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 _________

One speaker A is located in origin and another speaker B is located at point (3.0),
the units in the xy plane measure in meters and the speakers are the same. At a point P = (1,4) is one
microphone placed. The speakers are connected to a tone generator that generates sinus tones
(flat waves) so that speaker B lies ?/4 after A in phase and the sound speed is 350m/s.

a) Draw time graphs for both speakers' oscillations when the frequency is 500 Hz.
b) Determine the three lowest frequencies that give complete constructive interference in the point
c) Determine the three lowest frequencies that give complete destructive interference in point P.

Calculate the binding energy per nucleon for each of the following nuclei. (Use the table of atomic masses as necessary.)

(a) ²H
(MeV)

(b) ¹⁴N
(MeV)

(c) ²³Na
( MeV)

(d) ³²S
(MeV)

A 674-kg elevator starts from rest and moves upward for 2.90 s with constant acceleration until it reaches its cruising speed, 1.80 m/s.

(a) What is the average power of the elevator motor during this period?______________ hp

(b) How does this amount of power compare with its power during an upward trip with constant speed? (Give the power during an upward trip with constant speed.)____________________ hp