties * Use the concept of density to solve chemical problems * Knowledge Focus A.2: Dimensional analysis Objectives-Students will be able to: * [Retrieval] * List/recognize the SI units...
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...Part 1: (First question) 1.Using the scale on the interactive map, give the approximate distance in miles that the Pilgrims traveled in their journey from Plymouth, England, to Plymouth, Massachusetts. I get that they approximately traveled 3,349.375 miles. When clicking the red dots (which I didn't notice before) you get the distance from Plymouth, England to Plymouth, Massachusettes, which is 5.75. I then multiplied 5.75 with the mileage number that was given in the scale for evey one inch, which is 582.5. So, when I multiplied the 5.75 with 582.5 it gave me 3,349.375. Part 1: (Second question) 2.Using the scale on the interactive map, give the approximate distance in miles that Lewis and Clark traveled from St. Louis to Ft. Clatsop near the Pacific Ocean. I get that they approximately traveled 1,400.15 miles. When clicking the red dots you get the distance from St. Louis to Ft. Clatsop, which is 5.125. I then multiplied 5.125 with the mileage number that was given in the scale for every one inch, which is 273.2. So, when I multiplied the 5.125 with 273.2 it gave me 1,400.15 Part 2: I currently live in Altamonte Springs. I would describe the place as rainy, humid, sunny and tropical. Altamonte Springs in general is a small and safe city like a family place. Although Orlando city which nearby is a big fun city. We have Disney parks, Universal Studios, Water Parks and what not. A public in Altamonte Springs mix. In a ratio, 35% White, 30% Black, 15% Hispanic and 25% Asians...
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...and l are the mass, acceleration due to gravity, distance, period and length respectively. A MT2 B ML2 C MLT2 D MLT–2 [Answer: B] 2. Suppose A = BC, where A has the dimension LM–1 and C has the dimension LT–1. What is the dimension of B? A TM–1 B L2T–1M–1 C TML–2 D L2TM–1 [Answer: A] 3. (a) State the dimension for (i) velocity (ii) force (b) Suppose an equation related with force F, viscosity ƞ, speed v, radius r is given by this formula , where k is a dimensionless constant; x, y, and z are the power to which ƞ, v and r. Given that the dimensions of viscosity ƞ is ML–1T–1. Use dimensional analysis to determine the value of x, y and z. [Answer: (a) (i) LT–1, (ii) MLT–2; (b) 1, 1, 1] 4. (a) Discuss briefly whether in general the method of dimensional checking can positively confirm that an equation is correct. (b) Newton’s law of universal gravitation is represented by where F is the gravitational force, M and m are masses, and r is a length. Given that the dimensions of force is MLT–2. What are the dimensions and SI unit of the proportionality constant G? [Answer: (a) No; (b) L3M–1T–2, m3 kg–1 s–2] 5. The flow of a liquid with density ρ, round an obstacle of width b, changes from streamline to turbulence when the critical speed v is reached. If η is the viscosity of the liquid and given their relationship as below: where C is a dimensionless constant. Deduce...
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...Job Description: Quality Control / Inspector Principal Duties and Responsibilities: ï‚· Performs complete layout inspection by measuring dimensions, such as length, height, and distance, between reference points, using precision instruments such as micrometers, calipers, dial indicator, and CMM, to ensure product meets specifications. ï‚· Able to locate reference point(s) on part and measure dimension such as angle, arc, and radii, using combinations of aids, such as surface plate parallel bars, angle plates, gauge blocks, plug pins, V blocks, sine bars, and precision measuring instruments such as height gage. ï‚· Performs verification on Incoming, In-Process, and Outgoing products. ï‚· Visually compares work pieces against one another to assess/detect manufacturing variations in processes. ï‚· Assists and/or trains operators on part visual acceptability, and measurement and process procedures as required. ï‚· Reports quality problems or findings to Quality Control Manager and follows up to ensure that corrective action has/will take place. ï‚· Maintains record of inspections and prepares list of defects, interacts with other departments to ensure compliance with specification and to facilitate the acceptance of parts. Knowledge, Skills and Abilities Required: The ideal candidate will have: ï‚· Ability to interpret blueprints. ï‚· Basic Math & Geometry/Trigonometry. ï‚· Ability to work independently with limited supervision. ï‚· Flexibility based on plant production schedules...
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...Overhang Mike Paterson † ∗ ‡ Uri Zwick arXiv:0710.2357v1 [math.HO] 12 Oct 2007 Figure 1: A harmonic stack with 10 blocks. 1 Introduction How far off the edge of the table can we reach by stacking n identical, homogeneous, frictionless 1 blocks of length 1? A classical solution achieves an overhang asymptotic to 2 ln n. This solution is widely believed to be optimal. We show, however, that it is exponentially far from optimality by constructing simple n-block stacks that achieve an overhang of cn1/3 , for some constant c > 0. The problem of stacking a set of objects, such as bricks, books, or cards, on a tabletop to maximize the overhang is an attractive problem with a long history. J. G. Coffin [2] posed the problem in the “Problems and Solutions” section of this Monthly, but no solution was given there. The problem recurred from time to time over subsequent years, e.g., [18, 19], [12], [4]. Either deliberately or inadvertently, these authors all seem to have introduced the further restriction that there can be at most one object resting on top of another. Under this restriction, the harmonic stacks, described below, are easily seen to be optimal. ∗ A preliminary version of this paper [14] appeared in the Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’06), pages 231–240. This full version is to appear in the American Mathematical Monthly. † DIMAP and Department of Computer Science, University of Warwick, Coventry CV4 7AL, UK...
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...Lapodium Logistics Int’l Inc. Room 601, Roman Santos Bldg., Plaza Lacson, Sta. Cruz, Metro Manila1003 Philippines November 26, 2013 ASSAM Corp. Unit 1204, 139 Corporate Center Valero St. Salcedo Village Makati City . Attention: Mr. Jake Tansanco Subject: Standard FCL Quotation (1x20’ or 1x40’) Dear Sir: We would like to inform you the following charges: From Customs to Delivery |Measurement: Gross Weight : | |Duties, Taxes & Other Charges | |As per Computation | |Brokerage Fee with Vat | |As per CAO 1-2001 | |Processing | |1,000.00 | |Documentation | |500.00 | |Releasing | |500.00 | |Handling | |500.00 | ...
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