PH 314 Homework Set #2
Spring 2008

Assigned: Monday 04/07/2008

Due: Monday 04/14/2008 3:00 PM

When writing a solution, you must explain carefully and concisely, and demonstrate that you understand. When writing in English, you must use complete sentences. (A complete sentence has both a subject and a predicate.) When writing in mathematics, you must use complete equations. (A complete equation has a right-hand-side, an equal sign and a left-hand-side). When grading the homework and exams, the points awarded will be broken down into three main categories: 1) translate (translating the problem from English sentences to mathematical equations, drawing a diagram and explicitly converting prefixes), 2) equate (identifying the relevant relationships between the physical quantities) and 3) solve (using algebra, geometry, trigonometry and/or calculus to solve for the unknown quantity or quantities.) For full credit, the answer must include the units and three significant digits. The answer itself is only worth 10 to 20% of the points. How well you write down how you got the answer is worth 80 to 90% of the points.

1) According to observer A, observer B is moving at 0.750c to the right. According to observer B, observer C is moving 0.600c to the left. (a) According to classical relativity, what is the velocity of observer C (magnitude and direction) according to observer A? (b) According to Einstein's theory of relativity, what is the velocity of observer C (magnitude and direction) according to observer A? Give both magnitudes in terms of c.

2) How much does the mass of 10.0 kg of water increase when it is heated from 20.0 ^oC to 80.0 ^oC? The specific heat of water is 4186 J/kg C^o.

3) How fast does an electron have to be moving to have the same kinetic energy of a proton moving at 0.0100c? Give your answer in terms of c.

4) Krane, Chapter 2, Problem 34.

5) The best commercially available laboratory vacuum pump can reduce the pressure of a collection of gas molecules to 1.01 x 10^-13 Pa. What would be the molecular density of the gas molecules at that pressure if their temperature was 293 K? Treat the gas molecules as ideal and give the answer in molecules/cm³.

6) Ultracold rubidium atoms moving through a magnetic trap have a probability distribution function f(v) = A(4v - v²), where A is a constant and the speed is restricted to

0 < v < 4.00 m/s. (a) Determine the constant A. (b) What is the average speed of these atoms? (c) What is their rms speed? (d) What is their most probable speed?