# PSY380 Test (2014)

In 1610 the Church started its attack on Galileo. They stated: i) Suppose a cannon be fired, first due east, then due west. In one case the shot has the velocity of the earth as well as that of the force of the powder, in the other case only the difference of the two. But, in fact, no such difference is noted, and therefore the earth does not move. ii) If the earth rotates as fast as Copernicus says, birds could not keep up with it! …  Briefly, use physics to answer these two charges. (15%)

In both cases it depends on what inertial system of reference one takes into consideration.
If the inertial system is the earth itself, the gunshot will not have different velocities due east or west because the velocity of the shot is measured relatively to the earth itself. Hence an observer on the ground can not tell if the inertial system of reference is moving or is standing (second principle of relativity- there is no experiment made inside an inertial system that can tell to an observer if that system is moving or standing.)  If the inertial system of reference is a star, then of course the shot to the east will have a greater speed than a shot to the west and this can be seen.
Again it is a matter of the inertial system of reference taken into consideration. At very low altitudes air is rotating together with the earth (because of the friction forces) and hence in an inertial system of reference of a star a bird will always have a speed greater to the east than to the west.  If the inertial system of reference is the earth the air which is rotating together with the earth will ‘help’ the bird fly faster to the east.

It has been estimated that the Earth contains $10^{9}$ metric tons of natural uranium that can be mined economically. Of this total, 0.7% is 235U that can be fissioned to produce energy. Assume 208 MeV per fission; $1 MeV = 1.6*10^{-13} J$; 235 g of U has $6*10^{23}$ atoms.    (15%)
How many atoms of 235U are there in $10^{9}$ metric tons of natural uranium?

The number of atoms is
$N = 6*10^{23} *10^{9}*10{^3}*10{^3}* \frac {0.7}{100} *\frac{1}{235}=1.787*10^{34}$ atoms

What is the energy release possible from the 235U in $10^9$ metric tons of natural uranium?
$E = N *E_{fission} =1.787*10^{34} *208 *1.6*10^{-13} =5.95*10^{23}$ J

If all the world’s current power needs ($7*10^{12}$ W) were supplied by 235U fission, how long would this supply of uranium last?
$P =E/time$

$Time = E/P = 5.95*10^{23}/7*10^{12} =8.5*10^{10} s = 2694 years$

The first atomic bomb released energy equivalent to 20 kilotons of TNT. If 1 ton of TNT releases $4×10^{9} J$, how much uranium was consumed through fission in the bomb? Assume 208 MeV per fission; $1 MeV = 1.6*10^{-13} J$; 235 g of U has $6*10^{23}$ atoms. Hint: use the energy released and the energy per unit mass of uranium. (15%)

Total energy released is $E_{tot} = 4*10^{9}*20*1000 = 8*10^{13} J$
One gram of Uranium (235) releases the energy $E_1 =6*10^{23}*208*1.6*10^{-13} /235=8.5*10^{10} J$

Total mass of $U(235) = E_{tot}/E_1 =8*10^{13}/8.5*10{^10} =941.2 grams$

However the total mass of the bomb can not be told since U(235) is an isotope of the U (which is mainly formed by U(238), which is not fissionable).

You were stranded on a desert island with John, who wears glasses. He manages to start a fire. Is John nearsighted or farsighted? Explain how you know. Explain what nearsighted and farsighted mean, and how glasses correct the condition.                 (15%)

John is farsighted. If the glasses can start a fire then the lenses must be convex (the image of the sun is real, inverted and smaller). A convex lens added to the eye (which has also a convex lens) forms the image always at a shorter distance than normal without the lens.
Nearsighted or myopia is the defect of the eye in which the image of an object is produced in front of retina when the eye is relaxed. Farsighted or hyperopia is the defect of the eye in which the image of an object is produced behind of retina when the eye is relaxed.

Why?                                            (20%)
a. Why is the sky blue?
b. Why are clouds white?
c. Why is the sunset red?
d. If you are looking at a rainbow, where is the sun and why?

The sky is blue because the solar radiation is scattered by the molecules in the atmosphere. The blue color (shorter wavelength)  is more scattered by the molecules of air than the red color (longer wavelength) and hence the color of the sky to an observer looking at another part of the sky than the sun appears to be blue.
The clouds are formed by invisible drops of water (or ice). In a large cloud the light is mainly reflected (though all the visible spectrum) by the small droplets of water. Thus the clouds appear to be white.
Again the light is scattered by the molecules of the air in the atmosphere. At sunset the light coming from the sun is nearly tangent to the earth surface and hence its path to an observer is very long. Because of this almost all of the blue color (which is more scattered than the red color) is scattered by the air, leaving un-scattered only the red portion of the spectrum.
In a rainbow the light of the sun is diffracted by the small particles of water left in the atmosphere by rain. Thus the sun must be at the opposite part of the sky than the rainbow.