A dose of 3000cGy is delivered to a depth of 8cm where the percent depth dose is 76%. What is the dose to an underlying organ at 14cm depth where the percent depth dose is 58%? The dose at 14cm depth should be lower than the dose at 8cm for two main reasons - briefly explain these reasons.

You can determine the index of refraction of a substance by determining its critical angle. (a) What is the index of refraction of a substance that has a critical angle of 32˚ when in air? (b) What would the critical angle be for this substance when submerged in water?

1. Oil efficiency and national security. Right now, the United States is extremely dependent on oil for its automobile. Our dependence on oil has turned the Middle East into one of the most important areas in the world. If our automobiles were 40% efficient rather than 20% efficient, we would not have to import any oil. The global consequences of our oil inefficiency can reach as far as war in the Middle East. Getting more efficient use of oil is both a technological and a social issue. Who should pay for the research? The U.S. government? Private industry? Is this an economic question or is it a national security one?
2. Automobiles typically carry 100lb of gasoline. That has the energy content of 1500 lb of TNT. Is gasoline really as dangerous as this makes it sound? If so, why do we accept it in our automobiles? If not, why not? Do we accept gasoline only because it is a “known” evil?

- List three differences between the Sun’s core and the photosphere.

- Describe how sunspots are produced.

- Summarize in words the three steps in the proton-proton chain. Explain why energy is produced when hydrogen fuses into helium using Einstein’s E = mc² equation.

A ladder having a uniform density and a mass m rests against a frictionless vertical wall, making angle 48.0° with the horizontal. The lower end rests on a flat surface where the coefficient of static friction is µ_s = 0.370. A window cleaner with mass M = 2m attempts to climb the ladder. Given a ladder length of L, what fraction of the length of the ladder (x / L) will the worker have reached when the ladder begins to slip?

At time t = 9 sec, a particle of mass M = 3 kg is at the position (x,y,z) = (4,4,6) m and has velocity (2,1,-2) m/s.

1) What is the x component of the particle's angular momentum about the origin?

2) What is the y component of the particle's angular momentum about the origin?

3) What is the z component of the particle's angular momentum about the origin?

4) Now an identical particle is placed at (x,y,z) = (-4,-4,-6) m, with velocity (-2,-1,2) m/s. What is the x component of the pair's total angular momentum about the origin?

5) What is the y component of the pair's total angular momentum about the origin?

6) What is the z component of the pairs's total angular momentum about the origin?

7) Finally a thin rod of mass 9 kg is added between the two particles Since the particles are moving perpendicular to the line separating them and in opposite directions (you should convince yourself that this is true), then the particles + rod system rotates about its center of mass. What the angular frequency of rotation of the rod + particles system? (Note: The particles are moving perpendicular to the line separating them and in opposite directions (you should convince yourself that this is true), then the particles + rod system rotates about its center of mass.)

8) What is the magnitude of the total angular momentum of the system (particles plus rod)?

Gamma Ray Absorption

A gamma ray with energy E, hits a stationary nucleus of mass M and is completely absorbed. In terms of E, and M, find expressions for the following quantities.

a. The momentum of the nucleus after absorbing the gamma

b. The total relativistic energy of the nucleus after absorbing the gamma

c. The rest mass energy of the nucleus after absorbing the gamma

d. The kinetic energy of the nucleus after absorbing the gamma

Why do the voltage and current in the pickup coil cycle between negative and positive? Explain in detail using Faraday’s Law. Remember, Lenz’s Law is part of Faraday’s Law! Although it will not be covered explicitly in this class, this is known as alternating current.

a. How the magnetic flux through the loop changes as the magnet rotates (is the flux maximal when the magnet is horizontal or vertical on the screen? Why?)

b. How this changing magnetic flux works to create an emf (potential difference) in the coil which alternates over time (use the Faraday’s law equation)

What is the magnitude of the electric field at a point midway between a −6.5μC and a +5.0μC charge 10cm apart? Assume no other charges are nearby. Express your answer using two significant figures.

What is the magnitude of the force a +20 μC charge exerts on a +3.3 mC charge 39 cm away?

View the video "The Apple and the Moon," video 8 from  The Mechanical Universe and Beyond. In your own words describe Newton's three laws of motion. Give an example that illustrates each law. What are the four fundamental forces of nature? How do these force related to the forces which we may encounter in every day life (string forces, contact forces, spring forces, frictional forces)? How do the three laws of motion differ from Newton's other great achievement the Universal Law of Gravitation?   

There are two identical, positively charged conducting spheres fixed in space. The spheres are 34.8 cm apart (center to center) and repel each other with an electrostatic force of ?1=0.0765 N . A thin conducting wire connects the spheres, redistributing the charge on each sphere. When the wire is removed, the spheres still repel, but with a force of ?2=0.100 N . The Coulomb force constant is ?=1/(4??0)=8.99×109 N⋅m2/C2 . Using this information, find the initial charge on each sphere, ?1 and ?2 , if ?1 is initially less than ?2 . find q1 and q2.

A trucking moving at 25m/s emits a 400-Hz signal. The temperature that day is 40 o C.

a) Determine the speed of sound at 40o C

Determine the frequency and the wavelength experience by a stationary observer, when b) the truck is approaching the observer.

c) the truck is moving away from the observer.

d) the beat frequency if the observer hears the signal from a truck approaching and the signal from a trucking moving away at 25m/s,

e) the average frequency from part (c).

A cubical block of wood 0.100 m on a side and with density of 550 kg/m3 floats in a jar of water. Oil with a density of 750 kg/m3 is poured on the water until the top of the oil layer is 0.035 m below the top of the block. a) How deep is the oil layer? b) What is the gauge pressure at the block’s lower face?

A particle of diameter 0.2 μmand density 1 g cm-3is being carried by an airstream at 1 atm and 298 K in they direction with a velocity of 100 cm s-1. The particle enters a charging device and acquires a charge of two electrons (the charge of a single electron is 1.6 x 10-19C) and moves into an electric filed of constant potential gradient Ex= 1000 V cm-1perpendicular to the direction of flow. (Hint: The effect of gravity and drag force can be ignored.) (a)Determine the characteristic relaxation time of the particle. (b) Plot the particle trajectory assuming that it starts at the origin at time zero. (Please show detailed steps and equations used to plot the trajectory as marks will be given for that.)

An open container holds ice of mass 0.575kg at a temperature of -12.2?C . The mass of the container can be ignored. Heat is supplied to the container at the constant rate of 780J/minute . Part A How much time tmelts passes before the ice starts to melt? Part B. From the time when the heating begins, how much time does it take before the temperature begins to rise above 0 Degrees Celsius