Pad 11:50 AM * 75%. edu 7. Great moments in television: The engineer reported to

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Pad 11:50 AM * 75%. edu 7. Great moments in television: The engineer reported to the captain that the shields were failing. The captain asked the science officer how long they would hold up. The science officer reported that they would last another 47.18 seconds. Without knowing much about shields and photon torpedoes, what do you think of the science officer's answer? Explain your reasoning. The "world's greatest forensic anthropologist" and the "king of the lab" were at a murder scene. The king of the lab found a worm near the corpse. He said these worms move one foot per day and the worm was 38.3 inches from the body. The world's greatest forensic anthropologist then calculated that this meant the time of death was three days, four hours, and thirty-six minutes ago. Without knowing much about worms and corpses, what do you think of her calculation? a. b. 8. The speed of sound can be calculated from atmospheric pressure and density. You could look up the formula but let's pretend you don't know how. Standard atmospheric pressure is (very nearly) 100,000 pascals. One pascal is one kilogram per "meter second squared" (1 kg/ (ms)) Notice that the seconds are squared but the meters are not. The density of air is about 1.2 grams per liter. One liter is 1000 cm Using only the information above, estimate the speed of sound in air Now look up a measured value for the speed of sound in air, Calculate the relative error of your estimate. Express your result as a percentage. a. b. 9. While studying a problem in fluid dynamics, a student came up with some equations involving several variables that have the dimensions listed in the table below. Determine whether each equation (a through d) is dimensionally consistent or inconsistent. Note: the symbol r represents a radius and the symbol A represents an area. [m]= M (5)L 4R2 e) Can a consistent equation be wrong? f) Can an inconsistent equation be right? 10. The Schwarzschild radius of an object is the radius of a sphere of equivalent mass that would have such intense gravity that light could not escape (the object would be a black hole)The G-6.7x10"m kg *. The speed of light is approximately c = 3.0x10, mt/s . The mass of the Earth is 6.0x10 kg x Using only this information,

Explanation / Answer

7) b)

given the worm moves 1 foot a day, that means 12 inches in (24*60)=1440 minutes

hence it moves 38.3 inches in (1440*38.3/12)=4596 minutes=3 days &276 minutes=3 days, 4 hours and 36 minutes

therefore her calculation was absolutely right.

8) a) Given, P=106 kg/(m-s2), density, d=1.2 g/L= 1.2 kg/m3

From unit analysis, unit of pressure/density is (m/s)2 is that of velocity, so we take square root of the ratio to get veocity

sqrt(P/d) =sqrt( (106 kg/(m-s2) )/(1.2 kg/m3) )

= 912.87 m/s

actual value: 343 m/s

Error=166%

9) a) LHS: L2T-1

RHS: MLT-2/ML-1T-1= L2/T Therefore it is consistent

b)LHS: MLT-2

RHS: sqrt(L2L2T-2L2T-1ML-1T-2ML-1T-1)=ML2T-3INCONSISTENT

c) LHS:L

RHS: the first ratio has dimensions L but the second ratio has dimensions L3

Hence INCONSISTENT

d) this is INCONSISTENT since the dimensions of first ratio is ML-1T-1 and that of P is ML-1T-2

e) yes, because dimensional analysis does not take into account the value of constants in an equation

f)NO, a dimensionally inconsistent equation can never be right

Question 10 is incomplete.

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