ymond A. Serway, Chris Vuille - College Physics-Brooks Col... 51 / 1050 - 233% + 49 1. The period of a simple pendulum, defined as the time neces- sary for one complete oscillation, is measured in time units and is given by add 9. V wid nun e T= 2πT 80 10. QC cant ures 50 51 where { is the length of the pendulum and g is the accelera- tion due to gravity, in units of length divided by time squared. Show that this equation is dimensionally consistent. (You might want to check the formula using your keys at the end of a string and a stopwatch.) 2. (a) Suppose the displacement of an object is related to time according to the expression x = Bt². What are the dimensions of B? (b) A displacement is related to time as x = A sin (2πft), where A and fare constants. Find the dimensions of A. Hint: A trigonometric function appearing in an equation must be dimensionless. figu this answ 11. How 3.788 12. The s Expre (b) fi 13. A rect ± 0.1) rectan 52 23 104,652 2 AUG 31 17 O tv 5 2 NA X W

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.)

Check Your Understanding A high school track coach has just purchased a new stopwatch. The stopwatch manual states the stopwatch has an uncertainty of ±0.05 s. Runners on the track coach’s learn regularly clock 100-rn sprints of 11.49 s to 15.01 s. At the school’s last track meet, the first-place sprinter came in at 12.04 s and the second-place sprinter came in a 12.07 s. Will the coach’s new stopwatch be helpful in timing the sprint team? Why or why not?

Show that, when SI units for 0 and 0 are entered, the units given by the right-hand side of the equation in the problem above are m/s.

Convert 13.7 billion yeans (the age of the Universe) to the appropriate SI unit. Be sure to report your answer with the correct number of significant figures.

What are you feeling when you feel your pulse? Measure your pulse rate for 10 s and for 1 min. Is there a factor of 6 difference?

The pendulum on a cuckoo clock is 5.00-cm long. What is its frequency?

(a) Estimate the density of the Moon. (b) Estimate the diameter of the Moon. (c) Given that the Moon subtends at an angle of about half a degree in the sky, estimate its distance from Earth.

For the circvit shawn t2 =0.89 mA 5.68 B,-27.0 Kん こ Re =10.1 K Vz =85.63 Determire the Potchal acvOSS the souce Cin VJ 工 R, Re

Sketch is mendatory