Dimensional Analysis For this example, let ma and my be masses • 11, 12, 13 and x be lengths t₁ and to be times aloncipa hep up.edu A mass density is defined as mass per volume, and a volume has a dimension of [L]³. Which of the following could be mass densities? 11-12-13 ma mamb mp² 11-12 ma 1₁².122x
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- The density of nuclear matter is about 1018kg/m3 . Given that 1 mL is equal in volume to cm3 , what is the density of nuclear matter in megagrams per microliter (that is, Mg/L )?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.)When nonmetric units we used in the United Kingdom, a unit of mass called the pound-mass (lbm) was used, where 1 lbm = 0.4539 kg. (a) If there is an uncertainty of 0.0001 kg in the pound-mass unit, what is its percent uncertainty? (b) Based on that percent uncertainty, what mass in pound-mass has an uncertainty of 1 kg when converted to kilograms?
- 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.”A marathon runner completes a 42.188-km course in 2 h, 30 min, and 12s. There is an uncertainty of 25 m in the distance traveled and an uncertainty of 1 s in the elapsed time. (a) Calculate the percent uncertainty in the distance. (b) Calculate the percent uncertainty in the elapsed time. (C) What is the average speed in meters per second? (d) What is the uncertainty in the average speed?Please help me with the following and explain making sure the answer is really really correct 100%. I tried all kinds of calculations and it was wrong so I have no idea what's wrong. When I look at similar questions with different numbers it was 0. ... so i guess it has be something similar maybe but pleas make sure your work is correct pls pls ( wrong asnwer--> 1.31g and 1.35e-12)
- 2.) A single reading taken with a meter stick for the length of a cylinder is 5.5 cm. What is the prsable percent error in the reading? 3.) The following readings were taken with a meter stick for the length of a cylinder: 5.5 cm, 5.3 cm, 5.4 cm, 5.5 cm and 5.6 cm. Calculate the standard deviation of the mean, the stand error and the probable percent error. 4.) How many significant figures should be given in reporting the length of the cylinder in question 3? 5.) If the radius of the cylinder in question 2 is 2.4 ± 0.2 cm and its mass is 32.6 ± 0.5 gm, what will be the probable percent error in the density of the cylinder? What will be the probable error in density? How many significant figures should be given in reporting the density? Conclusions?? 02 6) (figure3) 6a)Befer to Figure 3. Given a track length of 90 cm and a height difference of 18 cm, what is sin 6 02 01 Fig. 2 Z)(figure 2) plane (see Figure 2). Attach the diagram in question#8 below. What would be the acceleration given…SOIE Edge /www.webassign.net/web/Student/Assignment-Responses/last?dep=25551922 -/2.35 Points] DETAILS OSCOLPHYS1 1.3.018. MY NOTES (a) How many significant figures are in the numbers 999.0 and 1000.0? 999.0 1000.0 (b) If the uncertainty in each number is 10, what is the percent uncertainty in each? (Give your answer to 4 significant figures.) 999.0 4.0 % 1000.0 4.0 % (c) Which is a more meaningful way to express the accuracy of these two numbers, significant figures or percent uncertainties? O significant figures O percent uncertainties Additional Materials Reading T-/2.35 Points] DETAILS OSCOLPHYS1 1.3.023. MY NOTES Ifi mar unner averages 73 mih. hew long dees it take him or her to run a 26.22-mi marathon?1. 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.
- Given that 1 maz is equal to 2.97 x 10-11 gal, how many nL are there in 79.8 maz? Report your answer to 3 significant figures. (NOTE: A maz is a fictitious unit of volume, the other units are actual units of volume.) Type your answer... PreviousCor_a syshem Comprised of 2p. eledmas with respeckive £,9, values, R 1 B oexperts.cheggindia.com/qa-expert-registration/ we WeTransfer Myanmar | Institute... w World health ranking O HDFC NetBanking 6 uab Online Banking Sharepoint M Inbox (2,039) - swa... pps ease note that on-boarding of all successful candidates will be in September. We have limited ancies and will grant answering rights on first come first serve basis for candidates mpleting the applications earlier than others. ubject test ote: - You are attempting question 5 out of 12 A Mother massages her palms to warm them up and places them on the cheeks of her child with force 5.0 N to keep the child warm on the chilling night. If arms move the distance of 16 cm as she moves her hands back and forth for the eight times with the kinetic friction of 0.45, calculate the internal energy of the hands if no heat is lost into the surroundings. (а) 1.6 J (b) 3.1 J (c) 2.9 J (d) 4.8J O A swer Type here to search 口i