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.

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.