Suppose the figure below represents a ray of light going from air through crown glass into water, such as going into a fish tank. Calculate the amount the ray is displaced by the glass (Δx in mm), given that the incident angle is 37.5° and the glass is 2.75 cm thick.

______ mm

A 3.50-kg ball, moving to the right at a velocity of +3.47 m/s on a frictionless table, collides head-on with a stationary 8.30-kg ball. Find the final velocities of (a) the 3.50-kg ball and of (b) the 8.30-kg ball if the collision is elastic. (c) Find the final velocity of the two balls if the collision is completely inelastic.

Suppose you are considering renting an apartment in a building in which the tenants are required to pay the cost of heating their apartments. The building has several apartments, each occupying an entire floor of the building. The building has a flat roof. You are attracted to the apartment on the top floor because of the view but your friend tells you that the heat bills will be higher for that apartment than for the ones on the lower floors.

a. [3pts] Is your friend likely to be right? Explain why or why not in terms of the expected thermal energy flows in and out of the apartments.

b. [4pts] Defend your answer to a. by calculating the amount of energy required to heat the top and lower apartments for a year in btu. Include the lowest apartment assuming that it is just above the ground (no basement below it). Suppose that the floor area of each apartment is 900 sq ft (30ft x 30ft) and that the height from one floor to the next is 10ft. Use 8500 as the number of ’degree days’ in Minnesota (Figure 5.12 and definition near the top of p. 137) and the R values given in Table 5-1 of the book (1978 values).

c. [3pts] Use the answer you got in b. to calculate the difference in cost (if any) between heating the top apartment for a year ,heating a lower apartment for year, and heating the ground floor apartment for a year, supposing that the cost of gas heating is $0.80 per ’therm’. 1 therm=100,000 btu.

10. A soap film (n = 1.33) is formed in a loop of wire that is mounted vertically is not exactly uniform in thickness because of its weight, but wedge-shaped in cross section. When the film is illuminated with green light of wavelength 520 nm, one sees that a distance of 2.40 cm separates two bright fringes that are 4 orders apart. By how much does the film differ in thickness over this distance?

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.)