Assignment: Jurisphagous Food Consumption Rates of
Tyrannosaurus rex
(or How many teachers does it take to feed one T. rex for a year?)
We will assume our T. rex is the size of Sue, a large specimen found in South Dakota in 1990 by Sue Hendrickson, then excavated and partly prepared by the Black Hills Institute of Geological Research of Hill City, South Dakota. Sue was claimed by a number of other groups, leading to prolonged court action, and eventually sold to a consortium of McDonald’s and the Disney company for US$7.6 million dollars, who gave her to the Field Museum of Natural History in Chicago. The mass of Sue is estimated by looking at the bone structure, re-contructing the muscle structure and size of the muscles from the bone structure, then working out a mass from the normal density of muscles and body in known animals like crocodiles. And to work out the number of teachers, we must work out how much energy a T. rex needs for a year to live, and how much energy one average teacher would supply.
a) Costs of acquiring Sue:
1)Auction houses charge a commission for advertising an object, and running the auction to sell the object. Sotheby’s charged 10% as a “buyer premium”, that is, a buyer must pay 10% more than the final bid. What was the total amount paid by McDonalds and Disney to acquire Sue?
2)If Sue had been bought by a New Zealand museum, with the exchange rate at NZ$1.00:US$0.7832
i)find Sue’s price in NZ dollars,
ii) If New Zealand had paid the Black Hills Institute the US$209,000 it cost to excavate and partially prepare the skeleton, and if New Zealand charges a tax of 15% on imported goods (including fossils like Sue), and if it would have cost at least NZ$35,000 to ship Sue to New Zealand, what would have been the final cost for a museum in New Zealand to have bought and shipped Sue to that country?
b) *Energy needed by a warmblooded T. rex :
We will assume, as in Jurassic Park and Lost World, that our T. rex was an active hunter and warm blooded and needed energy at a similar rate to a mammal like a lion. Warm blooded (endothermic-regulating its body temperature by internal controls) animals burn energy to produce the heat to keep a stable body temperature (37.60C for humans), as well as energy to move and hunt.
Mass of Sue, the T. Rex, is estimated to be about 6400 kg.
You will need to work out the number of seconds in one year.
Watts of energy used by mammals (joules of energy used in one second) = 10.96 x (body mass in kg.) 0.7
Use the information above to calculate the energy needed (in joules) for a T. rex for one year.
(show working clearly)
c) Food value of an average teacher:
We will assume the teacher has a body mass of 72.5 kg.
Predators only digest and use about 90% of the food they eat.
Meat has a food value of 7 x 106 joules per kg of body mass.
Use this information to calculate the usable energy (in joules) supplied by one average teacher.
(show working clearly)
d) Number of teachers needed:
Use your calculations in b and c to work out, to 3 significant figures, the
number of teachers needed to keep one full grown T. rex alive for a year.
(show working clearly)
e) Energy needed by a cold-blooded T.Rex:
If our T. Rex turns out to be ‘cold-blooded’ (ectothermic-using external things like sun and shade to control body temperature), more like a lizard or crocodile, it will need less energy, so its energy use then becomes
Watts of energy used by lizard (joules of energy used in one second) = 0.84 x (body mass in kg.)0.84
How many teachers will the T. rex need per year if it is cold blooded?
(show working)
f) A breeding pair of T. rex:
If we assume we can genetically re-create a breeding pair of T. Rex and confine them to the South Island of New Zealand, and if the ratio kg. of prey : kg. of predator is normally 97:3 for warm blooded predators, how many teachers will need to be living in the South Island of New Zealand to support our pair of T. rex? Give your answer in standard form(scientific notation) and rounded to 3s.f.
(show working)
g) Slightly more modern problems:
1)Assuming the two man-eating male lions in the film The Ghost and the Darkness were young males and only weighed 250 kg. each, how many railway workers and villagers would these man-eaters have taken in a year? Give to 2 s.f. (This is a true story.)
2) A full grown male tiger can have a mass of 285 kg. How many cows near a village in India would a tiger have taken in a year if an average cow is 210 kg? Give to 2 s.f. (This is a
true story – to save the tiger, a special fund is used to pay the villagers for the cows so they
won’t poison and kill all the tigers.)
*equations for energy use are taken from Fastovsky and Weishampel