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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.)When a 10,000-rn runner competing on a 400-rn track crosses the finish line, what is the runner’s net displacement? Can this displacement be zero? Explain.The CERN particle accelerator is circular with a circumference of 7.0 km. (a) What is the acceleration of the protons (m=1.671027kg)that move around the accelerator at 5of the speed of light? (The speed of light is v=3.00108m/s .) (b) What is the force on the protons?
- 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) ?on a Past time Job, you are sked to bay inderm ron d of densty oo y/m langth 32.4 Cm and मन a dinmeter 2.20 cm from a Storeye muchinist. Calculute hesume the to a he weignt of the tod, al. Free fon annerntion is : 9.80 m/s Jhe Exfsess ansuare numerreHIN in newHonsFast plz... I'll rate hand written plz
- hi please solve this physics problem . Please make sure its correctA particle bertorms linear s-H.M. along path :t 20 cm long- The barticle star= fram a distonce of 2 cm from mean $osition moves towords the besithve extremity- Find its ebech Ļ phace of moFon when the displacenmnent is S com.Please answer im confuse , I will give a high rate
- 1.95 farticle moves a circleof radius constant anguel speed Wo. At with time t=0 i# Starts to Slow down So that sts లరపా -ala deckibattona). is ngulal Show that to test after a time Wald trave lle d (a) it comes (6) and has a distance Riw2 If the bevo lutions ber minute loocm and develops a Constant ad/s. ca) how wil same frtiche ts trove ling at 36ts. in a Circle of 8adius declaiation of 5 it be before it long to sest and 6) what distonce will it Comes have trauelled?pength aam ulire uibeales in fandamenal. of mode St feequency 80flz.then l relocily of gseumnd uode. in aie is Ca) 330 m/s (6) 320 m/3 c) 900 m/ ca) 288 m/s.HOMEWORK Wednesday. May a1 2 d= Bem If the mopretic fred at VI print P is 3x104 T, In what is the curreat I7 -P-