Two polarizing sheets have their transmission axes crossed so that no light gets through. A third sheet is inserted between the first two so that its transmission axis makes an angle ? with the transmission axis of the first sheet. Unpolarized light of intensity I₀ is incident on the first sheet. Suppose that the middle sheet is replaced by two polarizing sheets. The angles between the transmission axes of the second, third and fourth sheets in the stack make angles of 30

A hydrogen discharge tube is used to illuminate a 10,000-line/cm diffraction grating. The grating produces first-order maxima at 24.2◦, 25.7◦, 29.1◦, and 41.0◦. a) Calculate the wavelength corresponding to each angle. b) Determine the angles for the wavelengths in (a) if they are produced instead by a 5,000 line/cm grating. (c) Find the location of the second-order maxima for these wavelengths and new grating. (d) Qualitatively discuss how the grating’s line density is related to the location and separation of the fringes.

You just got a new job at Six Flags to test roller coasters. The first roller coaster you test has a vertical circular loop with a diameter of 25 m. The empty car you are using has a mass of 135 kg. You can measure the speed of the empty car at all points along the loop and you find it has a speed of 27 m/s at the bottom and 9.5 m/s at the top of the loop.

(a) What is the magnitude of the normal force of the track on the car when the car is at the bottom of the loop?

(b) What is the magnitude of the normal force of the track on the car when the car is at the top of the loop?

(c) How much work is done by friction when the car travels from the bottom to the top of the loop?

(d) At one point during the experiment, the person looks at the scale and it reads 0 N. Explain how this is possible and what the person should do about it.

A curious person decides to do an experiment in their apartment building. They take their bathroom scale into the elevator on the 15th floor of the highrise they live in. When the elevator is stationary, they step on the scale and it reads 532 N, as expected since this is the person's weight. When the elevator starts moving, the person looks at the scale and it reads 420 N. The combined mass of the person and the elevator is 795 kg.

(a) Explain why the reading on the scale is less than the person's weight.

(b) What is the elevator's acceleration (magnitude and direction) when the scale reads 420 N.

(c) In the next part of the experiment, the person chooses a different floor to travel to and then the scale reads 670 N. Did the person choose to go to a higher floor or a lower one? And what is the acceleration of the elevator?

(d) Using the calculations you made in parts (b) and (c), find the tension in the elevator cable when the scale read 420 N and 670 N.

(e) At one point during the experiment, the person looks at the scale and it reads 0 N. Explain how this is possible and what the person should do about it.

Suppose a simple dye molecule can be modeled as having a hydrogen-like energy states with 6 electrons. Initially, the electrons settle to the lowest total energy state. Imagine that we illuminate this molecule with just right energy to excite the electrons from the n = 3 level to the n = 5 level. When such excited electrons decay back to their lower available energy states, photons of the same energy as the incoming photons are emitted. In addition, photons with different wavelengths can be emitted. This is known as fluorescence. (a) Draw the energy-level diagram (for n = 1 to n = 6) and show how electrons are filling the energy levels before light is illuminated. (b) After the illumination, the electron’s arrangement changes in the energy diagram. Draw the energy-level diagram again (for n = 1 to n = 6) and show how the electrons are filling the energy levels after the light illumination. (c) The excited electrons in (b) decays to the lower energy states. Identify two transitions producing photons with longer wavelengths than the incoming photons. Write your answer in this format: Eph (6 →1), if the photon is generated by the electron transitioning from n = 6 to n = 1 (this is not the correct answer). (d) Explain why other transitions (such as from n = 5 to n = 1) are not possible.

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

Four ideal linear polarizers are placed in a row with the polarizing axes vertical, 200 to vertical, 550 to vertical and 900 to vertical. Natural light of intensity I0 is incident on the first polarizer. a) Calculate the intensity of light emerging from the last polarizer. b) Is it possible to reduce the intensity of transmitted light (whilst maintaining some light transmission) by removing one of the polarizers? c) Is it possible to reduce the intensity of transmitted light to zero by removing a polarizer(s)?

For the circuit shown in the figure, calculate the following. (Assume  = 7.32 V and R = 5.70 Ω.)

A rectangular circuit begins at point a on its left side. On its top side, the circuit splits into two parallel horizontal branches.

• The top branch contains, from left to right, a 12.0 V battery and a 4.00 Ω resistor. The positive terminal of the battery is to the left of its negative terminal.
• The bottom branch contains a 2.00 Ω resistor.

The top and bottom branches recombine to meet at point b, which is to the right of the branches. The right side of the rectangular circuit extends down from the bottom branch, just to the right of the 2.00 Ω resistor and to the left of point b. The bottom side of the rectangle, from right to left, contains a resistor R and a battery labeled emf ℰ, where its positive terminal is to the right of its negative terminal. The circuit extends to the left from the negative terminal until it reaches point a, completing the circuit.

(a) the current in the 2.00-Ω resistor (Enter the magnitude.)
A

(b) the potential difference between points a and b,

ΔV = V_b − V_a

V

Let’s design a velocity selector device for a mass spectrometer. a.Illustrate the device and explain how it works. b.The electric field inside the device will operate at a level of 12.0E3 V/m. What will be the force on an ionized Calcium atom (q = +2 e) as it moves through the selector?c.If the magnetic field inside the device operates at a level of 0.250 T, what velocity will the device select?d.Explain what happens to negative ions travelling above or below the selection spe

Boxcar #1 has a mass of 2000 kg. Boxcar #2 has a mass of 1200 kg. Boxcar #1 is moving at 12.00 m/s to the right before they hit and stick together. A) Suppose that the velocity of Boxcar #2 before the collision is 8.00 m/s to the right. What is the velocity after the totally inelastic collision? B) Suppose, instead, that the speed after the totally inelastic collision is 3.00 m/s. What was the velocity of Boxcar #2 before the collision? Give all possible answers.

Early 20th-century physicist Niels Bohr modeled the hydrogen atom as an electron orbiting a proton in one or another well-defined circular orbit. When the electron followed its smallest possible orbit, the atom was said to be in its ground state. (a) When the hydrogen atom is in its ground state, what orbital speed (in m/s) does the Bohr model predict for the electron? m/s (b) When the hydrogen atom is in its ground state, what kinetic energy (in eV) does the Bohr model predict for the electron? eV (c) In Bohr's model for the hydrogen atom, the electron-proton system has potential energy, which comes from the electrostatic interaction of these charged particles. What is the electric potential energy (in eV) of a hydrogen atom, when that atom is in its ground state? eV

A space station in the shape of a uniform disk (mass 4.45x105 kg, radius 262 m) rotates with period 86.1 seconds. There are also 734 astronauts (whom you can treat as point particles) working inside the space station, each of mass 155 kg, and all standing on the outside rim and rotating with the station. Now, all the astronauts move to a conference room at the very center of the space station. Find the new period of the rotation of the space station.

A gear has an angular velocity equal to 20 rad/s initially, but it speeds up to 40 rad/s in 5.0 seconds, while experiencing angular acceleration that is constant. Compute the number of turns the gear has undergone during those 5.0 seconds?

28

32

52

39

20

24

Construct the geometric bucklings and critical flux profiles in finite cylinder reactor.

. Inside of a calorimeter (insulated container) is placed 200g of water at 20°C. The lid of the calorimeter is briefly lifted and 50g of lead is added initially at 200°C. What is the thermal equilibrium temperature? (3pts)

10. An object of mass 50kg is pushed in the +x direction with a force of 40N flat along a horizontal surface causing a net acceleration of 0.15m/s2 in the +x direction. What is the coefficient of kinetic friction between the surface and the object?