The distance from earth to the center of the galaxy is about 22500 ly (1 ly = 1 light-year = 9.47 ? 10¹⁵ m), as measured by an earth-based observer. A spaceship is to make this journey at a speed of 0.9950c. According to a clock on board the spaceship, how long will it take to make the trip? Express your answer in years (1 yr = 3.16 ? 10⁷ s).

Please be as detailed as possible in your response, thank you!

A solid conducting sphere of radius a carries a net positive charge 2Q. A conducting spherical shell of inner radius b and outer radius c is concentric with the solid sphere and carries a net charge –Q. Let c > b > a.

a) Discuss the distribution of the charges.

b) Calculate the surface charge density on the three surfaces i. radius a ii. radius b iii. radius c.

c) Find the electric field in all the regions. Express this as a function of r measured from the center of the spheres

An elevator accelerates upward at 1 m/s2. When the elevator is moving upward at 2 m/s, a bolt drops from the ceiling which is 2.5 m above the ?oor. Assume that the bolt does not experience air resistance. Calculate how long it takes for the bolt to hit the ?oor, how far it travels, and how fast it is going when it hits the ?oor of the elevator. Solve this problem in two reference frames, one ?xed with respect to the building and one ?xed with respect to the elevator. Only the fall time will be the same for the two reference frames. In this and subsequent problems you solve in dynamics, think about the advantages and disadvantages of various reference frames and clearly state what reference frame you ultimately choose for your solution.

In the time that it takes a whiteboard marker of mass 12 grams to fall 1 meter down to the Earth of mass 6 × 10 kg, 24 (a) how far does the earth move up towards the whiteboard marker? Derive your answer from Newton’s laws, and state when you are using which law. (b) Given that the smallest scale we have measured to date is 0.00000000000000000001 meters = 10 -20 m, can we measure this distance from part (a) yet? (c) Therefore, is part (a) a scientific question? A “scientific question” has to be measurable or falsifiable “in principle” (not necessarily in practice according to current technology).

Bonham the dog stands at the far end of a 14 ft, uniform boat pointing to shore (the drawings below are not exactly to scale). The boat is twice as massive as Bonham. Initially, the dog is 20 ft from shore. Eying his owner on shore, Bonham trots to the front of the boat and stops. Assuming no friction and no water current, and also that he walks the full 14 ft length of the boat (meaning his length is small by comparison), how close is Bonham from shore then?

three charges are placed on the corners of an equilateral triangle with side lenght L. calculate the force on the bootom right charge. Record your answer as a vector in i,j,k. your answer should be in term of k,L and Q

Two lasers are shining on a double slit, with slit separation d. Laser 1 has a wavelength of d/20, whereas laser 2 has a wavelength of d/15. The lasers produce separate interference patterns on a screen a distance 5.30m away from the slits.

1.Which laser has its first maximum closer to the central maximum? Laser one or Laser 2 ?

2. What is the distance ?ymax?max between the first maxima (on the same side of the central maximum) of the two patterns? Answer in m

3.What is the distance ?ymax?min between the second maximum of laser 1 and the third minimum of laser 2, on the same side of the central maximum?

Please show work, and units.

Imagine cart 1 with initial velocity v1i collides with cart 2 with initial velocity v2i = 0, where they then move together as a single mass (attached by velcro). Sketch the expected center of mass position over time graph. Assume t = 0 corresponds to the moment immediately after the impulse to cart 1 is delivered and assume equal masses (m1 = m2). Ignoring the effects of friction, is the above collision elastic or inelastic? Why?

harmonic if the period (the time for one cycle) does not depend on the amplitude (the maximum displacement from equilibrium). In the following set, identify the oscillations that are simple harmonic, the ones that are approximately simple harmonic, and the ones that are not simple harmonic. Please comment on why/how you make your identifications.

1. The pendulum in a grandfather clock

2. A boat in water pushed down and released

3. A child on a swing

4. A mass hanging from a spring

5. A ping pong ball bouncing on the floor.

A proton in a high-energy accelerator moves with a speed of c/2. Use the work

1. Did the values of μ measured directly and indirectly agree?

2. As the tension is increased, does the number of segments increase or decrease when the frequency is kept constant?

3. As the frequency is increased, does the number of segments increase or decrease when the tension is kept constant?

4. As the tension is increased, does the speed of the wave increase, decrease, or stay the same when the frequency is kept constant?

5. As the frequency is increased, does the speed of the wave increase, decrease, or stay the same when the tension is kept constant?

6. Suppose that String #1 is twice as dense as String #2, but both have the same tension and the same length. If each of the strings is vibrating in the fundamental mode, which string will have the higher frequency?

Two blocks are positioned on surfaces, each inclined at the same angle 45.6 degrees with respect to the horizontal. The blocks are connected by a rope which rests on a frictionless pulley at the top of the inclines, so the blocks can slide together. The mass of the black block is 4.10kg and the coefficient of kinetic friction for both blocks and inclines is μk 0.370. Assume static friction has been overcome and that everything can slide. A) What must be the mass of the white block if both blocks are to slide to the right at a constant velocity? B)What must be the mass of the white block if both blocks are to slide to the left at a constant velocity? C) What must be the mass of the white block if both blocks are to slide to the right at an acceleration of 1.5m/s^2? D) What is must be the mass of the white block if both blocks are to slide to the left at an acceleration of 1.5 m/s2? E)Now, re-do part (d) above, but now assuming no friction at all on either incline. So in the absence of friction, what must be the mass of the white block such that both blocks slide to the left at an acceleration of 1.5 m/s2?

(a) Keck-I has a 10m diameter mirror. HST (Hubble Space Telescope) has a 2.4m mirror.

What is the ratio of the light gathering power of Keck-I to the light-gathering power of HST?

[Compute the ratio (light gathering power of Keck)/(light gathering power of HST) and express as a decimal. Do not use scientific notation.]

(b) What is the ratio of the angular resolution limit of Keck to the angular resolution limit of HST? (Assume they are both observing at the same wavelength.)

[Compute the relevant ratio Keck/HST, express as a decimal, and enter below.]

(c) HST orbits at an altitude of 559 km above the Earth's surface. Assume its orbit is circular.

Compute its orbital period in hours.

(d) Compute its orbital speed (in km/s).

(e) If a satellite like Hubble was looking down at the Earth instead of up, what is the smallest physical size (in cm) on the Earth’s surface that it could resolve? [Hint: assume you are using the visible spectrum.]

The potential at the center of a uniformly charged ring is 44 kV , and 11 cm along the ring axis the potential is 31 kV .

Find the ring's radius.

Find the ring's total charge.

Which of these are actual evidence for the existence of a black hole in the center of the Milky Way, and which are not?

Stars are observed to disappear into the black hole

Bright quasar emission is detected from the center of the galaxy

Telescopes have been used to take high resolution images of the black hole's event horizon

Astronomers observe an extremely bright and compact radio source

The closest approach of stellar orbits near the center of the galaxy indicate the object is smaller than the solar system

Stellar velocities near the center of the galaxy indicate 4 million times the mass of the sun inside their orbit