Which of the following statements is correct? If an eguation is dimensionally correct it must be true änd 'if it is hot đimensionally correct it may be true. and if an equation is hot đimehšiónălly correct it cannot be true. If an.eguation is dimensionally correct it may be true "if it is hot dimensionălly'correct then'it cannot be Fue. fan eguation is dimensionally correct it may be true truề.
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- The first atomic bomb was detonated on July 16, 1945, at the Trinity test site about 200 mi south of Los Alamos. In 1947, the U.S. government declassified a film reel of the explosion. From this film reel, British physicist G.I. Taylor was able to determine the rate at which the radius of the fireball from the blast grew. Using dimensional analysis, he was then able to deduce the amount of energy released in the explosion, which was a closely guarded secret at the time. Because of this, Taylor did not publish his results until 1950. This problem challenges you to recreate this famous calculation. (a) Using keen physical insight developed from years of experience, Taylor decided the radius rof the fireball should depend only on time since the explosion, t, the density of the air, , and the energy of the initial explosion, E. Thus, he made the educated guess that r=kEabtcfor some dimensionless constant kand some unknown exponents a,b, and c. Given that [E]=ML2T-2 , determine the values of the exponents necessary to make this equation dimensionally consistent. (Hint: Notice the equation implies that k=rEabtcand that [k]=1 ). (b) By analyzing data from high-energy conventional explosives, Taylor found the formula he derived seemed to be valid as long as the constant khad the value 1.03. From the film reel, he was able to determine many values of rand the corresponding values of t. For example, he found that after 25.0 ms, the fireball had a radius of 130.0 m. Use these values, along with an average air density of 1.25kg/m3 , to calculate the initial energy release of the Trinity detonation in joules (J). (Hint: To get energy in joules, you need to make sure all the numbers you substitute in are expressed in terms of SI base units.) (c) The energy released in large explosions is often cited in units of “tons of TNT” (abbreviated “t TNT”), where 1 t TNT is about 4.2 GJ. Convert yow answer to (b) into kilotons of TNT (that is, kt TNT). Compare your answer with the quick-and-duty estimate of 10 kt TNT made by physicist Enrico Fermi shortly after witnessing the explosion from what was thought to be a safe distance. (Reportedly, Fermi made his estimate by dropping some shredded bits of paper right before the remnants of the shock wave hit him and looked to see how far they were carried by it.)Check Your Understanding Is the equation v=atdimensionally consistent? One further point thin needs to be mentioned is the effect of the operations of calculus on dimensions. We have seen that dimensions obey the rules of algebra, just like units, but what happens when we take the derivative of one physical quantity with respect to another or integrate a physical quantity over another? The derivative of a function is just the slope of the line tangent to its graph and slopes are ratios, so for physical quantities vand t , we hive that the dimension of the derivative of vwith respect to us just the ratio of the dimension of v over that of t : [dvdt]=[vt] . Similarly, since integrals are just sums of products, the dimension of the integral of vwith respect to t is simply the dimension of vtimes the dimension of t : [vdt]=[v][t] . By the same reasoning, analogous rules hold for the units of physical quantities derived from other quantities by integration or differentiation.Check Your Understanding Figure 1.4 says the mass of the atmosphere is 1019kg . Assuming the density of the atmosphere is 1kg/m3 , estimate the height of Earth’s atmosphere. Do you think your answer is an underestimate or an overestimate? Explain why. How many piano tuners are there in New York City? How many leaves are on that tree? If you are studying photosynthesis or thinking of writing a smartphone app tot piano tuners, then the answers to these questions might be of great interest to you. Otherwise, you probably couldn’t care less what the answers are. However, these are exactly the soils of estimation problems that people in various tech industries have been asking potential employees to evaluate their quantitative reasoning skills. If building physical intuition and evaluating quantitative claims do not seem like sufficient reasons tot you to practice estimation problems, how about the fact that being good at them just might land you a high-paying job? For practice estimating relative lengths, areas, and volumes, check out this PhET (https://openstaxcollege.org/l/21lengthgame) simulation, titled “Estimation.”
- Determine which one of the following equations is dimensionally consistent. A. F = mAz? B. FAV = mAæ² C. FAr = ; mAv² D. FAt = AV E. FAV = 2mAt² where F is force, m is mass, z is distance, V is velocity, and t is time. Select v6. Convert the following measurements mg.um kg.m а. 68 ms? hr2 b. 49mg/cm³ to ng/mm³ 7. Using Dimensional Analysis, check which of the following equations is or are correct. а. рgh3 — та b. avt = vh?Cube A is 2 inches on a side. Cube B is 8 inches on a side. Determine the following:1. The volume of each cube.2. How many Cube As can fit in Cube B (in regards to volume)?3. Noticing that B’s side is 4 times larger than A’s, can you see how you can get answer 2 any way other than finding both cube volumes?
- Q5. Suppose that in vereniere rzulere measurament, Length is 4-32 cm, omd the stamdared is o. 085 cm. the meon deviation othere hand, On the in Screew gauge measurce ment, the mean readius is o.621 cm and the standared the deviation is o. 000 725 Calculate cm . volume (using przo pogation of erercore in reulere and ercrcoe reelation) fore Verrniere Scrrew gauge measurements .Basic rules in considering a formula or writing an equation in Physics would be : 1. The fundamental or base quantities such as length [L], mass [M], time [T], are called dimensions 2. Dimensional analysis is a procedure to verify the experimental correctness of an equation. 3. Both sides of an equation must match in numerical values even though dimensions are not matched 4. Dimensions may be treated like algebraic quantities. Which of the above rules are correct? . Rules 2 and 4 • Rules 1 and 3 • Rules 1 and 2 . Rules 1 and 41. The following data are the measurements of the dimensions of a box: l = 8.6 ± 0.5 cm h = 20.19 ± 0.01 mm w = 0.75 ± .02 mHow should the volume of the box be reported (central value ± uncertainty) incm3? Show solution.2. If the accepted value of the volume of the box in the previous question is 1300 cm3, is the measurement acceptable? Explain.
- Hi could you please answer these with complete solution PROBLEM : Several carpet installers make measurements for carpet installation in the different rooms of a restauran reporting their measurements with inconsistent accuracy, as compiled in Table 1.6. Compute areas for (a) the banquet hall, (b) the meeting room, and (c) the dining room, taking into account significant figures. (d) What total area of carpet is required for these rooms?p Search Lab 1 Measurements MG Su2t (3) - Word References Mailings Review View Help gn Laynut AaBbCcD AaBbCeDe AaBbC AaBbCcC AaBbCcD T No Spac. Heading 1 Heading 2 Heading 3 Aa- A E -E-E- E T I Normal Paragraph Styles Questions 1 a) Which is greater in length, 1 millimeter or 1/16 inch? 2. Consider using the same meter stick and the same scale to measure two objects of different lengths. (One object is exactly 1.674532 cm in length and the other is exactly 85.839287 cm, but you won't be able to measure that preciseiy with a meter stick.) When you measure these objects using the meter stick, which of your length measurements is likely to have the higher percent error? Explain. (Hint: think of where the error comes from every time you use a measuring device and how that would affect the error of the measurernent associated with a smell versus a larger object) Focus %23 $ 曲 TAY 10 144 & * 6. 8. 9. R YI need help in these questions. Please do them correctly and 100% Please i have only 30 minutes. No need to add lengthy exlanations. Just tell correct answers. Its very important so please tell correct answers