A mass spectrometer is designed to calculate masses of atoms. A source produces positive ions of
mass m and charge q. The ions move with a velocity v to the right, pass through a narrow slit S1 and
enter a region between two charged plates. In this region they experience both an electric and a
magnetic field. The electric field E is caused by the 2 charged plates; the upper plate is (-) charged
and the lower plate is (+) charged. The magnetic field is B1 and points out of the page. The ions
exit this region through slit S2 . When they exit, they experience a new magnetic field B2, that is also
directed out of the page. The ions are then collected inside a collector.
a) Draw the electric field between the charged plates.
b) With what velocity should ions enter in order to follow a straight trajectory from S1 to S2?
c) Draw the trajectory followed by the ions in the region of magnetic field B2? Why does the
trajectory look like this?
d) Where should the collector be placed in the plane containing S2 to collect the ions?
e) What is the mass of the ion in terms of field strengths, charge, and S2-collector distance?

The initial temperature of the lake at the edge of the mountain glacier is 6.40'C, and the volume of water is 185,000m^3. There is iceberg which the mass is 17.3*10^6kg, temperature is -10'C. The iceberg fell and floated on the lake. 

If there is no energy exchange except between the lake and the iceberg, what is the final temperature of the lake and the iceberg?

If there is remaining ice, how much ice is left?

A family on vacation in San Francisco drives from Golden Gate Park due south on 19th Avenue for 2.2 miles and then turns west on Sloat Boulevard and drives an additional 1.1 mile to go to the zoo. The driving time for this trip is 18 minutes. What is the family’s net displacement for this trip? What is the average speed for the trip? What is the average velocity? (Remember to specify the direction of the net displacement and the velocity vectors. This requires giving a reference, like “of the north”, and a direction the angle is measured, like “east” in the direction “20.0° east of north”.)

Kristi Yamaguchi a former figure skater who is the 1992 Olympic Champian, a two-time World Champian and 1992 US Champion. In her 1992 Long Program, she made a sharp turn with a radius of 22.6 m and with a speed of 16.1 m/s. Use Newton's second law to determine the acceleration and the angle of lean of Kristi 55.0-kg body.

Please explain and show work if possible.

A uniform stick, mass m and length l, is placed in a horizontal plane by hanging it from a massless string attached to the center. A ball of mass M moving with speed V in the plane of the stick. The ball strikes the stick at a distance d from the center. the collision is elastic. Find the resulting translational and rotational speeds of the stick and the resulting speed of the ball. show that the relative speed of the ball and the point of contact on the stick is the same before and immediately after the collision.

A thin, circular disk of radius R = 30 cm is oriented in the yz-plane with its center as the origin. The disk carries a total charge Q = +3 μC distributed uniformly over its surface. Calculate the magnitude of the electric field due to the disk at the point x = 15 cm along the x-axis.

A river 16.0 m wide and 4.0 m deep drains a 3000.0 km2 land area in which the average precipitation is 48 cm/year. One-fourth of this rainfall returns to the atmosphere by evaporation, but the remainder ultimately drains into the river. What is the average speed of the river?

A 248 nC point charge is at co-ordinate (0, 0.2) . A 85 nC charge is at (0, -0.2). Find the electrostatic field at (0.4, -0.7). The Coulomb constant is k = 8.99 10^9 N m^2 / C^2 and the coordinates are given in meters.

An electron of charge q = -c is first traveling perpendicular to a constant electric field. Illustrate a diagram depicting the trajectory of the electron, and name the shape of the trajectory (whether it's linear, circular, parabolic, hyperbolic, or elliptical). Explain why the electron has the trajectory you found out.

Prove that Maxwell’s equations yield the wave equation for the electric field [HINT: ∇ × (∇× ) = ∇(∇·) − ∇ · ∇]

1. Write the Schrodinger equation for particle on a ring, and rearrange it until you have the following: ? 2? ??2 = − 2?? ℏ 2 ? …

a) Assuming that ?? 2 = 2?? ℏ 2 , (where ml is a quantum number and has nothing to do with mass), show that the following is a solution for the Schrodinger equation you obtained: ?(?) = ? ? ????…

b)Now think about bounds of variable ?. Using that argue that ?(?) = ? ( ?+2pi), and prove that ml can be 0, ±1, ±2, ±3, ±4, Normalize that ?(?)

c)Prove that particle on the ring will have discrete energy levels described by the following equation, ??? = ?? 2ℏ 2 2? …

d) Now we will apply these solutions to Benzene molecule. Each double bond in benzene is 1.4Å, so you know the circumference of benzene. Now calculate the radius of benzene using the circumference. There are six -electrons on benzene, which are free to move around the ring due to conjugated double bonds. Make an energy level diagram using equation 6, and calculate the wavelength for the lowest energy electronic transition. Experimentally observed transition for benzene is at 200 nm. (Hint: The ground state will be ml = 0, and then rest of the energy levels are going to be doubly degenerate.)

1 Larmor radius and gyration frequency (10 P) Calculate the Larmor radius and the gyration frequency (4 P) for:

1. An electron in the Earth’s ionosphere at 300 km altitude, where the magnetic flux density is B ≈ 0.5 · 10−4 T, considering that the electron moves at the thermal velocity (p kT /m) with T = 1000 K. (1 P)

2. An oxygen ion O+ in the Earth’s ionosphere for the same conditions as above. Is there a difference in Larmor radius and gyration frequency between the ion and the electron? Explain. (3 P)

3. A 3.5 MeV He++ ash particle in an DT fusion reactor. Use the kinetic energy of the particle to calculate the velocity, assuming that v|| is negligible.

1. When a radioactive element decays, it is because the balance of neutrons and protons inside the nucleus was unstable. Explain what happens in each of these kinds of decay to make the nucleus more stable (these are the three most common decay types):

a. Fission

b. Beta-decay ( β )

c. Alpha-decay ( α )

Which of these is more often associated with the production of energy (and weapons)?

Why do you think that is?

As a result of federal laws and the 14th amendment to the us constitution federal courts _________