A capacitor is fully charged and then connected in series to an inductor with zero resistance wires. This is an ideal L-C circuit that will oscillate the current direction. Explain HOW and WHY this circuit oscillates and discuss energy conservation in this oscillation behavior. Your response should be at least 3 paragraphs to show your mastery of the concepts.

In a two-page paper, identify the physics principles contained within the following scenario. Explain how these principals connect to Einstein's theory of relativity or in modern applications in physics. If you use a GPS option on your car or a mobile device, you are using Einstein's theory of relativity. Finally, provide another example from your own experience, then compare and contrast your scenario to the provided example below.

Scenario:

Mandy took a trip to Rome, Italy. She gazed out over the open ocean 20,000 feet below as her airplane began its descent to her final destination of Rome. It had been a long flight from New York to Rome, but she as she stretched, and her bones creaked as though she was old, she knew that in fact, she was a tiny bit younger than her compatriots back home, thanks to traveling at hundreds of miles per hour. In fact, time for her was running slowly compared to her friends in New York for two reasons: the speed at which she had traveled and the height of the airplane above the Earth. Neither, though, were noticeable.

When two lenses are used in combination, the first one forms an image that then serves as the object for the second lens. The magnification of the combination is the ratio of the height of the final image to the height of the object. A 1.90 cm -tall object is 56.0 cm to the left of a converging lens of focal length 40.0 cm . A second converging lens, this one having a focal length of 60.0 cm , is located 300 cm to the right of the first lens along the same optic axis.

A. Find the location and height of the image (call it I1) formed by the lens with a focal length of 40.0 cm .

B. I1 is now the object for the second lens. Find the location and height of the image produced by the second lens. This is the final image produced by the combination of lenses.

s′2, |y′2| =

Two identical particles, each of mass m, are located on the x axis at x=+x0 and x=-x0

a.

Determine a formula for the gravitational field due to these two particles for points on the y axis; that is, write g⃗ g→ as a function of y, m, x0, and so on.

Express your answers in terms of the variables y, m, x0, and appropriate constants. Enter your answers separated by a comma.

b.

At what point (or points) on the y axis is the magnitude of g⃗ g→ a maximum value, and what is its value there? [Hint: Take the derivative dg⃗ /dy.]

Express your answer(s) in terms of the variables y, m, x0, and appropriate constants. If there is more than one point, enter each point separated by a comma.

c.

What is the maximum value of the magnitude of g⃗ g→?

Express your answers in terms of the variables y, m, x0, and appropriate constants.

Members of the astronomy club just posted an article about the discovery of a small comet which orbit is in the same orbit plane as the Earth. In the article it is reported that the observation took place when the comet was eclipsed by the sun just passing the aphelion, in a relative distance at that moment of 3.82 UA and an orbit with eccentricity of e=0.777.

They are calling you to form part of the group of immediate reaction to determine if the comet is a rick to planet Earth. Do the calculation of the ellipse of the comet and the earth to see if it is a risk to the planet.

Determine the direction of the effective value of g⃗ g→ at a latitude of 60 ∘∘ North on the Earth.

Explore gravitational forces, especially as they apply to circular and elliptical orbits.

1. With a big mass and a little one, simulate some orbits. What's necessary for there to be orbital motion? What kinds of orbital shapes can you make? What does the big mass do?

2. Try to make a circular orbit. Write down some observations about that process. Once you can do that pretty well, make another orbit at the same radius, but with a heavier planet how is this different (or not) from the previous orbit? What about circular orbits that are different distances from the big mass do they move faster/slower? ...are their orbital periods (time for an orbit) shorter or longer?

3. How does an object move differently in the different parts of an elliptical orbit?

4. How do different elliptical orbits compare in orbital period?

5. What happens if you make a big mass "orbit" another big mass that looks different from what you've seen before? When does that start happening what sorts of masses do this?

Lab 1: Measurements and uncertainty estimation

Introduction:

The purpose of this lab is to measure a quantity related to the static friction of glass. Static friction is the force required to start moving an object from rest. You will place a coin on the glass and lift one end until the coin begins to move. Your goal is to measure the angle at which the coin moves and understand what affects the precision and accuracy of your measurements.

1) Pick a coin to use based on your birth month and the list here:

2. Place the coin “heads up” (with the persons head facing up) flat on a horizontal surface made of glass (could be a mirror, tablet, smartphone screen, etc.). Keep one end fixed and elevate the other end slowly until the coin moves (watch carefully as the coin may move suddenly or very slowly).
3. Stop moving the surface.
4. Measure the inclination angle (the angle from your table to the surface you’ve used). Do this by measuring the height of the raised surface and the length of the surface to infer the angle by a well-known trigonometric identity.
5. Considering your measuring technique and device, estimate the uncertainty in the angle. You may assume that the percent uncertainty in the sine of the angle is equal to the percent uncertainty of the angle itself.
6. Repeat this measurement (including uncertainties) a total of 5 times.
7. Tabulate your data (include absolute uncertainties):

FOR HEADS

8) Compute the average angle and average uncertainty. Compute the difference between the measured angles in each trial and the averaged angle. Quantitatively how do the differences compare to the average uncertainty?

9) Based on 8) would you say that the average uncertainty accounts for the different trial measurements (i.e. are the differences large or small compared to the uncertainty)?

10) Repeat the steps 2-9 for the coin “tails up”.

FOR TAILS

11. Compute the difference between the measured angles in each “tails up” trial to the average of the “heads up” trail. Quantitatively compare this to the average uncertainty of the “heads up” trial.
12. Based on your measurements and your answer from 11) would you say that the angle depends on which side of the coin is facing up? Explain.
13. List at least 2 things that contributed to the uncertainty of your measurements and explain how you might improve them.
14. List at least 2 things that might have contributed to any inaccuracy of your measurements and explain how you might improve them.

There are two identical, positively charged conducting spheres fixed in space. The spheres are 39.6 cm39.6 cm apart (center to center) and repel each other with an electrostatic force of ?1=0.0675 NF1=0.0675 N . A thin conducting wire connects the spheres, redistributing the charge on each sphere. When the wire is removed, the spheres still repel, but with a force of ?2=0.115 NF2=0.115 N . The Coulomb force constant is ?=1/(4??0)=8.99×109 N⋅m2/C2k=1/(4πϵ0)=8.99×109 N⋅m2/C2 .

Using this information, find the initial charge on each sphere, ?1q1 and ?2q2, if ?1q1 is initially less than ?2q2 .

?1=q1= C

?2=q2= C

Write down the condition for thin film interference. Calculate the position (angular) and the distance between the 3rd and 4th dark lines of the interference pattern on the screen when the slits are spaced 0.450 mm apart and are placed 80.0 cm from the screen. The slits are illuminated with coherent light of wavelength 550nm. Also calculate the distance between the 3rd and 4th dark lines when the entire apparatus was immersed in water. How this separation compares with separation in air and why? (nwater = 1.333)

1.          One of the aspects of the uncertainty principle, is that in making measurements, one changes the system being measured. Give an example of this in your everyday existence.

A conductive sphere is placed in a uniform electric field parallel to the z axis

How much is the induced dipole moment in the sphere?

An object is located to the left of a convex lens whose focal length is f=34 cm. The magnification (m) produced by the lens is 4.0. Find an expression for magnification in terms of “f” and object distance (do). To increase the magnification to 5.0, calculate the distance through which the object should be moved. Also explain your result with free hand ray diagram. At what position of the object the magnification becomes infinity?

A 1325 kg elevator starts from rest and moves upwards for 4 seconds with a constant acceleration until it reaches a speed of 2.1 m/s. After 4 seconds, the speed of the elevator remains constant. A) What is the average power of the elevator motor during the first 4 seconds? B) What is the average power of the elevator when t=9 seconds?