The left end of a long glass rod 8.60 cm in diameter, with an index of refraction 1.55, is ground and polished to a convex hemispherical surface with a radius of 4.30 cm . An object in the form of an arrow 1.53 mm tall, at right angles to the axis of the rod, is located on the axis 23.5 cm to the left of the vertex of the convex surface.

Find the height of the image of the arrow formed by paraxial rays incident on the convex surface.

Palladium-103 (Pd-103) has a half-life of 17 days. Its molar mass is 0.10291 kg/mol.

1) What is the decay constant of Pd-103?

2) What is the initial activity of a 750-gram sample of Pd-103?

3) What is the activity of the sample after 51 days?

4) After how many days will the activity decrease to 1/20th of the initial activity?

A cow that is 2 meters long watches a train passing at 90% of the speed of light. According to the cow the train measures 15 meters.

What is the factor  of temporal expansion between time in the benchmark of the cow and time in the benchmark of the train?

b. How tall is the cow according to the train passengers? vs.

How long does the train take to pass the cow according to the cow?

d. According to the train passengers, how long does the train take to pass the cow?

e. According to the passengers of the train, how long is the train?

f. How long does the nose of the train take to pass the cow according to the cow?

g. How long does the nose of the train take to pass the cow according to the train passengers?

During a tennis match, a player serves the ball at 28.6 m/s, with the center of the ball leaving the racquet horizontally 2.33 m above the court surface. The net is 12.0 m away and 0.900 m high. When the ball reaches the net, (a) what is the distance between the center of the ball and the top of the net? (b) Suppose that, instead, the ball is served as before but now it leaves the racquet at 5.00° below the horizontal. When the ball reaches the net, what now is the distance between the center of the ball and the top of the net? Enter a positive number if the ball clears the net. If the ball does not clear the net, your answer should be a negative number. Use g=9.81 m/s2.

] Accreting, spinning, magnetized systems tend to:

1. Accelerate
2. Grow in mass
3. Produce jets
4. Produce supernovae
5. Cannot be predicted

[28] If space had been found to be negatively curved, the other evidence might have us conclude that:

1. The universe will re-collapse
2. The need for dark energy is even greater
3. There might be little or no dark energy
4. Omega =1 exactly
5. None of the above

[29] The “anthropic principle” addresses the idea that:

1. The universe seems conducive to life
2. The universe is homogeneous everywhere
3. The universe can be explained via rational explanations
4. The study of cosmology is common to all human cultures
5. None of the above

30. The “principle of equivalence” states that:
    1. Masses of fundamental particles are the same everywhere
    2. All universes in a multiverse are similar  
    3. Acceleration in a gravitational field in similar to the acceleration by a rocket D) Mass and energy are equivalent (E = mc²)

31. Type Ia supernovae are:
    1. Exploding neutron stars
    2. Exploding hydrogen rich white dwarf stars
    3. Exploding helium / carbon white dwarf stars
    4. Exploding massive stars stripped of their hydrogen envelopes
    5. Exploding hydrogen-rich massive stars

A person stands at the center of a turntable, holding his arms extended horizontally with a 1.5 kg dumbbell in each hand. He is set rotation about a vertical axis, making one revolution in 2 seconds. Find the new angular velocity if he pulls the dumbbells in to his middle. His moment of inertia (without dumbbells) is 3 kgm2 when his arms are out stretched, dropping to 2.2 kgm2 when his hands are at his middle. The dumbbells are 1 m from the axis initially and 0.2 m from it when moved to his middle.

40.0 gram of ice at −15.00 °C is put into a Styrofoam cup calorimeter (of negligible mass) containing water at +15.00 °C. When equilibrium is reached, the final temperature is 6.00 °C. How much water did the calorimeter contain initially? The specific heat of ice is 2090J/(kg • K), that of water is 4186 J/(kg • K), and the latent heat of fusion of water is 33.5 × 104J/kg.

A)416 g

B)579 g

C)425 g

D)613 g

E)780 g

D. What is the typical background radiation we are exposed to? What additional exposure would we get from a chest x-ray? A CT scan of the torso? A coast-to-coast flight? A year of living in Denver, CO? Approximate or representative values are sufficient.
Please stay within the same unit system (i.e., choose either Sievert or rem) for easier comparison in (F).

E. Before flat-screen TV sets became widespread, color TV sets used huge cathode ray tubes (CRT). To generate TV images with sufficient brightness, the electron beam was accelerated with an appreciably high voltage. What were typical acceleration voltages in those TV sets? Would they represent an x-ray hazard? Provide a reason for your answer!

Note: Provide the sources for your answers (D) and (E) as well!

Note also: In (E), a government mandate that the x-ray dose had to remain below allowed limits is not a valid reason, because a government mandate is not an engineering solution -- not by a far shot.

A 73 g ice cube at -45°C is placed in a lake whose temperature is 76°C. Calculate the change in entropy of the cube-lake system as the ice cube comes to thermal equilibrium with the lake. The specific heat of ice is 2220 J/kg·K.

A problem involves a car of mass m going down a track from a height H, and round a loop of radius r. The loop is frictionless.

It asks for the minimum cut-off speed required, at the highest point in the loop (call it point D), such that the car makes it round the loop without falling. I know the solution; I should set the centripetal accleration equal to 9.81. In other words, contact force with the track at point D is equal to zero.

But I tried solving it by conservation of energy. At point D, the car is at a height 2r from ground level. Therefore, in order for the car to reach that height at point D, it must initially have a potential energy of mg(2r). Meaning, it should be released from a height H = 2r.

I got the wrong answer and I'm confused why that happened. Isn't that how conservation of energy work? Please clarify, where's the error in my solution?

Montréal is 510 km from Toronto, 12 degrees north of east. At an altitude of 9,000 meters, the windspeed is 80 km/h out of the north. For the entire 510 km, the aircraft flies at 9,000 meters at an airspeed of 300 knots. Draw a triangle whose sides represent the velocity vectors that correspond to the groundspeed, airspeed, and windspeed. Determine:

(a) the aircraft heading (direction in which the nose of the aircraft points), in degrees from north.

(b) the groundspeed of the aircraft, in km/h.

(c) the flight time, in hours.

Light with a wavelength range of 142-295 mm shines on a silicon surface in a photoelectric effect apparatus.

-What is the longest wavelength of the light that will eject electrons from the silicon surface?

-With what maximum kinetic energy will electrons reach the anode?

A concave lens has a focal length of magnitude 10 cm. It is placed a distance of 25 cm from a concave mirror with a focal length of magnitude 15 cm. An object is set a distance of 22 cm in front of the lens. The observer is at the same location as the object, so the light from the object goes through the lens, reflects off the mirror, and comes back through the lens to the observer.

Draw the ray diagram for the image from the first lens only.

Describe the final image (location and magnification).