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What is the direction of the induced current in each circular loop shown when the current I in the long wire is decreasing? Answer as clockwise or counterclockwise for each
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- 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) ?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?Mount Everest, at 29,028ft , is the tallest mountain on Earth. What is its height in kilometers? (Assume that 1m=3.281ft .)
- A good-quality measuring tape can be off by 0.50cm over a distance of 20m . What is its percent uncertainty?An electron has a mass of 9.1110-31kg . A proton has a mass of 1.6710-27kg . What is the mass of a proton in electron-masses?A surveyor measures the distance across a river that flows straight north by the following method. Starting directly across from a tree on the opposite bank, the surveyor walks 100 m along the river to establish a baseline. She then sights across to the tree and reads that the angle from the baseline to the tree is 35 . How wide is the river?
- 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.)A generation is about one-third of a lifetime. Approximately how many generations have passed since the year 0 AD?Check Your Understanding Given that 1 lb (pound) is 4.45 N. were the numbers being output by SM_FORCES too big or too small?
