Consider a shallow-water wave of length 1.5km propagating in an ocean that is 62.5m deep.

a) Calculate the wave’s speed C and period T. (3P)

b) Now suppose that this wave propagates into a region in which there is a current of strength U that opposes the wave propagation. Explain how this modifies the dispersion relation and the wave speed. (2P)

c) Assuming that the wave’s frequency ω remains constant, create a plot of the wavelength λ as a function of the current speed U. As U increases, what do you expect to happen to
i) the wave’s length?
ii) the wave’s amplitude?

iii) the wave’s steepness? (5P)

d) Still assuming that ω remains constant, what happens as the speed of the current U approaches the phase speed C that you calculated in part a? Is this physical? What behavior would you expect to see in real, nonlinear waves if they encountered such a current? (3P)

A 1000. kg remote-controlled stunt car traveling at 17.0 m/s north collides with a 900. kg remote-controlled stunt car traveling at 18.0 m/s east. What is the speed of the entangled cars immediately after the collision? 7.2 m/s 7.7 m/s 10.2 m/s 12.4 m/s

If you length a bar magnet describe the affect in the shape of its magnetic field?

State v. Stewart

Did she shoot him dead in self-defense?

1. Calculate the filling factor of a photovoltaic cell whose dimensions are 15 cm per side, and a thickness of 200 µm of which 99% correspond to the “p” type absorbent layer and where there is also a amount of 13500 electrons. The thickness of the space loading region junction is 200 nm.
The cell is subjected to standard test conditions, which produces every second a generation of electron-hollow pairs of 2.0x10¹⁹ cm⁻³ and which translates into an increase in its density of 4.0x10¹³ cm⁻³. The efficiency of the cell is measured at 20%.
Consider that the cell is in thermal equilibrium (300K), its prohibited band is 1.12 eV and that the mobility coefficients are 1360 cm² / Vs for electrons and 450 cm² / Vs for holes.

1)Describe TWO differences between viscous and inviscid flows in Balance Law of Linear Momentum.

Question 5. The 2.50 µc point charges are located on the x-axis. One is at x = 1.00 m, and the other is at x = -1.00 m. Determine the electric field on the y-axis at y = 0.500 m. Answer in Newtons per Coulombs.

Question 6. The 2.50 µc point charges are located on the x-axis. One is at x = 1.00 m, and the other is at x = -1.00 m. Calculate the electric force on a -3.50 µc placed on the y-axis at y=0.500 m. Answer in newtons.

Can the Hubble Space Telescope (2.4 m diameter) or the largest optical telescope on Earth
(the Keck Telescope in Hawaii with 10 m diameter) observe manmade items left on the moon
(e.g. the flag ~ 1.25 m long and lunar rover ~ 3 m long)? Show your work. If not, calculate the
smallest size each telescope can resolve on the Moon and the minimum telescope aperture
size required to resolve these objects.

If the Sun were to become a black hole but maintain all of its mass, what would be its Schwarzschild radius? Given this and the fact that Earth’s average distance from the Sun is about 150 million km, would the gravity of the black hole pull Earth into it? Why or why not?

As part of an interview for a summer job with the Coast Guard, you have been asked to help determine the search area for two sunken ships by calculating their velocity just after an accident. According to the last radio transmission from the luxury liner Apollo (3.9 × 104 metric tons), it was going due east at a steady speed of 21 knots in calm seas through a rare fog just before it was struck broadside by the freighter Blake (6.1 × 104 metric tons), which was traveling north at steady speed of 11 knots. The transmission also noted that when the freighter's bow pierced the hull of the liner, the two ships stuck together and sank. What was the speed and direction of the ships after the collision ? (Take zero degrees to be straight east and counter-clockwise as positive.)

1)____ knots

2)____ degrees

A 38.0-kg crate is being pushed along a horizontal surface. The applied force is 94.0 N directed at an angle of 18.0° below the horizontal and the coefficient of friction is .21.

a)  Draw a free body diagram for the crate.

b)  Write expressions for the x and y components of the applied force (no numbers).

c)  Sum forces in the x and y direction (no numbers).

d)  Solve:  What is the acceleration of the crate?

The cube in the figure has edge length 1.20 m and is oriented as shown in a region of uniform electric field. Find the electric flux through the right face if the electric field (a) is in the positive x direction and has magnitude 7.52 N/C, (b) is in the negative y direction and has magnitude 2.68 N/C, and (c) is in the xz plane, has x component -3.16 N/C, and has z component 4.82 N/C. (d) What is the total flux through the cube's surface for each field? (a) Number Units (b) Number Units (c) Number Units (d) Number Units

Thermodynamics and Statistical Mechanics problem:

Write the formula for the partition function Z of an electron in a hydrogen atom. If the sum is finite, to what value does it converge? If the sum is infinite, prove it

A child of mass m_c = 35 kg stands on the rim of a frictionless merry go round, which acts like a solid disk of mass m_m = 55 kg and radius r = 1.1 m. With the merry go round at rest, they throw a rock of mass m_r = 1.0 kg with a velocity v = 18 m/s relative to the ground in a direction horizontal to the ground, and tangent to the rim of the merry go round.

1. What is the magnitude of the angular momentum of the rock around the axis of the merry go round?
2. What is the angular velocity of the merry go round after the rock is thrown?
3. One of the child’s friends holds their hand against the rim of the merry go round and causes it to stop in a time interval of 3.2 s. What is the magnitude of the frictional force applied?