Consider two-dimensional incompressible plane viscous flow between parallel plates a distance 2h apart, with the origin along the centerline. The plates are very wide and very long, so that the flow is essentially axial. The present case is where the upper plate moves at velocity V but there is no pressure gradient. Neglect gravity effects. Determine the velocity profile for this flow.

A simple harmonic oscillator consists of a block of mass 3.70 kg attached to a spring of spring constant 260 N/m. When t = 1.60 s, the position and velocity of the block are x = 0.199 m and v = 3.920 m/s. (a) What is the amplitude of the oscillations? What were the (b) position and (c) velocity of the block at t = 0 s?

A mass-spring oscillator consists of a 3.40-kg block attached to a spring of spring constant 103 N/m. At time t = 1.40 s, the position and the velocity of the block are x = 0.150 m and v = 3.18 m/s respectively. What is the amplitude of oscillation? What was the position of the block at t = 0? What was the speed of the block at t = 0?

6. Contrast the classical and Quantum-mechanical cases for a delta-function potential bar-
rier, referring to the values of the transmission and reflection coefficients in each case.
Make use of the table below. (6)
Case Classical Quantum-mechanical
E > Vmax (i) (iii)
E < Vmax (ii) (iv)
(v) What is R + T equal to? Explain.
[2

A scientist measuring the resistivity of a new metal alloy left her ammeter in another lab, but she does have a magnetic field probe. So she creates a 7.5-m-long, 4.0-mm-diameter wire of the material, connects it to a 1.5 V battery, and measures a 5.0 mT magnetic field 1.0 mm from the surface of the wire.

Let X be the space of all continuous functions from [0, 1] to [0, 1] equipped with the sup metric. Let Xi be the set of injective and Xs be the set of surjective elements of A and let Xis = Xi ∩ Xs. Prove or disprove: i) Xi is closed, ii) Xs is closed, iii) Xis is closed, iv) X is connected, v) X is compact.

In a mass spectrometer, a positive ion with charge q=1.602x10^-19 coulombs is accelerated by a potential difference of 1000 volts (Ec=-V). Once out of the influence of the electric field, a uniform magnetic field of B=0.01 weber/m² deviates it into a circular trajectory of 182m radius. Determine
a) the velocity of the ion
b) the mass of the ion in kg and in units of atomic mass.

1.Consider a 15-year monthly annuity-style loan for $300,000. The fixed interest rate is 8.125% MEY. Amortize the loan and graph (1) payment, interest paid and principal paid v time, and separately (2) the loan balance over time. Make sure the graphs are at the top of a separate tab and suitable cleaned up.(USE EXCEL SPREADSHEET)

1.      The personal financial planning process involves the following:

Step

i.       Determining your current financial situation

ii.      Define your financial goals.

iii.     Develop a plan of action.

iv.     Implement your plan.

v.      Review your progress, reevaluate, and revise your plan.

Evaluate the practical aspect of the above planning process. (300 words)

A series RLC circuit consists of a 58.0 ? resistor, a 2.50 mH inductor, and a 450 nF capacitor. It is connected to a 3.0 kHz oscillator with a peak voltage of 5.60 V. What is the instantaneous emf E when i = I ? What is the instantaneous emf E when i = 0A and is decreasing? What is the instantaneous emf E when i = - I ?