Problem 2. Kinetic energy K has dimensions kg · m²/s². It can be written in terms of the momen- tum p and mass m as p2 K = 2m (a) Determine the proper units for momentum using dimensional analysis. (b) The unit of force is Philia (0.1) the newton N, where 1N 1kg · m/s?. What are the units of momentum p in terms of a newton and another fundamental SI unit?

(a) If your speedometer has an uncertainty of 2.0 km/h at a speed of 90 km/h, what is the percent uncertainty? (b) If it has the same percent uncertainty when it reads 60 km/h, what Is the range of speeds you could be going?

(a) A car speedometer has a 5% uncertainty. What is the range of possible speeds when it reads 90 km/h? (b) Convert this range to miles per how. Note 1 km = 0.6214 mi.

CASE STUDY On planet Betatron, mass is measured in bloobits and length in bots. You are the Earth representative on the interplanetary commission for unit conversions and find that 1 kg = 0.23 bloobits and 1 m = 1.41 bots. Express the density of a raisin (2 103 kg/m3) in Betatron units.

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.)

Problem 2. Kinetic energy K has dimensions kg m² /s². It can be written in terms of the momen- tum and mass m as p2 K 2m (a) Determine the proper units for momentum using dimensional analysis. (b) The unit of force is hill Philiy %3D (0.1) the newton N, where 1N 1kg · m/s?. What are the units of momentum p in terms of a newton and another fundamental SI unit?

Please add the solution to the problem

Kinetic energy K has dimensions kg ·m2/s2. It can be written in terms of the momentum p and mass m as K =p2/2m (a) Determine the proper units for momentum using dimensional analysis. (b) The unit of force is the newton N, where 1N = 1kg · m/s2. What are the units of momentum p in terms of a newton and another fundamental SI unit?  Show complete step-by-step process and solution.

A light-year (ly) is the distance light travels in one year (at speed of 2.998 ×× 108 m/sm/s ). An astronomical unit (AU) is the average distance from the Sun to Earth, 1.50 ×× 108 kmkm.1 yearyear = 3.156 ×× 107 ss. a. How many meters are there in 6.50 lyly ? Express your answer using three significant figures.       b. How many AUAU are there in 6.50 lyly light-year?   Express your answer using three significant figures.

According to Timothy Treadwell in 2001 "Now, the bears I live with average, the males are on average twelve hundred pounds. They're the largest bears in the world and they've been clocked at 41 [mph] and they've run a hundred meter dash in 5.85 seconds which human on stimulants doesn't even approach. a. Compute the speed of a grizzly bear using Mr. Treadwell's hundred-meter statement. b. Compute the momentum of a grizzly bear using the speed you calculated in part a. and the average mass stated by Mr. Treadwell. c. How fast would a 250 lb man have to run to have the same momentum you calculated in part b? d. How fast would a 4000 lb car have to drive to have the same momentum you calculated in part b?