You have been picked to be a guest star on the show Terra Noval In your episode,

Question

You have been picked to be a guest star on the show Terra Noval In your episode, the colony is starving until you and your team manage to trap and kill a Tyrannosaurus Rex - which, of course, is an enormous amount of food. It is decided to bake it whole (somehow you seem to have an oven big enough.) Unfortunately, no one has any idea how long to bake it for - the only cookbooks you have deal with turkeys. But fortunately, YOU have taken PHYSICS! a) How should the time of cooking t behave as a function of the total mass of the animal m (in kg), the density of dinosaur flesh p (in kg/m3), the thermal conductivity (of dinosaur flesh) k (in kg m/(s3K)), and the specific heat (of the dinosaur) c(in m /(s2K))? (Should t be proportional to m and/or to k and/or to c or should it vary more, or less, rapidly than linearly?) (K here refers to Kelvins.) Do not forget to show your work, including all relevant equations, and explain what you are doing in ENGLISH. (N.B. This problem is like problem 1.44 in the online homework.) b) If p, k, and c are well-approximated by the values for a turkey (a good first guess, since all living flesh is mostly water - not to mention, birds are the descendants of dinosaurs!), how long will it take to bake your catch (a typical T Rex) as if it were a turkey (i.e., same temperature, etc.)? A Skyhook balloon with a scientific payload rises from the ground at a rate of 1000 feet per minute, taking data the whole time. At an altitude of 30,000 feet the balloon bursts and the payload freefalls. (Such disasters do occur!) You need at least 35 minutes' worth of data. Do you have it, or will you have to send up another one (they are expensive!)? Some idiot is standing underneath, watching, open-mouthed, when it falls. If you ignore air resistance (i.e., "freefall"), what is the payload's speed at impact on top of the idiot? (N.B. This problem is like problem 2.56 in the online homework.) (Hint: it really helps to draw a graph of velocity vs time.) (You can do this in non-SI units if you like, BUT REMEMBER: NO NAKED NUMBERS!!!)

Explanation / Answer

1> mass = m
density =

thermal conductivity = k

specific heat = c

time taken = t

heat supplied = mct

heat consumed = kA/l

where A = area of dinosaur flesh

l = length of dinosaur flesh

heat supplied = heat consumed

mct = kA/l

t = kA/mcl

Hence k is directlly proportional to k

inversely proportional to m

inversely proportional to c.

2> speed = 1000 ft/min

at altitude of 30000 ft, data taken = 30 minutes

Since the payload will have inertia, time taken to reach maximum height

t = u/g = 1000/ 32.2*60*60 = 0.009 minutes

Hence we do not have 35 minutes of data and we will need to send another one up!

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