In a young's double slit experiment

a) There is no diffraction

b) Diffraction is so small it is not easily seen

c) Diffraction is readily apparent in the interference pattern

d) Diffraction disappears when the slit separation is integer times the slit width

You have been asked by your supervisors at A&L Engineering to design a roller coaster for a new theme park. Because this design is in the initial stages, you have been asked to create a track for the ride. Your coaster should have at least two peaks and two valleys, and launch from an initial height of 75 meters. Each peak and valley should represent a vertical change of at least 20 meters. In your design, you should plan for a mass between 400 and 600 kilograms.

Once you have designed the track, you have been asked to calculate the kinetic energy, potential energy, momentum, and work done by the cart at various points throughout the track. Unless otherwise stated, you can ignore the effects of friction. Following your calculations, you have been asked to describe the energy transfers detailed by these equations.

Directions

To complete this roller coaster design report, complete the following:

1. Create a diagram of a roller coaster track containing at least two peaks and two valleys. As you complete your report, you may wish to design a more complicated coaster. However, it should still have two peaks and two valleys that meet the requirements below and that you are comfortable using in calculations and descriptions of energy and momentum. Your diagram should include the following information:
   • An initial height of 75 meters
   • At least two peaks and two valleys representing drops of over 20 meters
   • A set mass for your roller coaster cart between 400 and 600 kilograms

2. Calculate the kinetic energy, potential energy, and momentum of the cart at the initial drop for both peaks, and for both valleys. If your coaster has more than two peaks and two valleys, select which peaks and valleys you wish to use in your calculations and clearly mark them on your diagram. In your calculations, be sure to explicitly state the equations you use and what values you will be substituting to calculate the final value.

3. Describe the energy transfers that occur as the cart moves along the track. This should be a narrative description of the energy transfers that occur at the initial launching point, peaks, and valleys. In your descriptions, address the following:
   • At each of the identified points, how was kinetic energy transferred to potential energy, and vice versa?
   • What happens to the total energy of the cart as it moves along the track? Why?
   • How is the principle of conservation of energy applied in this situation?

In addition to your description of the motion of the cart on the track, you have been asked to model the motion of the cart as it comes to a stop at the end of the coaster. For these calculations, assume that the cart will inelastically collide with a cart of equal mass at rest on a flat surface.

4. Calculate the momentum and kinetic energy of the cart before and after an inelastic collision. In your calculations, be sure to explicitly state the equations you use and what values you will be substituting to calculate the final value.

5. Describe the energy transfers that occur as a cart inelastically collides with an object of equal mass at rest. This should be a narrative description of the energy transfers that occur as the cart inelastically collides with a cart of equal mass. In your descriptions, address the following:
   • What was the kinetic energy of each cart before and after the collision?
   • What happens to the total energy of the system, now including both carts, as a result of the inelastic collision?
   • Describe how the principle of conservation of energy is applied in this situation.

Following the inelastic collision of the carts, the two carts fuse into an object with double the mass of the original cart. There is then a frictional section of the track to slow the cart to a stop over 20 meters. Describe the amount of work due to friction and frictional force exerted to stop both carts over 20 meters.

6. Calculate the work due to friction and frictional force. In your calculations, be sure to explicitly state the equations you use and what values you will be substituting to calculate the final value.

7. Describe the energy transfers that occur as the cart is brought to a stop. This should be a narrative description of the energy transfers—written to describe these concepts to a nontechnical audience—that occur as the cart is brought to a stop. In your descriptions, address the following:
   • What is the kinetic energy of the cart system before and after it has been brought to a stop?
   • What happens to the total energy of the system as a result of this change in motion?
   • Describe how the principle of conservation of energy is applied in this situation.

During a relaxed walking pace, an animal's leg can be thought of as a physical pendulum of length L that pivots about the hip.

(a) What is the relaxed walking frequency for a cat (L = 30 cm), dog (60 cm), human (1 m), giraffe (2 m), and a mythological titan (10 m)?

(b) Derive an equation that gives the walking speed (amount of ground covered per unit time) for a given walking frequency f.

[Hint: Start by drawing a picture of the leg position at the start of the swing (leg back) and the end of the swing (leg forward) and assume a comfortable angle of about 30° between these two positions. To how many steps does a complete period of the pendulum correspond?]

(c) Find the walking speed for each of the animals listed in part (a).

1. Assume an airplane flew horizontally with a constant velocity and dropped one bale of hay every two seconds to a herd of cattle below. If the air resistance can be ignored, (a) what is the motion of the bales as relative to the ground? (b) what is the motion of the bales as relative to the airplane? (c) As the bales are falling through the air, will their distance of separation before hitting the ground increase, decrease or remain constant?

1.
(a)What resolution is required to resolve the Na D lines at 589.0 and 589.5 nm in first order?
(b)A grating contains 1000 lines. Will it resolve two lines of 1500.0 and 499.8 nm in first order if all 1000 lines are illuminated?
(c)Please write down three possible dispersive optical layouts.

Principles of instrumental analysis

With proper Rheological diagrams and suitable examples for each, discuss all the different types of non-Newtonian fluids whose viscosity changes with the applied shear rate only.(Time independent)..... the diagrams should be between viscosity and shear rate.

A spaceship of proper length L_p = 500 m moves past a transmitting station at a speed of 0.83c. (The transmitting station broadcasts signals that travel at the speed of light.) A clock is attached to the nose of the spaceship and a second clock is attached to the transmitting station. The instant that the nose of the spaceship passes the transmitter, the clock attached to the transmitter and the clock attached to the nose of the spaceship are set equal to zero. The instant that the tail of the spaceship passes the transmitter a signal is sent by the transmitter that is subsequently detected by a receiver in the nose of the spaceship.

(a) When, according to the clock attached to the nose of the spaceship, is the signal sent?
  µs

(b) When, according to the clocks attached to the nose of the spaceship, is the signal received?
  µs

(c) When, according to the clock attached to the transmitter, is the signal received by the spaceship?
  µs

(d) According to an observer that works at the transmitting station, how far from the transmitter is the nose of the spaceship when the signal is received?
m

1. Why were the two Keck 400” telescopes placed atop Mauna Kea?

2. What are adaptive optics designed to overcome? How is this done?

3. Explain the basic principle and goals behind the Very Large Array in Socorro, New Mexico.

4. What are some advantages of radio telescopes over optical telescopes?

A 5 m³ tank contains superheated steam at 300°C and 22500 mmHg. The tank (and the steam inside) is cooled until the pressure inside is reduced to 2 bar. At this point, liquid water and saturated steam coexist together in the tank. How much heat was removed from the tank, what is the final temperature, and how many kilograms of steam condensed in the process?

A solid spherical shell with a 12.0 cm inner radius and 15.0 cm outer radius is filled with water.
A heater inside the water maintains the water at a constant temperature of 350 K. The outer
surface of the shell is maintained at 280 K. The shell is made of Portland cement, which has a
thermal conductivity of 0.29 W/(mK).
(a) Starting from the basic equation for thermal conduction, derive the rate at which heat flows
out of the water. Derive a symbolic result first, and then substitute to get a numerical answer.
(b) The heater is turned off at time t = 0. How much time elapses between the time the heater is
turned off and the time the water cools to 330 K? Obtain your result starting from the basic
equation for thermal conduction.

What does it normally mean if a bell curve is skewed to one side and how does one counteract such a problem in the experiment? Be detailed.

0. The hobo is on his way back through town on a faster train. Turns out he’s also a competent trombone player.
   1. What frequency would he actually be playing if the train is approaching you at 25 m/s and you hear a perfect 220 Hz note (an A)?
1. 2. As the train approaches, you happen to be watching a friend at band practice. When she stands still, you hear a 2 Hz beat frequency as she, too, is holding out the same note (though not quite in tune). What are the two possible frequencies that you are hearing from her (in combination with the hobo)?
2. 3. When she slightly extends her slide, the beat pattern effectively disappears (i.e. she’s perfectly playing 220 Hz). Which frequency did you hear her playing in part b? Explain.

.Construct an engaging 3-paragraph paper that ties Waves and Sounds to the real world. (no more than 500 words please) The paragraphs should address the following points:

Paragraph 1: Outline a general definition and description of the Wave and sounds. Include descriptive features (as applicable) about the physics concepts – dependent factors, relevant terminology, conventions, common units of measure, etc.

Paragraph 2: Summarize one or more impacts of the physics concept(s) to everyday life or aviation operations.

Paragraph 3: You have two options for this paragraph: Provide a real example, from an article or documented report (aircraft performance, incidents or accidents, for example), of the aviation impact of this physics concept. Give us “your take” on the relevance and importance of this topic from your own perspective, by providing personal points of view or related experiences.