Physics midterm question: roller coaster hills

Physics 5A (currently Physics 205A) Midterm 2, spring semester 2008
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Conceptual Question 6.6

In the design of a roller coaster, is it possible for any hill of the ride to be higher than the first one? If so, discuss how. If not, then discuss why this would be impossible. Explain your reasoning using the properties of energy conservation.

Solution and grading rubric:

• p:
  Correct. Either of two answers suffices using properties of energy conservation: (a) if the roller coaster car starts at rest from the first hill, and no additional energy is put into the system after it is released, then the second hill can at most be as high as the first (under ideal conditions only), or lower; or (b) if the car has been given sufficient kinetic energy at the top of the first hill, then it may make it over a second hill that is higher.
  
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
  
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. Argument somehow based on momentum conservation; but at least recognizes that the second hill must be at most as high as the first hill unless something is done.
  
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Typically states that the second hill can be higher, but does not clearly explain how this would be possible.
  
• x:
  Implementation/application of ideas, but credit given for effort rather than merit.
  
• y:
  Irrelevant discussion/effectively blank.
  
• z:
  Blank.
  

Grading distribution:
p: 27 students
r: 0 students
t: 7 students
v: 2 students
x: 0 students
y: 0 students
z: 0 students

A sample of a "p" response (from student 2607) is shown below:
Another "p" response (from student 5711):
A sample of a "v" response (from student 7937), where it is argued that each subsequent hill can be higher than the first:

Physics midterm question: sound wave intensity

Physics 5A Midterm 2, Spring Semester 2008
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Problem 11.3

[3.0 points.] The intensity of a sound wave from a jet airplane as it is taking off is 12 Watts/m^2 at a distance of 10 m. What happens to the intensity of the sound waves as they travel out to a distance of 20 m from the jet airplane?
(A) It decreases by a factor of 1.4.
(B) It decreases by a factor of 2.0.
(C) It decreases by a factor of 4.0.
(D) (The intensity of the sound waves remains the same.)

Correct answer: (C)

The intensity of a spherical sound wave, with no reflections or absorption, is inversely proportional to the square of the radius, as measured from the (isotropic) source. Thus doubling the distance from the source results in reducing the intensity by a factor of four.

Student responses
Sections 4987, 4988
(A) : 7 students
(B) : 10 students
(C) : 15 students
(D) : 3 students

Astronomy in-class activity: mass transfer in close-pair binaries

Astronomy 10 In-class activity 23 v.07.04.30, Spring Semester 2008
Cuesta College, San Luis Obispo, CA

Astronomy 10 learning goal Q10.2

Students find their assigned groups of three to four students, and work cooperatively on an in-class activity worksheet to summarize the three stages of initial mass transfer in a close-pair (mass transferring) binary star system.Star B is more massive than Star A, due to its being closer to the center of mass, and also because of its larger Roche lobes. As a result, Star B will end its main sequence lifetime earlier than Star A, and become a giant or supergiant.

As a result of Star B expanding and filling its Roche lobe up to the "neck" or "pinch point," hydrogen will then be transferred to Star A. This makes their masses become more equal, making their separation distance decrease, while increasing their orbital speeds. As a result, centrifugal forces increase, such that the size of Star B's lobe shrinks (while it is expanding in its giant/supergiant phase), making the "spillage" from Star B to Star A rapid.

Eventually the masses of Star B and Star A equalize; this is when their separation distance is the smallest, and their lobes are equal in size, but the physical size of Star B (still) fills its (smaller) Roche lobe.

As Star B still transfers hydrogen to Star A, this makes their masses become unequal, making their separation distance increase, while decreasing their orbital speeds. As a result, centrifugal forces decrease, such that the size of Star B's lobe expands. This makes it harder for Star B to "spill over" hydrogen out of its Roche lobe, and the transfer of material slows, and eventually stops when Star B is unable to exceed its much larger Roche lobe.

(Transfer from Star A, when it eventually ends its main sequence lifetime, to Star B will eventually occur, but this discussion is outside the scope of this course.)

Thus with all observations of close-pair binary star systems where mass transfer is taking place, it is more likely to see a less-massive star feeding a more-massive star than vice versa.

Follow-up post:

Astronomy clicker question: masses, densities, and event horizons

Astronomy 10, Spring Semester 2008
Cuesta College, San Luis Obispo, CA

Astronomy 10 learning goal Q10.1

Students were asked the following clicker question (Classroom Performance System, einstruction.com) near the end of their learning cycle (specifically, following the astronomy in-class activity: masses, densities, and escape velocities).

[0.3 points.] Why is a black hole the only object that has an event horizon?
(A) Because of its mass.
(B) Because of its density.
(C) Because of both its mass and density.
(D) (Neither its mass nor density matters.)

Correct answer: (B)

Student responses
Section 5166
(A) : 1 student
(B) : 21 students
(C) : 14 students
(D) : 3 students

Astronomy in-class activity: masses, densities, and escape velocities

Astronomy 10 In-class activity 23 v.07.04.25, Spring Semester 2008
Cuesta College, San Luis Obispo, CA

Astronomy 10 learning goal Q10.1

Students find their assigned groups of three to four students, and work cooperatively on an in-class activity worksheet to determine the relationship between the escape velocity with mass and/or density.

Start off with filling some of the entries for the students, before they start working in their groups. The main sequence star on the left is the smallest and least massive of the main sequence stars: "G2," "1.0 M_Sun." Point out the progression in increasing size and mass of the main sequence stars, from right-to-left. Also point out the progression in decreasing size from left-to-right for the compact objects, and also the increasing escape velocities. Undoubtably the compact object with zero size and an infinite escape velocity is the black hole.
There will be several ties for the list of increasing masses:

G2 = white dwarf; A3 = neutron star; B3 = black hole.

However, there is no trend in escape velocities for this list, such that there is no relationship between the mass and escape velocity.

There are also several (approximate) ties for the list of increasing densities:

G2 = A3 = B3; white dwarf, neutron star; black hole.

Since the escape velocities also increase from left-to-right along this list, there is a direct relationship between the density of an object and its escape velocity.

Follow-up post: Astronomy clicker question: masses, densities, and event horizons.

Physics clicker question: Doppler effect

Physics 5A, Spring Semester 2008
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Multiple-Choice Question 12.8

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

[0.6 participation points.] A source emits a 440.0 Hz sound. In which situation would an observer hear the highest frequency? (Take the speed of sound to be 340.0 m/s.)
(A) Source is stationary, observer moves at 5.0 m/s towards source.
(B) Source moves at 5.0 m/s towards observer, observer is stationary.
(C) Source and observer both move at 5.0 m/s towards each other.
(D) (More than one of the above choices.)
(E) (I'm lost, and don't know how to answer this.)

Sections 4987, 4988
(A) : 3 students
(B) : 5 students
(C) : 17 students
(D) : 4 students
(E) : 1 student

Correct answer: (C)

The frequency detected by the observer is given by:

f_observer = ((1 - (v_observer/v_sound))/(1 - (v_source/v_sound))*f_source.

In each of cases (A)-(C), the numerator in the parenthesis above is less than the numerator, so f_observer is always higher than f_source (i.e., in each case the motions of the source and observer relative to each other are towards each other). However, the Doppler shift is the greatest when both the source and observer are moving towards each other with respect to the lab frame. Thus for (C), f_observer = (345.0/335.0)*f_source = 453.1 Hz, although most students had determined this without having done any calculations.

[Follow-up question]

[0.6 participation points.] In which situation would the observer hear the second highest frequency? (Use the same (A)-(E) choices from question (10).)

Sections 4987, 4988
(A) : 4 students
(B) : 6 students
(C) : 1 student
(D) : 18 students
(E) : 0 students

Correct answer: (B)

Inexplicably, one student chose (C) as the second highest frequency heard by the observer.

The modal response (D) means that most students said that (A) and (B) would both give the same higher f_observer. However, for (A) v_observer = -5 m/s, v_source = 0, then f_observer = (345.0/340.0)*f_source = 446.5 Hz; and for (B) v_observer = 0, v_source = +5 m/s, then f_observer = (340.0/335.0)*f_source = 446.6 Hz.

Physics quiz question: independent versus dependent wave parameters

Physics 5A Quiz 6, Spring Semester 2008
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Multiple-Choice Questions 11.5, 11.6, and 11.8

[3.0 points.] A wave has a frequency and wavelength of 200 Hz and 0.750 m, respectively. If the frequency of the wave source is changed, which wave parameters will also change as a result?
(A) The wavelength.
(B) The speed of the wave.
(C) (Both the wavelength and the speed of the wave will change.)
(D) (Neither the wavelength nor the speed of the wave will change.)

Correct answer: (B)

The speed of a wave depends on the properties of the medium, and not on frequency, which is a source parameter. However, wavelength is the parameter that is dependent on both speed and frequency, and thus changes as a result of changing the frequency of the source.

Student responses
Sections 4987, 4988
(A) : 9 students
(B) : 4 students
(C) : 20 students
(D) : 1 student

Physics quiz question: stress and strain of different cross-section bars

Physics 5A Quiz 6, Spring Semester 2008
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Conceptual Question 10.4(b)

[3.0 points.] A cylindrical steel bar of radius 2.50 cm is compressed by the application of forces of magnitude 1.50 x 10^3 N at each end. What magnitude forces (at each end) would be required to compress by the same amount a steel bar of the same length, but a radius of 1.25 cm?
(A) 375 N.
(B) 750 N.
(C) 1.06 x 10^3 N.
(D) 1.50 x 10^3 N.

Correct answer: (A)

Hooke's law relating stress (F/A) and strain (delta(L)/L)) is:

(F/A) = Y*(delta(L)/L),

where Y is the Young's modulus for the material. Since the radius is reduced by a factor of two, then the area is reduced by a factor of four, such that the force required to cause the same amount of strain in this smaller cross section bar would be one-fourth the original force. Response (B) is one-half of the original force, while response (C) is sqrt(2) = 0.707 times the original force.

Student responses
Sections 4987, 4988
(A) : 8 students
(B) : 19 students
(C) : 3 students
(D) : 3 students

Astronomy clicker question: entering the event horizon

Get into vortex you say, by ?rico Lopez
icanhascheezburger.com
January 3, 2008

Astronomy 10, Spring Semester 2008
Cuesta College, San Luis Obispo, CA

Astronomy 10 learning goal Q10.1

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

[0.3 points.] Why is entering the event horizon (the "Schwarzchild radius") surrounding a black hole considered a "point of no return?"
(A) All matter is crushed into nothingness.
(B) All matter is instantly converted into energy.
(C) The escape velocity is faster than the speed of light.
(D) Time runs backwards.

Correct answer: (C)

If students ask about what's inside the event horizon of a black hole, point out that they could certainly try to enter it and find out for themselves. However, in the very unlikely event that would be able to survive the journey, they would not be able to tell anyone in the outside universe about their discoveries, as nothing, not even light would be able to escape from within the event horizon. So they should bring a friend to share in the experience. Otherwise, it'd be lonely in there...

And yes, the expression on the middle kitten is priceless.

Student responses
Section 4160
(A) : 9 students
(B) : 4 students
(C) : 17 students
(D) : 0 students

Section 5166
(A) : 7 students
(B) : 7 students
(C) : 23 students
(D) : 0 students

Physics clicker question: sound wave frequency

Physics 5A, Spring Semester 2008
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Problem 11.52(c)

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

[0.6 participation points.] Consider a cello string, which vibrates at its fundamental frequency of 65.4 Hz. The velocity of sound waves in air is 340 m/s. The frequency of sound waves created by the cello string is:
(A) lower than 65.4 Hz.
(B) equal to 65.4 Hz.
(C) higher than 65.4 Hz.
(D) (I'm lost, and don't know how to answer this.)

Sections 4987, 4988
(A) : 2 students
(B) : 12 students
(C) : 15 students
(D) : 0 students

Correct answer: (B)

While the wavelengths of the string standing wave and sound wave will be different, their frequencies must be the same. It is instructive to think about the fact that the string is vibrating transversely 65.4 times per second, and it is "slapping" the air (and thus generating a sound wave) with this same frequency.