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- Consider the equation s=s0+v0t+a0t2/2+j0t3/6+s0t4/24+ct5/120 , were s is a length and t is a time. What are the dimensions and SI units of (a) s0 , (b) v0 , (c) a0 , (d) j0 , (e) s0, and (f) c ?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 .Roughly how many heartbeats are there in a lifetime?
- A generation is about one-third of a lifetime. Approximately how many generations have passed since the year 0 AD?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?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.)
- 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) ?If P=500, What is the length of BE, BE? What are the value of α and Φcan someone explain what physics formula should we use for this physics question,and show the solution step by step why answer is 19m/s?
- The period of a simple pendulum, defined as the time necessary for one complete oscillation, is measured in time units and is given by T=2πlg where l is the length of the pendulum and gis the acceleration due to gravity, in units of length divided by time squared. Show that this equation is dimensionally consistent.Present the conversion of Jm-1 to its simplest MKS unit, then identify the derived dimensions for the said unit.If massQ/mass A in AQ= 0.271 and mass Q/ mass A in AxQy = 0.362, what is the formula of AxQY?