?V.I. Arnold Mathematical Methods of Classical Mechanics Second Edition Page 50?

Determine the major semi-axis of the ellipse which the center of the earth describes around the common center of mass of the earth and the moon. Where is this center of mass, inside the earth or outside? (The mass of the moon is 1/81 times the mass of the earth.)

NOT JUST 'INSIDE' OR 'OUTSIDE', with specific solution.

If the cross-sectional area of the manometer is 10 cm² and the amount of water added is 50 ml, what will be the height difference between the two arms of the manometer?

How do the following types of radiation interact with matter?

a) radio waves

b) microwaves

c) infared

d) visible light

e) ultraviolet, x-rays and gamma rays

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a) How do wavelength and frequency change as you move through the EMR spectrum?

b) What is special about the visible range of the EMR spectrum?

(Please type your responses and be succinct.)

Use the quantum particle wavefunctions for the kinetic energy levels in a one
dimensional box to qualitatively demonstrate that the classical probability distribution
(any value of x is equally allowed) is obtained for particles at high temperatures.

A box of physics books slides down a ramp inclined at an angle of 40 degrees to the horizontal. The total length of the ramp is 10m. The coefficient of kinetic friction between the box and the ramp is .2 for the top 8m and zero for the bottom 2m. Upon reaching the bottom of the ramp, a spring bounces the box back upward.

(a) Find the distance that the box travels back up the ramp on the return bounce.

(b) Your answer shouldnt depend on the spring constant of the spring at the bottom. Why not?

1. Please answer the following questions.

    ?What is equipartition principle? Why is the latent heat of vaporization

     for water so much larger than the latent heat of fusion?

    ?Describe the Gauss's Law. If our space is four dimensional, what will

      you expect the r dependence of the coulomb's law?

Imagine you have two converging lenses. Lens A has a focal length of 12.5 cm. Lens B has a focal length of 50.0 cm. The diameter of each lens is 6.50 cm. Assume a near point of 25.0 cm.

a)     How could you make a microscope with 4x magnification using these lenses?

b)     How could you make a telescope with 4x magnification using these lenses?

c)     Which of these is more practical? Why?

? Explain why entropy in an isolated system must reach its maximum. Biological system use energy (ultimately from the sun) in organizing highly ordered organisms, such as humans. Does this mean that biological system violate the second law of thermodynamics? Explain your answer. (5%)

Derive the exponential expression that describes the radioactive decay in the number of nucleotides, N over a time, t. Give an example of another physical phenomenon which is described by an exponential relationship such as this. b) A radioactive nucleotide has a half-life of 20.0 years. What fraction of an initially pure sample of this nuclide will remain at the end of (i) 50.0 years, and (ii) 100.0 years. c) Give an account of nuclear binding energy, accompanied by a labelled graph of binding energy per nucleon versus the number of nucleons that explains why some elements undergo fission reactions whilst some undergo fusion reactions. d) Calculate the nuclear binding energy in MeV of the 92 protons and 146 neutrons in the nucleus of a 238U atom. Note the following: the mass of 238U atom = 238.05079 u; the mass of the Hydrogen atom = 1.00783 u; and the mass of the neutron = 1.00866 u, where u is the atomic mass unit.

(a) Describe the nuclear processes of alpha and beta decay, and describe what parameter is increasing in the nucleus as a result of these decays. [3] (b) Where a stationary neutron combines with a proton to form a deuteron, a gamma ray of energy 2.2233 MeV is emitted. The masses of the proton and the deuteron are 1.007276467 u and 2.013553212 u, respectively. Determine the mass of the neutron, stating any laws used and defining variables. [4] (c) Uranium ore mined today contains 0.72% of fissionable 235U, with the remainder being 238U. For use in a reactor, the ore needs to be refined to increase the fraction of 235U to 3%. How many years ago would natural uranium ore have been a practical reactor fuel, with a 235U/238U ratio of 3.0%? [3] Take 235U to have a half-life of 7.0 × 108 y and 238U to have a half-life of 4.5 × 109 y

Present an application of a wave phenomena to studies in a field of science or engineering other than physics. Your examples may be taken from, but are not limited to, sound engineering, instrument making, medical imaging, non destructive testing, oil explorations, earth quake prediction, and Tsunami warning systems. No matter what field you choose the wave phenomena.

what media, if any, do the waves propagate?

Are the waves in this application transverse, longitudinal, or both? If either transverse or longitudinal waves are missing from the application explain why?

On what parameters of the media (pressure, temperature, mass, density,... ) does the wave speed depend?

In general, what is the relationship between the wavelength, the frequency, and the wave speed?

Define diffraction, diffusion, constructive interference, and destructive interference as general properties of waves.

Discuss how diffraction, diffusion, constructive interference, and destructive interference appears in your application. If it does not appear explain why not.

Choose true or false for each statement regarding concave mirrors.
true false  If an object is placed 4.1 cm from a concave mirror with f = 4 cm, then its image will be enlarged and real.
true false  A concave mirror produces an enlarged real image when the object is placed just beyond its focal point (Region 2).
true false  If an object is placed 7.9 cm from a concave mirror with f = 4 cm, then its image will be enlarged and real.

Choose true or false for each statement regarding convex mirrors.
true false  If an object is placed 7.9 cm from a convex mirror with f = 4 cm, then its image will be reduced and real.
true false  A convex mirror produces a reduced real image when the object is placed far beyond its focal point (Region 1).
true false  If an object is placed 4.1 cm from a convex mirror with f = 4 cm, then its image will be reduced and real.

Choose true or false for each statement regarding the sign conventions for mirrors.
true false  Virtual images appear behind a mirror and have a positive value for the image distance.
true false  The magnification m is positive for inverted images.
true false  The magnification m is negative for upright images.