Astronomy clicker question: the cheerleader effect

Astronomy 10, Spring Semester 2007
Cuesta College, San Luis Obispo, CA

Astronomy 10 learning goal Q4.3

Students were asked the following clicker question (Classroom Performance System, einstruction.com) at the beginning of their learning cycle:

[0.3 points.] What makes up the core of the Earth?
(A) Very hot liquid metal.
(B) Very hot solid metal.
(C) Very cold liquid metal.
(D) Very cold solid metal.

Student responses
Section 4136
(A) : 17 students
(B) : 14 students
(C) : 0 students
(D) : 0 students

Section 5076
(A) : 12 students
(B) : 5 students
(C) : 0 students
(D) : 0 students

Correct answer: (B).

The reason for this is the "cheerleader effect"--imagine an inverted pyramid of cheerleaders, where the bottom cheerleader has to support the weight of all the other cheerleaders on top of her.

Also there is a competition between temperature and pressure in the core of the Earth. Temperatures that are high enough will melt solid into liquid, while pressures that are high enough will squeeze liquids back into solids. In the outermost core, temperature wins over pressure, so the outer core is hot and liquid. In the innermost core, where it is squeezed from all sides by the outer core, mantle, and crust, pressure wins over temperature, so the innermost core is extremely hot, but under the immense pressures there, is solid!

Physics bon mot: the gift

General physics bon mot

"...Tests are a gift. And great tests are a great gift. To fail the test is a misfortune. But to refuse the test is to refuse the gift, and something worse, more irrevocable, than misfortune."
--Lois McMaster Bujold

Tests, apparently, are the gifts that just keep on giving... Students usually groan after reading this quote, on the announcements page just before their first physics midterm.

Physics midterm problem: thrown rock impact

Physics 8A Midterm 1, Fall Semester 2006
Cuesta College, San Luis Obispo, CA

Physics 8A learning goal Q3.4

[20 points.] A Physics 8A student stands on the roof of a building and throws a rock with a velocity of magnitude 20.0 m/s at an angle of 58.0 degrees above the horizontal, which is released at a height of 25.0 m above the ground. Ignore air resistance. Determine the magnitude (in m/s) and direction (with respect to the horizontal) of the velocity of the rock just as it strikes the ground. Show your work and explain your reasoning.

(Cf. Young and Freeman, University Physics, 11/e, Exercise 3.23.)

Solution and grading rubric:

• p = 20/20:
  Correct. Breaks v_0 into v_0x and v_0y. Since a_x = 0, then v_x = v_0x. Either uses the quadratic formula to solve for t, and then plugs in t to find v_y, or uses the "time-eliminated" equation to immediately solve for v_y. Finds magnitude of v (29.8 m/s) using the Pythagorean theorem, and the direction (–69.2 degrees or +291 degrees) using inverse tangent.
  
• r = 16/20:
  Nearly correct, but includes minor math errors.
  
• t = 12/20:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least finds v_y, and/or time t.
  
• v = 8/20:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Progress made in isolating unknowns in the kinematic equations of motion.
  
• x = 4/20:
  Implementation of ideas, but credit given for effort rather than merit.
  
• y = 2/20:
  Irrelevant discussion/effectively blank.
  
• z = 0/20:
  Blank.
  

Grading distribution:
p: 13 students
r: 3 students
t: 6 students
v: 8 students
x: 4 students
y: 0 students
z: 0 students

Physics midterm problem: box on box

Physics 8A Midterm 1, Spring Semester 2007
Cuesta College, San Luis Obispo, CA

Physics 8A learning goal M1.5

[20 points.] Two boxes are stacked upon each other. A horizontal force of 40.0 N is applied as shown to the top box. The magnitude of the friction force between the surfaces of the upper and lower boxes is 23.0 N. Both boxes accelerate to the right with a constant magnitude of 2.00 m/s^2, as they move together across a frictionless floor. Determine the mass of the upper box, and the mass of the lower box. Show your work and explain your reasoning.

(Cf. Young and Freeman, University Physics, 11/e, Exercise 4.24, Problem 4.39.)

Solution and grading rubric:

• p = 20/20:
  Correct. Only horizontal motion is of interest here, such that a complete free-body diagram involving vertical forces is not necessary. Newton's second law is applied to the top box, where the net force is equal to the vector sum of the given applied force (right) and friction force (left), and set equal to the mass of the top box times the given acceleration; m_top = 8.50 kg. Then Newton's second law is applied to the bottom box, where the net force only consists of the friction force (right, which is the third law pair to the friction force of the bottom box on the top box), and set equal to the mass of the bottom box times the given acceleration (which must be the same as the top box); m_bottom = 11.5 kg. There may be minor round-off discrepancies, and skipped steps as long as the relevant application of Newton's laws and force vector directions and summations are clearly indicated.
  
• r = 16/20:
  Nearly correct, but includes minor math errors. Successful at finding mass of one box only, or of both boxes combined only.
  
• t = 12/20:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least some attempt at applying Newton's second law to part of or the whole system, but free-body diagram is problematic or fragmented; or attempt at free-body diagram with problematic application of Newton's second law, and Newton's third law.
  
• v = 8/20:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Serious attempt at a free-body diagram, or some attempt at applying Newton's laws.
  
• x = 4/20:
  Implementation of ideas, but credit given for effort rather than merit.
  
• y = 2/20:
  Irrelevant discussion/effectively blank.
  
• z = 0/20:
  Blank.
  

Grading distribution:
p: 7 students
r: 14 students
t: 9 students
v: 3 students
x: 3 students
y: 0 students
z: 2 students

Under an ocean of air

Sirius under high magnification and poor seeing, 2004
Bowen Celestial Observatory, 8" reflector (obsolescent)
Cuesta College, San Luis Obispo, CA
http://www.youtube.com/watch?v=yV1RUsZORig

Astronomy 10 learning goal M1.4

Even if the sky was perfectly clear at night, at a location as distant as possible from urban light pollution, there is always turbulence to contend with--the cause of poor seeing, and the twinkling of stars.

To help students understand this, draw an analogy with being at the bottom of a swimming pool. No matter how clear the water is, unless it is perfectly still, you will not get a steady view of what is above the water. Literally at sea level we are at the bottom of an ocean of air! This unsteadiness, while making the stars twinkle, degrades images taken through telescopes.

So what are some ways to alleviate the effects of atmospheric turbulence?

• Go to higher altitudes--the less air you look through, the less of an effect it has.


• Wait for lucky seeing--moments when the air in your line of sight just happens to be perfectly still. This can be done in a systematic way by recording a digital movie, throwing out the frames where the image is unacceptably distorted, and "stacking" the frames where the image is acceptably steady and clear. In a related method, speckle interferometry is where the frames of this digital movie are much faster than the unsteadiness caused by atmospheric seeing, thus "freezing" out its effects, and all frames are stacked after compensating for slight shifts in position.


• The effects of atmospheric turbulence can be "undistorted" by adaptive optics, where shape of a flexible objective mirror of a reflector is changed on the fly by a computer, in order to bring a guidestar from a twinkling, wobbling mess back to a point image. Thus the rest of the field of view would also presumably be undistorted as well. This has allowed very large aperture telescopes to be built, thus maximizing light-gathering power and improving resolving power.


• Or go to outer space--the most costly method by far, and precludes large apertures as a trade-off. But extremely-long exposures are possible, as you would not even have to worry about day or night (along with the weather and cloud cover), thus resulting in effectively powerful light-gathering.

Car-bird wave-particle duality

Astronomy 10 learning goal M1.1

The "car-bird" story, as an analogy for the wave-particle duality of light. (This expands on an earlier idea from an unknown source.)

Ask the students if they have seen "Encino Man" (Buena Vista Pictures, 1992), starring Brendan Fraser (along with Pauly Shore and Sean Astin). (Of course students have seen it, but depending on their age, they will have either seen this movie in theaters, or on cable.)

Suppose a student unfreezes and befriends Encino Man, and takes him for a ride. Encino Man is startled to see a car, but the student tells him that it's called a "car." Eventually Encino Man understands that most everything else with wheels and driving on roads are cars as well.

Then the student points out and tells Encino Man what a bird is. Encino Man replies that yes, he knows what a bird is, he just didn't know what _you_ called one...and he doesn't appreciate being patronized.

Later, the student takes Encino Man to the airport. Encino Man is fascinated by the rather large "car" driving around at the airport, but to his surprise, it then becomes a "bird" as it takes off into the air! "It's a car-bird!" he exclaims. Of course, he's referring to an airplane, but Encino Man, for lack of a better label, describes it in terms of the characteristics it displays. It behaves like a car, and other times it behaves like a bird, therefore it can be said to have car-bird duality. But an airplane is _not_ literally a car-bird--that's just how it behaves!

A similar analogy can be made with light. For lack of a better label, light is described in terms of the characteristics it displays. It behaves like a wave (it has wavelength and frequency), and other times it behaves like a particle (its amounts of energy are quantized as photons), therefore it can be said to have wave-particle duality. But light is not _literally_ a wave-particle--that's just how it behaves!

Ten types of people, not three

Physics 8A learning goal M1.2

There are only two types of motion:
Equilibrium motion = velocity (magnitude _and_ direction) constant.
Non-equilibrium motion = velocity (magnitude and/or direction) changes over time.

There are three Newton's laws:
Newton's first law (N1) deals with equilibrium motion.
Newton's second law (N2) deals with non-equilibrium motion.

What happened to Newton's third law (N3)? (Answer: it doesn't deal with any type of motion; it discusses a fundamental property of forces.)

Which leads to the old computer science joke:
"There are three types of people in the world. Those who understand binary...and those who don't."

_Actual_ computer science students have informed me that the joke has _ten_ types of people in the world, not three...

Urban light pollution

Astronomy 10 learning goal M1.4

Droll announcer at the planetarium at the Boston Museum of Science:

"Welcome to the planetarium at the Boston Museum of Science.
These will be the only stars you will ever see in Boston."

Of course, with a heavy South Boston accent. At least that was the way I remember it.