At 17°C, a rod is exactly 18.08 cm long on a steel ruler. Both the rod and the ruler are placed in an oven at 250°C, where the rod now measures 18.25 cm on the same ruler. What is the coefficient of thermal expansion for the material of which the rod is made? The linear expansion coefficient of steel is 11 x 10-6 1/C°.

1. (6 pts) What is the significance of each of the following in the study of astronomy:

(a) Dark Matter

(b) 21 cm Radiation

2. (5 pts) Describe the overall structure and main parameters of the Milky Way galaxy.

3. (10 pts) Describe the main characteristics of Einstein’s Theory of General Relativity.

4. (4 pts) Explain the major characteristics/properties of Pulsars.

Learning Goal:

To understand the use of Hooke's law for a spring.

Hooke's law states that the restoring force F⃗  on a spring when it has been stretched or compressed is proportional to the displacement x⃗  of the spring from its equilibrium position. The equilibrium position is the position at which the spring is neither stretched nor compressed.

Recall that F⃗ ∝x⃗  means that F⃗  is equal to a constant times x⃗ . For a spring, the proportionality constant is called the spring constant and denoted by k. The spring constant is a property of the spring and must be measured experimentally. The larger the value of k, the stiffer the spring.

In equation form, Hooke's law can be written

F⃗ =−kx⃗ .

The minus sign indicates that the force is in the opposite direction to that of the spring's displacement from its equilibrium length and is "trying" to restore the spring to its equilibrium position. The magnitude of the force is given by F=kx, where x is the magnitude of the displacement.

After driving a portion of the route, the taptap is fully loaded with a total of 24 people including the driver, with an average mass of 66 kg per person. In addition, there are three 15-kg goats, five 3-kgchickens, and a total of 25 kg of bananas on their way to the market. Assume that the springs have somehow not yet compressed to their maximum amount. How much are the springs compressed? (Enter the compression numerically in meters using two significant figures.)

1. Use Excel to plot x(t) versus time for 2 periods of the motion. Use the equations from
the lecture notes that are from the book. Put this in an Excel sheet call x_t

x(t) = A cos(ωt)

2. Use Excel to plot v(t) versus time for 2 periods of the motion. Use the equations from
the lecture notes that are from the book. Put this in an Excel sheet call v_t

v(t) = -ωAsin(ωt)

3. Use Excel to plot a(t) in m/s2 versus time for 2 periods of the motion. Use the equations
from the lecture notes that are from the book. . Put this in an Excel sheet call a_t

a(t) = -ω2Acos(ωt)

Is the charge of the capacitor at the beginning of each cycle (starting from the lowest voltage)? Explain in terms of the voltage increase and flow of charges?

How could the value of an unknown capacitance be determined using the experimental procedures?

Can an inert gas in a detention situation be used to “dampen” a sharp peak in detonation pressure and convert that peak into a more sustained pressure building?

A pendulum bob swings back and forth.  Ignore air resistance.  At point A, the potential energy is 15 J and the pendulum bob is at a height of 1 meter.

a) What is the mass of the pendulum bob? Show work by typing the equation and plugging in numbers.

b) What is the total mechanical energy of the pendulum? Explain.

c) At which point on the diagram will the maximum kinetic energy occur and what is the maximum kinetic energy of the pendulum? Explain.

d) What is the potential energy at point B and D? The height of the pendulum bob at B and D is 0.5 meters. Show your work by typing the equation and plugging in numbers.

e) At point B and D, what is the relationship between kinetic energy and potential energy? Explain.

f) What is the speed of the pendulum at point C? Show work by typing the equation and plugging in numbers.

1. Discuss stellar parallax, how it works, and how it is used as a tool in astronomy.

2. Which spectral class has the highest surface temperature?

Which spectral class has the coolest surface temperature?

What is the spectral class of the sun?

3. One of our tools for measuring cosmic distances is Cepheid Variable Stars. Explain how they allow the determination of distances.

4. The Hertzsprung-Russell diagram is a tool as useful to astronomers as the Periodic Table is to chemists. Explain the structure of the H-R diagram and what it tells us.

5. There are several key steps necessary for the creation of a star. Provide an overview description of these key steps.

If a heavy nucleus were to fission into only two product nuclei, they would be very unstable. In what way? Why? How would they decay?

The ancient Greeks, Copernicus, and Brahe all thought that the idea that stars are much further away from Earth than planets was difficult or impossible to explain. What is the modern, scientific explanation for this?

A point charge +q is at the origin. A spherical Gaussian surface centered at the origin encloses +q. So does a cubical surface centered at the origin and with edges parallel to the axes. Select "True" or "False" for each statement below.

1. Suppose (for this statement only), that q is moved from the origin but is still within both the surfaces. The flux through both surfaces is changed.

2.If the radius of the spherical Gaussian Surface is varied, the flux through it also varies.

3. The area vector and the E-Field vector point in the same direction for all points on the spherical surface.

4. The E-Field at all points on the spherical surface is equal due to spherical symmetry.

5. The Electric Flux through the spherical surface is less than that through the cubical surface.

1. What is the relationship between the history of the hearsay rule and the history of the trial by jury?

2. What is the rationale for allowing some confessions into evidence even though the confessions are hearsay? Do you believe such evidence should be heard? If so, why? If not, why? Explain.

Newton's 2nd law says that when a larger force is applied to an object of mass m, the object will experience a larger acceleration. At the same time, you've learned that all objects experience the same acceleration in a free fall, even if their weights (the forces of gravity acting on them) are different. That sounds like a contradiction: on one hand, from the Newton's 2nd law, a larger force means larger acceleration, on the other hand when applied to motion under gravity - a larger weight (force) means the same acceleration for all objects. How do you reconcile these statements? Why isn't it a contradiction? Does gravity violate the Newton's second law or is there another explanation. Be as thorough and clear in your explanation as possible.

Read the Operating Instructions for the Cs/Ba-137m Isotope Generator. Place a watch glass under the radio nuclide cow and elute a few drops of radioactive barium 137 onto the filter paper. Place your sample under the Geiger tube immediately after elution. Any delay will result in loss of accuracy. Why?