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- 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?Mount Everest, at 29,028ft , is the tallest mountain on Earth. What is its height in kilometers? (Assume that 1m=3.281ft .)Check Your Understanding Light navels about 9 Pm in a year. Given that a year is about 3107s , what is the speed of light in meters per second?
- A fluid ounce is about 30mL. What is the voIume of a 12 fl-oz can of soda pop in cubic meters?The speed of sound is measured to be 342 m/s on a certain day. What is this measurement in kilometers per hour?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?
- In SI units, speeds are measured in meters per second (m/s). But, depending on where you live, you’re probably mole comfortable of thinking of speeds in terms of either kilometers per hour (km/h) or miles per hour (mi/h). In this problem, you will see that 1 m/s is roughly 4 km/h or 2 mi/h, which is handy to use when developing your physical Intuition. More precisely, show that (a) 1.0m/s=3.6km/h and 1.0m/s=2.2mi/h .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.”The arc length formula says the length sof arc subtended by angle in a circle of radius r is given by the equation s=r . What are the dimensions of (a) s, (b) r , and (c) ?
- A good-quality measuring tape can be off by 0.50cm over a distance of 20m . What is its percent uncertainty?(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?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.)