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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.)dV An oil tanker aground on a reef is forming a circular oil slick about 0.1 foot thick. To estimate the rate (in cubic feet per minute) at which the oil is leaking from the tanker, it was found that the radius of the slick was increasing at 0.31 foot dt dR dV per minute (- = 0.31) when the radius R was 400 feet. Find using T 3.14. dt dt Tanker A=TR? V=0.1A R dV ft3 /min dt (Type an integer or a decimal. Round to the nearest whole number as needed.)wwife pevity T00ml sample of blood has a mass of 53.2 g a)Caleulate the density of the blood. W Calculate the specifie gravity of the blood. Answer
- Archinede's Assignment > a metal sphere whose diameter ;s 6 Ocm weiphs 2000 N. How much would this sphere veigh if placed water (density Suzo? 1000 2) A weoden boat is placed in a freshuater labelgaroo Il ţ of tha boat remeins aboue the water level, fo00 what is the dengity of the boet?Carbon dioxide is metered into an air conduit which is 12 sq ft in cross-sectional area at a constant rate of 7.0 lb per hour. A sample of the mixture downstream was analyzed by an Orsat apparatus and con- tained 11 and 1/2 per cent CO2, by volume. What is the air velocity?Let ρAl represent the density of aluminum and ρFe that of iron. Find the radius of a solid aluminum sphere that balances a solid iron sphere of radius rFe on an equal-arm balance.
- Although aluminum foil is very thin, it does have some thickness. We cannot typically “measure” the thickness ofsuch a thin object directly, but the thickness can be determined “indirectly”. Assume that the density of aluminum is2.70 g/cm3 and that the shape of the square aluminum foil is a rectangular cuboid. Then by using the experimental data of the length of the aluminum square 5.10cm, Width is 5.00cm and the mass of aluminum is 0.11g. Determine the thickness of aluminum foil in micrometers. Show your work.Ź. Determine +he dimensions inthe mut system for (a) the product of mass times velaciity, b) the prodenct of force H'mes volume .(C) the pressure divided bythe volu me and d) Klnetic eneryy d ivided area,lutorial problem For the following liguid level- Flow rate in a tank of outer penimeler of(28)xm amd thickness (0-5)cm The steady-s ralues are faken from Laborahory:- hcm) 100 150 27 200 38 250 52 Determine time constant of the haok (theorehical cnd exper.menlal then compare between them, also, determine response of Liguid level what do you expect the liguid-level be when the flow increased from 100 /h to 120 e/h?
- When researchers find a reasonablycomplete fossil of a dinosaur,they can determine the massand weight of the living dinosaurwith a scale model sculpted fromplastic and based on the dimensionsof the fossil bones. The scale of themodel is 1/20; that is, lengths are 1/20actual length, areas are (1/20)2 actualareas, and volumes are (1/20)3 actualvolumes. First, the model is suspended from one arm of a balanceand weights are added to the other arm until equilibrium isreached. Then the model is fully submerged in water and enoughweights are removed from the second arm to reestablish equilibrium. For a model of a particular T. rex fossil, 637.76 ghad to be removed to reestablish equilibrium.What was the volumeof (a) the model and (b) the actual T. rex? (c) If the density ofT. rex was approximately the density of water, what was its mass?A car engine moves a piston with a circular cross sectionof 7.500 ± 0.002 cm diameter a distance of3.250 ± 0.001 cm to compress the gas in the cylinder. (a)By what amount is the gas decreased in volume in cubiccentimeters? (b) Find the uncertainty in this volumeThe aquation of o friopuartivne. longelidinal cucve in ciese is, Y=10x103sin 880 a (t-) where. 330 all the guentities aue in $T. units. Find fhe o) Fuquny (6).Qaualength weloaly of wane.