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.

Explain the liquid junction potential in the electrochemical cells. Propose a suitable solution for this problem.

1.During the magnetic resonance relaxation process after a 90° pulse:

A, Longitudinal magnetization increases

B. Transverse magnetization increases

C. Proton density increases

2. T1 and T2 values depend on:

A. Voxel size.

B. Direction of magnetic field.

C. Type of tissue.

3.Tissue characteristics which can produce a relative and increased intensity (brightness) contrast in a magnetic resonance image include which of the two following factors (choose two):

A. Short T1 values.

B. Long T1 values.

C. Short T2 values.

D. Long T2 values.

4. The process of averaging is used in MRI for the purpose of:

A. Reducing acquisition time.

B. Reducing image noise.

C. Improving detail.

D. Combining T1 and T2 contrast.

5. The amount of time necessary to acquire an MR image depends on which two factors (choose two):

A. TR

B. TE

C. Field of view

D. Matrix size

6. T1 increases with magnetic field.

A. True

B. False

In recent times the principle of the Michelson intereferometer is being used in an attempt to detect gravitational waves (LIGO experiment). A successful measurement requires an accuracy of 10-16cm. Assuming t hat the light is reflected only once in each arm and the wavelength of the laser is 632.8 nm, calculate the relative change of the intensity in the center of the image. (for simplicity assume that the intensity is zero for minimum and 1 for maximum of the interference patterns and that the alignment is such that intensity in the center of the screen is at 0.5).

Suppose you kept your accelerating voltage and coil current constant. How would your circular beam change if we were using a proton beam instead of an electron beam? Explain your reasoning.

Equipment used:

Thread, dense spherical mass like a marble or a bearing, perhaps about 0.5 – 1.0 cm in diameter. Otherwise, use a
mass that is approximately spherical, e.g., a tangerine or apple.

Method of obtaining g:

Measure the period of 4 lengths of thread from 75 cm to 1.50 cm. Be sure to measure the length from the support
point to the center of mass of the spherical mass at the bottom end of the thread. For each length of thread, pull
the string from the bottom mass out to about 10 degrees from the vertical, then let the pendulum oscillate back
and forth 20 times while measuring the time with a stopwatch. Determine the period, T, by dividing the elapsed
time by 20.

Plot the period squared versus the length of the pendulum. The resulting curve should be a straight line with a
period involving the acceleration of gravity. Put your data for the length of the pendulum and the period squared
into Excel. Use LINEST to find the best fit slope for the data and the error in the slope. Calculate the acceleration of
gravity and the estimated error of the measurement for g.

Please give an excel file here.

A block with a mass of 0.488 kg is attached to a spring of spring constant 428 N/m. It is sitting at equilibrium. You then pull the block down 5.10 cm from equilibrium and let go. What is the amplitude of the oscillation?

A block with a mass of 0.976 kg is attached to a spring of spring constant 428 N/m. It is sitting at equilibrium. You then pull the block down 5.10 cm from equilibrium and let go. What is the amplitude of the oscillation?

A block with a mass of 0.488 kg is attached to a spring of spring constant 856 N/m. It is sitting at equilibrium. You then pull the block down 5.10 cm from equilibrium and let go. What is the amplitude of the oscillation?

A block with a mass of 0.488 kg is attached to a spring of spring constant 428 N/m. It is sitting at equilibrium. You then pull the block down 10.2 cm from equilibrium and let go. What is the amplitude of the oscillation?

A block with a mass of 0.488 kg is attached to a spring of spring constant 428 N/m. It is sitting at equilibrium. You then pull the block down 10.2 cm from equilibrium and let go. What is the frequency of the oscillation?

A music fan at a swimming pool is listening to a radio on a diving platform. The radio is playing at a constant frequency tone when this person, clutching the portable radio, jumps. Describe the observed frequency or pitch for the following three observers. Explain your reasoning.

a) The person holding the radio

b) A person left behind on the platform

c) A person below the platform floating on a rubber raft

A star with apparent visual magnitude mV = 3.5, absolute magnitude MB = 2.0 has parallax of 0.03 arcseconds. Does this star look red or blue in the sky? Estimate its spectral type.

Consider an optical fiber that has a 200-μm core diameter and a 240-μm cladding diameter. (a) Show that the size of the active area in a bundle with two rings is 1.13 mm2. (b) Show that the ratio of the active area to the total cross sectional area of the bundle is 53 %.