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Consider a particle of mass m moving in a two-dimensional harmonic oscillator potential :

U(x,y)= 1/2 mω^2 (x^2+y^2 )

a. Use separation of variables in Cartesian coordinates to solve the Schroedinger equation for this particle.

b. Write down the normalized wavefunction and energy for the ground state of this particle.

c. What is the energy and degeneracy of each of the lowest 5 energy levels of this particle?

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1. If you have never taken a philosophy class before, in a general sense what do you know and think about philosophy? What are your fears, excitements, curiosities etc about taking this philosophy class?
2. What is your experience with online classes? What expectations, excitements, challenges, worries etc do you have about this online class?

Fire hoses used in major structure fires have inside diameters of 2.500 in (1 in = 2.54 cm). The nozzle of the fire hose have an inside diameter of 1.200 in. When firefighters are fighting a fire 2020.007 cm above the ground, the pressure in the nozzle is less than at ground level. When measured, the gauge pressure in the nozzle is 0.000 Pa.

(a) How are the firefighters able to fight a fire with zero water pressure? Explain your answer.

(b) What is the value of the water pressure as it emerges into the air from the nozzle? Explain your answer.

a crate of stuffed kittens with a mass of 1kg compresses a spring a distance of 2.84m. The spring has a spring constant of 250N/m. The crate is released and slides across a rough surface with a kinetic friction coefficient of 0.38 for a distance of 62m before colliding with and sticking to another crate. The second crate is filled with cans of smoked turkey and has a mass of 2kg. The two crates then slide horizontally off a vertical cliff with a height of 15m and land on the level ground below. Use g -9.8m/s^2, and answer the following:(no picture needed)

a) what maximum acceleration does the crate of stuffed kittens achieve due to the spring?

b) How fast is the crate of stuffed kittens moving when it collides with the crate of smoked turkey?

c) how fast are the two crates moving when they launch horizontally off the cliff and how fast are the two crates moving just before they hit the ground?

d) How much farther would the spring need to be compressed in order to double the final speed of the two crates at the moment they are about to hit the ground?

5a. The tires on a new compact car have a diameter of 2.0 ft and are warranted for 56,000 miles. How many revolutions will the tires go during the warranty period?

5b. A top-loading washing machine has a cylindrical basket that rotates about a vertical axis. The basket of one such machine starts from rest and reaches an angular speed of 5.0 rev/s in 10.0 s. The lid of the machine is then opened, which turns off the machine, and the basket slows to rest in 13.0 s. Through how many revolutions does the basket turn during this 23 s interval? Assume constant angular acceleration while it is starting and stopping.

The equation of a transverse wave on a string is y=(5mm)Sin[(10m-1)x+(200s-1)t]. The tension in the string is 50 N. (a) What is the wavelength of the wave? (b) What is the frequency of the wave? (c) What is the speed of the wave? (d) Find the linear density of this string.

Submarine A is underwater traveling northbound at a speed of 30 m/s. Behind sub A, sub B is also underwater, but at a speed of 15 m/s and traveling southbound. Sub A sends a 10000 Hz sonar wave that travels at 1500 m/s. What is the frequency of the sonar wave detected by sub B?

The power dissipated in a resistor is given by P=V2/R , which means power decreases if resistance increases. Yet this power is also given by P=I2R , which means power increases if resistance increases. Explain why there is no contradiction here.

A 75kg surfer is paddling out on a 10.5ft wooden longboard with density 167kg/m3 . Seawater has specific gravity of 1.03. Assuming none of the surfer is submerged at the moment, how much of the surfboards 7cm thickness is submerged? You may assume the board is perfectly flat and the surfer has reached behind the breaks where the ocean is calm.

width of board not given

1. Provide an example of an inertial frame of reference and a non-inertial frame of reference. Explain the difference.

2. Using the Michelson-Morley experiment as an example, explain why classical mechanics was unable to explain natural phenomena.

3. Using at least one of Einstein's "thought-experiments", explain how special relativity addresses how it is possible for observers in two different inertial reference frames to “disagree” about time and distance intervals.

4. Describe how special relativity explains the conditions under which classical mechanics breaks down.(When would you, as an observer begin to notice the effects of time dilation and length contraction?)

5. In the early 20th century, the law of conservation of mass was replaced by the law of conservation of mass-energy. Why was this change needed, and how does E=mc² relate to the special theory of relativity?

1. Make a list of five or more important & interesting properties of the Pluto/Charon system.

2. What is the Kuiper belt, what type of bodies does it contain (also name a few) & what is their significance?

3. How are comets classified, where do they originate & what information do they bring?

4. What are meteoroids, meteors & meteorites?

5. Characterize the asteroids, their locations, compositions & importance.

Draw the equipotential and electric field line patterns for the following configurations:

1. A parallel plate capacitor

2. A parallel plate capacitor with a small, non-conducting cube placed between the two plates. (i.e. The cube does not take up the entire space between the plates)

3. A parallel plate capacitor but with one of the plates replaced by a circular conductor.

4. A parallel plate capacitor but with one of the plates replaced by an irregularly shaped (pointed) conductor. Why would high voltage engineers avoid using pointed conductors?

Describe your design for a transformer that steps up voltage from 120 to 1200 V. (Talk about the numbers of turns and the material of the core, specifically.) Will the input and output be AC or DC electricity (there is only one right answer for this one unless you get fancy)? Compare the input current to the output current (hint: the output power in the secondary coils should be calculated to be the same (actually slightly less, due to inefficiencies) as the input power in primary coils.  

Talk briefly about another device that uses induction for practical purposes.

Light with wavelength 530 nm in air (n = 1) passes through a soap bubble (n = 1.33), where its wavelength becomes ≈ 400 nm.

A What is the phase difference between a light wave reflected off the surface of the bubble and one that passes into it before being reflected?

B The thickness of the bubble is 100 nm. Does this lead to constructive or destructive interference?

C What would happen for a soap film covering a glass surface (n = 1.5)? How does this affect the difference in phase?

Give in depth explanation.

Consider a 200 kg spacecraft orbiting the Earth. The vehicle’s position at a given time (lets call it time zero), relative to a non-rotating reference frame with origin at Earth’s centre, is r = −5310i + 5040j km. Its velocity vector at time zero is v = −4.85i − 6.37j km/s.

1. Calculate the distance from Earth’s centre to the spacecraft, the speed of the spacecraft, and the specific angular momentum (magnitude and direction) relative to Earth’s centre at time zero.

2. Calculate the length of the orbit’s semi-major axis, and the orbital period, τ.

3. Calculate the orbit’s eccentricity, the altitude of the space craft at its point of closest approach,

   and the angle of the space craft from periapsis at time zero.