14N16O has a force constant, k, of 1550 N/m and a moment of inertia, I, of 1.642x10-46 kg m2.

a. What is the wavenumber of the photon that will be absorbed during the v=2 to v=3 vibrational transition if it acts as a harmonic oscillator?

b. What is the wavenumber of a photon that will be absorbed during the same transition in part (a) if the molecule behaves instead as an anharmonic oscillator with an anharmonicity constant of 0.007392?

c. Given what you know about the harmonic and anharmonic oscillator models, which of the two models do you think would give a better fit to these transitions in real life? Briefly justify your answer, using what you know about the applicability of these model systems to support your conclusion.

d. What is the wavenumber of the photon that will be absorbed during the J=7 to J=8 transition if it acts as a rigid rotor?

e. Comment on the relative magnitudes of the vibrational and rotational transitions in 14N16O. Why are vibrational modes excited by infrared radiation, while rotational modes are excited by microwave radiation?

In my physics class, we are going over the Doppler Effect. We were given four different equations for two different scenarios:

- When the observer is stationary but the source is moving

- When the observer is moving but the source is stationary

I was given a problem where both the observer AND the source are moving at some velocity. The source is emitting a given frequency while traveling at a given velocity. The observer is OBSERVING that frequency at a given frequency provided in the problem, but their velocity is unknown. Seeing as the source is traveling at a CONSTANT velocity, can I treat it as though the source, relative to the observer, is stationary, and it is only the observer that is moving? I was thinking of using the receding observer equation of: f_- = (1 - v₀/v)*f_s , where v₀ is the speed of the observer and v is the velocity of sound in air, 343 m/s. Would this be correct? Or can I not treat the source as stationary even though it is moving at a constant velocity?

Thank you in advance! Please comment if you need clarification.

Consider an object that begins rolling from rest at the top of an inclined plane. Assume that there is no slipping between the object and the ramp, and that the bottom of the ramp is defined as h = 0.

1. What form(s) of energy does the object have at the top of the ramp, before it begins moving?

   (a) Gravitational Potential (c) Rotational Kinetic (b) Translational Kinetic (d) Thermal

2. What form(s) of energy does the object have when it has just reached the bottom of the ramp? (a) Gravitational Potential (c) Rotational Kinetic

   (b) Translational Kinetic (d) Thermal

3. Using your answers to #1 & #2, write an equation that describes energy conservation for the object.

4. How is the angular velocity of rotation, ω, related to the center of mass velocity, v, for an object with radius r?

   (a) ω=v·r (b) ω=v·r2 (c) ω=v/r (d) ω=v2/r

5. Using your answers to #3 & #4, solve for the final velocity of the rolling object as a function of its initial height and other physical parameters.

A circuit is constructed with four resistors, one inductor, one battery and a switch as shown. The values for the resistors are: R₁ = R₂ = 56 Ω, R₃ = 45 Ω and R₄ = 91 Ω. The inductance is L = 255 mH and the battery voltage is V = 24 V.

1)

The switch has been open for a long time when at time t = 0, the switch is closed. What is I₁(0), the magnitude of the current through the resistor R₁ just after the switch is closed?

_______A

2)

What is I₁(∞), the magnitude of the current that flows through the resistor R₁ a very long time after the switch has been closed?

_______A

3)

What is V_L(0), the magnitude of the voltage across the inductor just after the switch is closed?

______V

4)

What is I_L(∞), the magnitude of the current through the inductor after the switch has been closed for a very long time?

___________A

5)

What is I₂(0), the magnitude of the current through the resistor R₂ just after the switch is closed?

_______________A

1. For each of the following production functions (a-c) answer the following questions (i-v):

i) Calculate the marginal products MPL and MPK.

ii) Calculate MRTSL;K and determine if this is diminishing as good L increases.

iii) If Q0 = 100, w = 8 and r = 2, determine long-run cost minimizing combination of labor and capital and the associated total cost.

iv) If Q0 = 100, w = 8 and r = 2, determine short-run cost minimizing combination of labor and capital and the associated total cost if the firm is stuck with K = 4 unit of capital in the short run.

v) Do we have too much or too little capital in the short run, and how much money is the firm losing by being stuck with K = 4 unit of capital in the short run?

(a) Q(L;K) = 10L^1/2K^1/2.

(b) Q(L;K) = 4L^2 + 4K^2.

(c) Q(L;K) = 4LK + 6K.

Question 1: Austin v. New Hampshire (P&I Clause) New Hampshire, which levies no personal income taxes, adopted an income tax that effectively applied only to nonresidents. The Commuters Income Tax was imposed on the income of nonresidents earned in New Hampshire. The state also levied a tax on residents income earned outside the state, but immediately nullified its effect through another provision that exempted such income from tax. Does the New Hampshire Commuters Income Tax violate the Privileges and Immunities Clause? Why or why not?

Question 2: Michelin Tire Corp v. Wages (I&E Clause) Michelin stored tires and tubes imported from France and Nova Scotia in a warehouse in Georgia while they were awaiting distribution to franchised dealers throughout the Southeast. The county assessed ad valorem property taxes against the tires and tubes, and the taxpayer challenged the assessment under the Import-Export Clause. What was the ruling of the Court and why?

n insurance portfolio consists of two homogeneous groups of clients; N i, (i = 1 , 2) denotes the number of claims occurred in the ith group in a fixed time period. Assume that the r.v.'s N 1, N 2 are independent and have Poisson distributions, with expected values 200 and 300, respectively.

The amount of an individual claim in the first group is a r.v. equal to either 10 or 20 with respective probabilities 0.3 and 0.7, while the amount of an individual claim in the second group equals 20 or 30 with respective probabilities 0.1 and 0.9.

Let N be the total number of claims, and let S be the total aggregate claim.

Find E { S } and V a r { S }.

(Hint: Compute E { Y i } and E { Y i 2 } proceeding from the result of Question 10 and use Propositions 1-2 that we proved in class regarding E { S } and V a r { S } in the case where N is a Poisson r.v.)

8. A professor tests whether the loudness of noise during an exam (low, medium, and high) is independent of exam grades (pass, fail). The following table shows the observed frequencies for this test.

Part A) Conduct a chi-square test for independence at a 0.05 level of significance. (Round your answer to two decimal places.)

Decide whether to retain or reject the null hypothesis.

Part B) Compute effect size using Cramer's V. (Round your answer to two decimal places.)

9. What is Cramer's V for each of the following values for the chi-square test for independence? (Round your answers to two decimal places.)

Part A) X² = 3.63, n = 50, df_smaller = 1

Part B) X² = 9.27, n = 120, df_smaller = 2

Part C) X² = 12.23, n = 160, df_smaller = 3

Use the following assumptions for this question. The commercial banking system has a target reserve ratio of 5% and there is no cash drain. A new immigrant to the country makes a cash deposit of $1,000. In the following table show how deposits, reserves, and loans change as the new deposit permits the banks to “create” money.

1. A) Complete the entire table.
2. B) You have now completed the first five rounds of the deposit-creation process. What is the total change in deposits so far as a result of the single new deposit of $1000?
3. C) This deposit-creation process will go on forever, but it will have a finite sum. In the text, we showed that the eventual total change in deposits is equal to 1/v times the new deposit, where v is the target reserve ratio. What is the eventual total change in deposits in this case?
4. D) What is the eventual total change in reserves? What is the eventual change in loans?