In January 2006, astronomers reported the discovery of a planet comparable in size to the earth orbiting another star and having a mass of about 5.5 times the earth's mass. It is believed to consist of a mixture of rock and ice, similar to Neptune. Take mearth=5.97×1024kg and rearth=6.38×106m.

1) If this planet has the same density as Neptune (1.76 g/cm3), what is its radius expressed in kilometers?

Express your answer in kilometers.

2)

What is its radius expressed as a multiple of earth's radius?

Express your answer in units of earth's radius.

Horseshoe bats (genus Rhinolophus) emit sounds from their nostrils, then listen to the frequency of the sound reflected from their prey to determine the prey's speed. (The "horseshoe" that gives the bat its name is a depression around the nostrils that acts like a focusing mirror, so that the bat emits sound in a narrow beam like a flashlight.) A Rhinolophus flying at speed v bat emits sound of frequency f bat; the sound it hears reflected from an insect flying toward it has a higher frequency f refl.

If the bat emits a sound at a frequency of 80.9 kHz and hears it reflected at a frequency of 83.9 kHz while traveling at a speed of 3.8 m/s , calculate the speed of the insect.

Use 344 m/s for the speed of sound in air. Express your answer using two significant figures.

A hydraulic lift in a garage has two pistons: a small one of cross-sectional area 3.60cm2 and a large one of cross-sectional area 250cm2 .

a) If this lift is designed to raise a 3300-kg car, what minimum force must be applied to the small piston?

b)If the force is applied through compressed air, what must be the minimum air pressure applied to the small piston?

Let B = 5.40 m at 60.0°. C and A have equal magnitudes. The direction angle of C is larger than that of A by 25.0°. Let A · B = 27.9 m2 and B · C = 36.9 m2. Find the magnitude (in m) and direction (in degrees) of A.

An electron and a 140-g baseball are each traveling 120 m/s measured to a precision of 0.075 % .

Part A: Calculate the uncertainty in position of the electron.

Part B: Calculate the uncertainty in position of the baseball.

Part C: Compare the uncertainty in position of each.

A basketball player makes a jump shot. The 0.530-kg ball is released at a height of 1.90 m above the floor with a speed of 7.12 m/s. The ball goes through the net 3.02 m above the floor at a speed of 4.24 m/s. What is the work done on the ball by air resistance, a nonconservative force?

Compare the production of bremsstrahlung and characteristic radiation.  Describe the specific contribution that each type makes to the x-ray emission spectra (the intensity vs. photon energy graph).  Finally, identify all major factors affecting the curve’s shape and position.

A 0.005-kg bullet is fired with a speed of 400 m/s into a pendulum with mass 1 kg suspended from a massless cord 2 m long.

a. If the bullet is embedded after the collision, calculate the vertical height of the pendulum rise.

b. If the bullet is made of rubber and it bounces back at a speed of 400 m/s, calculate the vertical height of the pendulum rise.

A hollow sphere of radius 0.170 m, with rotational inertia I = 0.0150 kg

A child pushes a merry-go-round that has a diameter of 4.00 m and goes from rest to an angular speed of 18.0 rpm in a time of 47.0 s.

1) Calculate the average angular acceleration of the merry-go-round. (Express your answer to three significant figures.)

2) Calculate the angular displacement of the merry-go-round. (Express your answer to three significant figures.)

In quantum field theory with a mass gap, why do states in the asymptotic future/past turn out to have a Fock space structure? For a free quantum field theory, that's trivial, but why is that the case for interacting theories? In fact, the more one thinks about it, the less clear it becomes. If the quanta of the "fundamental" field is unstable, it doesn't show up in the asymptotic Fock space. If the quanta is confined, it also doesn't show up. If there is a stable bound state, it does show up. If there is a stable solitonic particle, it also shows up.

I am very aware of the LSZ formalism, but that presupposes the existence of an asymptotic Fock space structure as a starting point. Besides, it doesn't handle stable solitons.

Make a prediction of the vertical position versus time (y vs. t) for a ball in free fall from bouncing vertically on a table. You want to predict the entire motion from right after the first contact with the table (on its way up), to the top of the motion, and back down to the table at the instant before the ball hits the table for the second time (on its way down, but hasn’t hit yet). Graph only predictions for that one bounce, not multiple bounces.

(a) Sketch a graph of vertical position versus time (y vs. t) for a ball in free-fall.

(b) Explain your prediction – how is the physical motion of the ball reflected in the graph you drew? Is the equation for this motion linear or quadratic?

6. Consider the probability distributions of hydrogen angular states. (a) (5 pts) For what values of θ is the angular probability density maximum and minimum for l = 1, m = 0? (b) (5 pts) For what values of θ is the angular probability density maximum and minimum for l = 3, m = ±1? This may be difficult to do analytically, so make a plot with your computer, or simply sketch the function

5. The wireless networking standard known as Wi-Fi encompasses several frequency bands in the microwave part of the electromagnetic spectrum. The two most common are the 2.4GHz and 5GHz bands.

a) Wi-Fi channels in the 2.4GHz band range from 2.401GHz to 2.473GHz in the US. What range of wavelengths correspond to these frequencies?

b) Wi-Fi channels in the 5GHz band range from 5.170GHz to 5.835GHz in the US. What range of wavelengths correspond to these frequencies?

A charge of q = 4.00 ✕ 10−9 C is spread evenly on a thin metal disk of radius 0.160 m. HINT (a) Calculate the charge density (in C/m2) on the disk. C/m2 (b) Find the magnitude of the electric field (in N/C) just above the center of the disk, neglecting edge effects and assuming a uniform distribution of charge. N/C