In a city park a nonuniform wooden beam 9.00 m long is suspended horizontally by a light steel cable at each end. The cable at the left-hand end makes an angle of 30.0∘ with the vertical and has tension 630 N. The cable at the right-hand end of the beam makes an angle of 50.0∘ with the vertical.

a) As an employee of the Parks and Recreation Department, you are asked to find the weight of the beam.

b) Find the location of its center of gravity.

Consider how the intensity of light changes as it passes between two Polaroid disks at different angles to each other. (For this scenario, suppose that the polaroid closest to the light source remains fixed with the zero degree marking pointing straight up. Therefore, the second Polaroid disk is the one being rotated, and the angles for the graph should be the angle between the zero degree marking of the first disk and the position of the second disk. )

a. With intensity on the y axis, and angle in 45 degree increments on the x axis, sketch a graph of how the intensity of a light varies under various orientations of the two disks.

b. What is the mathematical relationship here? Explain how you arrived at this conclusion.

c. Based on the fact that the intensity of a light wave is proportional to the square of the electric field magnitude, explain why the transmitted intensity should have this mathematical dependence on the angle.

1. A parallel beam of 1-MeV photons is normally incident on a 1.2-cm aluminum slab (ρ = 2.70 g cm^–3 ) at a rate of 10³ s^–1 . The mass attenuation and mass energy- absorption coefficients are, respectively, 0.0620 cm² g^–1 and 0.0270 cm² g^–1.
   1. What fraction of the photons is transmitted without interacting?
   2. What fraction of the incident photon energy is transmitted by the slab?
   3. How much energy is absorbed per second by the slab?
   4. What fraction of the transmitted energy is carried by the uncollided photons?
   5. If the mass energy-transfer coefficient is 0.0271 cm² g^–1, what fraction of the initial kinetic energy transferred to the electrons in the slab is emitted as bremsstrahlung?

A hydrogen molecule (H₂) in its electronic, vibrational and rotational base state, absorbs a photon of frequency 1,356 x 10¹⁴ Hz and has a transition to a state with n = 1, l = 1, while remaining in the same electronic state. Then it has a transition to the state with n = 0 and l = 2, emitting a photon with a frequency of 1,246.x 10¹⁴ Hz

a) Calculate the moment of inertia of the molecule

b)  Determine the frequency of vibration and R_e

a) Use a diagram and short comments to contrast the general properties of Fraunhofer and Fresnel Diffraction.

b) Show how a simple positive lens made from glass with normal dispersion has chromatic aberration. Use a diagram. Does blue light focus in front or behind red light?

A 78.5kg ice hockey goalie, originally at rest, catches a 0.120kg hockey puck slapped at him at a velocity of 36 m/s. Suppose the goalie and the ice puck have an elastic collision and the puck is reflected back in the direction it came.

a) What would the final velocity of the puck be in this case? Be careful with the sign!

b) What would the final velocity of the goalie be in this case?

The CO microwave spectrum has lines at 0.86 nm, 1.29 nm, and 2.59 nm.

a) What transitions do these lines correspond to?

b) What is the bond lenght of this molecule?

Explain what illusory motion is and discuss the different forms of it

Is about Statistical mechanics:

a) Find the thermodynamic potentials of the ideal gas in its natural variables, in the representation of energy and entropic. Hint: Make use of the Sackur-etrode equation

b) Is it possible to do the same as in part (a) for Van der Waals gas? Justify your answer mathematically and theoretically.

c) What happens with entropy in systems where some of the thermodynamic variables are intensive. Discuss it for at least two thermodynamic potentials (justify this part mathematically).

A liquid mixture of benzene-toluene is to be distilled in a fractionating tower at 101.3 kPa pressure. The feed of 100 kg mol/h is liquid, containing 45 mol benzene and 55 mol% toluene, and enters at 327.6 K. A distillate containing 95 mol benzene and 5 mol toluene and a bottoms containing 10 mol benzene and 90 mol toluene are to be obtained. The reflux ratio R is 4: 1. Determine the kg moles per hour distillate, kg moles per hour bottoms, number of theoretical trays needed, feed tray location, condenser and reboiler heat loads, minimum number of stages (i.e., total reflux), and minimum reflux ratio Rmin (i.e., infinite number of stages).

The concentration of oxygen inside a 5000 L tank at 1 atm is to reduced by pressure purging prior to charging a fuel into the tank. The tank is charged with nitrogen up to a high pressure and then vented down to atmospheric pressure. If the process is repeated, the concentation of the oxygen will decrease. It is possible to do this many times in order to ultimately reach desired concentration. You can assume that a fully charge tank contains all nitrogen.

1. Speculate on why the tank is being purged.
2. Estimate the gauge pressure (atm) to which the tank must be charged if the purge is to be done in a one charge vent cycle. Then estimate the mass of nitrogen (kg) used in the process.
3. Suppose that nitrogen at 700 kPa (g) is used for the charging. Calculate the number of charge vent cycles required and the total mass of nitrogen used.
4. Explain why multiple cycles at lower gas pressure are preferable to a single cycle. What is a disadvantage of multiple cycles?

Classical Mechanics problem:

Suppose you are on a perfectly spherical planet and measure the free-fall acceleration to be g = g₀ at the North Pole. (This planet is not necessarily Earth!) At the equator, you measure g = λg₀ (with 0 ≤ λ ≤ 1). Find g(θ), the free-fall acceleration at colatitude θ as a function of θ.