Construct the explicit form of the lowest three eigenfunctions of the harmonic oscillator.

Say the density of air is 1.23 kg/m3 and the density of helium is 0.164 kg/m3 when both are at STP. Let's model a balloon as a sphere of radius 0.12 m, with mass 2 g.

1) What is the mass of the helium that would fill a single balloon?

2) What is the buoyant force on a single balloon?

3) What is the net force on a single balloon?

4) If we attach 0.5 m of string (properties: 800 feet weighs 1 pound), what is the net force now on the balloon?

5) How many balloons would you need to have a 1 kg kitten in equilibrium, hovering just above the ground? (assume all of the strings are vertical, this is actually another problem)

List three unique meteorological features of Superstorm Sandy

A particular beam of light, with an intensity of 440 W/m², is linearly polarized at an angle of +5.00° to the vertical. You have three polarizers, which have their transmission axes aligned as follows:

Polarizer A - the transmission axis is at +19.0° to the vertical;
Polarizer B - the transmission axis is at +72.0° to the vertical;
Polarizer C - the transmission axis is at +25.0° to the vertical.

You will select two of these polarizers, and have the light pass through one and then the other.

(a) If you want to maximize the intensity of the light emerging from the second polarizer, which two polarizers should you select, and in what order should the light pass through them?

(b) For the situation in (a), when you maximize the intensity of the light emerging from the second polarizer, what is that intensity?
___________ W/m²

(c) If, instead, you want to minimize the intensity of the light emerging from the second polarizer, which two polarizers should you select, and in what order should the light pass through them?

(d) For the situation in (c), when you minimize the intensity of the light emerging from the second polarizer, what is that intensity?
____________ W/m²

For the remaining parts of the problem, we now replace the original polarized light by unpolarized light of the same intensity. For reference, the intensity is 440 W/m², and the three polarizers have their transmission axes aligned as follows:

Polarizer A - the transmission axis is at +19.0° to the vertical;
Polarizer B - the transmission axis is at +72.0° to the vertical;
Polarizer C - the transmission axis is at +25.0° to the vertical.

(e) If you want to maximize the intensity of the light emerging from the second polarizer, which two polarizers should you select, and in what order should the light pass through them?

(f) For the situation in (e), when you maximize the intensity of the light emerging from the second polarizer, what is that intensity?
___________ W/m²

(g) If, instead, you want to minimize the intensity of the light emerging from the second polarizer, which two polarizers should you select, and in what order should the light pass through them?

(h) For the situation in (g), when you minimize the intensity of the light emerging from the second polarizer, what is that intensity?
____________ W/m²

question about defibrillator.
. Why you apply the shock

. What is done when defibrillator

. How defibrillator work

. Then why we chose Biophasic

A plane wave of frequency 900 MHz is and trave ling along -y direction with the electric field amplitude of 300 V/m (in vacuum). The value of electric field is -300 V at t=0 and y=0. Choose a magnetic field direction and define the polarization. Write the wave equation of the electric and magnetic field..

Choose an isotope and describe its radioactive decay process and how it is used. Write a minimum of 150 words.

The velocity of a particle moving in the xy plane is given by ,v=(5t-4.5t^2)i+8.3j with in meters per second and t (> 0) in seconds. At t = 2.4 s and in unit-vector notation, what are (a) the x component and (b) the y component of the acceleration? (c) When (if ever) is the acceleration zero? (d) At what positive time does the speed equal 10 m/s?

A camera lens has a focal length of 100 mm (thick lens). The photographer first adjusts the location of the lens to look at an object very far away (infinite distance). Then he tries to take a picture of a person 2 meters away from the lens. How is he going to adjust (move) the lens relative to its original position? What is the distance of the adjustment?

Steam locomotives have an efficiency of 18.0% and operate with a hot steam temperature of 425°C.

(a) What would the cold reservoir temperature (in °C) be if this were a Carnot engine? °C

(b) What would the maximum efficiency of this steam engine be if its cold reservoir temperature were 150°C? %

A car is going at 11.2 m/s on a horizontal straight road. When the traffic light is 30 m away, it turns red.
The reaction time of the driver is 0.3 s.
The car stops just before the traffic light with constant deceleration when the break is applied.

1. Find the time it takes for the car to stop, from the moment the light becomes red.

2. Plot speed of the car on y-axis and the time on the x-axis, taking t=0 at the

   moment when the traffic light turns red.

3. In the table provided below fill-up the blanks. It will help you to plot the graphs.

4. Plot the acceleration as a function of time.

5. Plot the distance covered as a function of time, using the v vs. t graph, taking zero

   at t=0.

The intensity pattern formed by a diffraction grating of N slits is

where θ is the angle of diffraction. The radiation reaches the grating at normal incidence.

Using the formula above and m = 0, ±1, ±2 ... and p = an integer ≠ mN

1. show that
   • the interference maxima occur for β = mπ
   • and minima occur for  β = pπ/N .
2. show that the orders m=pd/a (of interference) are missing if d/a is an integer .

Q2.

a) Explain what is meant by diffraction of waves, and give two examples of when diffraction is useful.

b) A loudspeaker has a diameter of 0.15 m. Using the principle of circular hole diffraction, calculate the angle at which the first minimum occurs when a. Sound of frequency 3400 Hz ( = 0.10 m) is emitted. b. Sound of frequency 10 kHz ( = 0.034 m) is emitted.

c) Use these answers to give one reason why woofers (speakers with a larger diameter used for lower frequencies) and tweeters (speakers with smaller diameters used for higher frequencies) are used in speaker cabinets to improve sound quality.

d) Give another reason why different diameter speakers are used for different frequencies.

Two projectiles with 50kg mass each are launched in opposite directions towards each other, both at an angle of 30 degrees off the horizontal. They both have the same initial velocity of 75m/s and they are separated by a distance of 200m.

a.) What is their combined initial kinetic energy?

b.) Right before they collide, how high off the ground are they?

c.) What is their total momentum here? (both directions)

d.) When they collide they stick together and lost kinetic energy. What is it now?

e.) How high does this combined projectile get?

f.) When the thing finally lands, what's the impact velocity?

1) Does the fact that the speed of light is a definite, predictable quantity conflict with the uncertainty relations?

2) How could you tell if electrons in very distant galaxies obey the Pauli exclusion principle?

Can you answer these question,please?