A little time ago I published a recommended High School Science test paper, designed to better prepare those who were planning to pursue Natural Sciences of all kinds at a “University”. It’s been revisedf a little:-
Improved science paper for GCSE, devised by David Davis for the Libertarian Alliance, a free-market, civil liberties and Classical liberal education think-tank and publishing house in London, originally issued in Sept 2009.
TIME ALLOWED: THREE HOURS
1 Estimate the DC current, flowing in a one-turn copper coil which follows the earth’s equator, which would cancel the Earth’s magnetic field at either pole. (Take the horizontal component of field at lat 86o 30` N and longitude approx 30o W to be 0.18 gauss: vertical component = 0.9 gauss. State the relationship between the c.g.s Gauss unit and the MKS Telsa unit.)
2 Calculate the cross-sectional area of a square copper turn, smoothed and unblacked but not polished, and fully suspended, whose surface temperature will not exceed 800 K in dry air temperature of 310 K. Assume the specific conductivity of the supports to ground as being 0.2 Joule m-2 sec-1. If the young’s Modulus of the supporting material is 50GPa, calculate the minimum cross-sectional area of each support assuming you place one every five metres of copper conductor. State how many supports will need to be ordered to circle the Earth at your designated line, and, in still air, their minimum height to prevent the ground temperature rising more than 5 K.
3 Calculate the gravitational field strength existing between the Milky Way and a hypothetical galaxy 13 billion LY away. Use 2E42 Kg for the mass of the Milky Way: make an informed estimate of the mass of your further galaxy, stating clearly any assumptions you have made. Using your figures thus obtained, and your informed estimate of the mass of Galaxy M31 whose data regarding mass, position and relative speed you already will know, decide where approximately to place your spacecraft so that the resultant vector of gravitational forces from the three galaxies on it is zero, assuming no other interactions.
4 Estimate the cross-sectional area of each of two Duct-tape fixtures, (tape is of 48mm width and 0.5mm thickness) applied always parallel to the direction of force, which would be required to separate reliably two opposite charges of 1C each at a distance of one meter in free Space. (Young’s Modulus of Duck Tape is assumed to be 4E9 Pa.)
5 Estimate the number of moles of human DNA on the Earth as of now, its total estimated mass, and the molar mass of human DNA. (Assume that one haploid human genome, complete, = 1 molecule. Also assume that the mean volume of all human cells is about 1.9 picoLitres.)
Ignore human gametes in this answer, but also estimate the total number of human gametes present on the planet at any moment. Use your knowledge of human population trends and age-band-statistics to derive as accurate an estimate for this number as possible, differentiating male from female gametes. State the assumptions you have made about the relative frequency of each gamete.
6 Calculate the reduction in heat capacity of the Gulf Stream over a calendar year, caused by a wind farm of 10,000 turbines directly in the path of the airstreams above it at latitude 55oN, each turbine having an installed generating output of 100Kw, at a height of 100M and operating at a 16% duty cycle. Use your own knowledge of geography, natural climate movements, astronomy, the heat capacities of water and moist air. (You may assume that the Sun’s radiated power output is about 3.92E26 Watts and is deemed for this question to be constant.) Estimate the extra mass, surface area and volume of North Polar ice that would build up in the Barents, Norwegian and Greenland Seas in one year, assuming that no other areas are affected, as a result of this set of turbines. (For quickness of solution, assume polar ice above latitude 65 radiates IR into space at 25 Watts/M2 at all temperatures above 230K.) Specific heat capacity of water in liquid phase = 4.18KJ per Kg per degree K.
7 You are to deliver a shell weighing 1.5 imperial tons, at a range of 60 miles, from a barrel of diameter 460mm, at a target at the same elevation as the emplacement. (g = 9.81m/s2) Devise a suitable mathematical model from which the answers could be derived, and then calculate, in no particular order:
(a) The barrel length
(b) The time of flight
(c) The maximum height reached by the projectile
(d) The required muzzle velocity at 40o barrel elevation
(e) The mean gas pressure (assume uniform) in the barrel
(f) The acceleration of the projectile in the barrel
(g) The muzzle velocity (you may neglect air resistance for this question.)
8 Calculate the number of 25Kg sacks of rice that would be required, and also the total volume of rice grains in cubic miles, if the Great King had been able to grant the wish of the Resident-Court-Mathematician who had invented Chess for him. The inventor asked for “one grain of rice on the first square, two on the second, four on the third, eight on the fourth, sixteen on the fifth…..”. Assume a grain of rice is a cylinder of length 7mm and diameter 1.25mm and that they pack approximately efficiently. State your grain-packing-density assumptions in your answer.
If the sacks used above are made of polythene, and must be 850 microns thick, estimate the area of film to be manufactured including excess cutting-flash needed on the packing lines, this amount’s mass, and the number of barrels of Saudi Heavy Crude that may have been used to make it. Use your knowledge of thermal cracking procedures, the mean composition of linear alkanes in Saudi heavy Crude, and also of the average mass of a “barrel” and how much of this is realistically convertible into monomers for this question’s use. Density of polythene (MDPE type) is about 0.932 g/cm3.
9 Calculate the rate of change of mean global temperature, stating in which direction it will move, if unbroken polar ice caps cover the Earth down to latitudes 50 North and 50 South. Assume the boundary is a straight line in both cases. State what percentage (to 3sf) of the earth’s current land area would have to be moved by tectonic drifting to be below latitudes 50N/50S, to bring about the cooling you have calculated.