In the state of Indiana it was once proposed to round the value of a to 3. Using the Percent Error formula given below, and using the actual value of pi approximated to 5 decimal places, n = 3.14159, answer the following questions. |Accepted Value-Experimental Value| Accepted Value Percent Error = × 100 A) What percent error would be introduced in calculations involving

In the state of Indiana it was once proposed to round the value of a to 3. Using the Percent Error formula given below, and using the actual value of pi approximated to 5 decimal places, n = 3.14159, answer the following questions. |Accepted Value-Experimental Value| Accepted Value Percent Error = × 100 A) What percent error would be introduced in calculations involving

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter1: Units And Measurement

Section: Chapter Questions

Problem 83AP: A marathon runner completes a 42.188-km course in 2 h, 30 min, and 12s. There is an uncertainty of...

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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.)
Estimates and Fermi Calculations Assuming the human body is made primarily of water, estimate the volume of a person.
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?
(a) A person's blood pressure is measured to be 1202 mm Hg. What is its percent uncertainty? (b) Assuming the same percent uncertainty, what is the uncertainty in a blood pressure measurement of 80 mm Hg?
A good-quality measuring tape can be off by 0.50cm over a distance of 20m . What is its percent uncertainty?
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…
Given that P = ". Find the maximum percentage error in calculating P 2/m if the percentage error in measuring m and n is 2% and 3%, respectively.
Measurement, Uncertainty, Significant FiguresProblem 1 (III): Calculate the volume of the cylinder shown below if the following dimensions are measured as:d=(3.92±0.005)cmandh=(5.45±0.01)cmAlso, determine both the absolute and percent uncertainty of the calculated volume.(For full credit, fill in the table shown on the top of the next page and show sample calculations.)quantity value Abs. unc. Rel. unc.rhV=πr^2 hProblem 2 (III) Repeat problem 1, but instead of the volume, find the total surface area for the measured cylinder. Find the absolute and percent uncertainty for the calculated surface area. (Again, for full credit, fill in the table below and show sample calculations).quantity value Abs. unc. Rel. unc.rhArea of top/bottom (πr^2)Surface area of curved side (2πrh)Total surface areaUnit conversionProblem 3 (II) How many nanoseconds are there in one “microcentury”?Problem 4 (II) An angstrom (symbol Å) is a unit of length, defined as 〖10〗^(-10) m, which is on the order of the…
A person's blood pressure is measured to be: 115 ± 7 mm Hg. What is its percent uncertainty? (Express your answer to the correct number of significant figures and proper units. Use unrounded values in your calculations.)
A 885 meter is having an accuracy of ± 0.59% of FSD. Calculate the %error for a measurement of 14, 47,99 reading. (i)Full scale error value= (ii) %Error for 14= % error for 47 % error for 99
Express each approximation of p to six significant figures:(a) 22/7and (b) 355/113. (c) Are these approximations accurate to that precision?
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?