20171117

Physics quiz question: moment of inertia of ring vs. smaller disk of same mass

Physics 205A Quiz 5, fall semester 2017
Cuesta College, San Luis Obispo, CA

A ring and a solid disk rotate about their centers. The ring and the solid disk each have the same mass of 1.2 kg. The ring has a radius of 0.25 m, and the solid disk has a smaller radius than the ring. (Iring = M·R2, Idisk = (1/2)·M·R2.)

The rotational inertia of the ring is __________ the rotational inertia of the solid disk.
(A) less than.
(B) equal to.
(C) greater than.
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (C)

The rotational inertia of the ring of mass M = 1.2 kg and radius R = 0.25 m is:

Iring = M·R2 = (1.2 kg)·(0.25 m)2 = 0.075 kg·m2.

The rotational inertia of the disk of mass M = 1.2 kg and a radius smaller than 0.25 m, along with the factor of (1/2) then must be smaller than the rotational inertia of the ring:

Idisk = (1/2)·M·R2 = (1/2)·(1.2 kg)·(some value less than 0.25 m)2,

such that Iring > Idisk.

Sections 70854, 70855
Exam code: quiz05nWaW
(A) : 6 students
(B) : 4 students
(C) : 39 students
(D) : 0 students

Success level: 80%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.34

Physics quiz question: comparing lever arms for loaded beam forces

Physics 205A Quiz 5, fall semester 2017
Cuesta College, San Luis Obispo, CA

A uniform beam with a mass of 10 kg and length 2.0 m has a 3.0 kg load hanging from its end, and is suspended by a horizontal cable attached to a wall. (Calculate all torques with respect to the pivot.) The __________ force has the longest perpendicular lever arm.
(A) horizontal cable tension.
(B) beam weight.
(C) load.
(D) (There is a tie.)

Correct answer (highlight to unhide): (A)

The weight of the boom acts at its center of gravity, straight downwards. The perpendicular lever arm ℓw for the weight force w extends from the pivot to perpendicularly intercept the weight force line of action, such that this will be a horizontal line of length:

w = (1.0 m)·cos(70°) = 0.34 m.

Similarly the perpendicular lever arm ℓload for the load force Fload extends from the pivot to the perpendicularly intercept the load force of action, such that:

load = (2.0 m)·cos(70°) = 0.68 m.

The perpendicular lever arm for the horizontal cable force extends from the pivot point to perpendicularly intercept the tension force of action, such that:

cable = (2.0 m)·sin(70°) = 1.9 m.

Sections 70854, 70855
Exam code: quiz05nWaW
(A) : 21 students
(B) : 11 students
(C) : 14 students
(D) : 3 students

Success level: 43%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.53

Physics quiz question: water pressure at bottom of graduated cylinder

Physics 205A Quiz 5, fall semester 2017
Cuesta College, San Luis Obispo, CA

A graduated cylinder is filled with 10 cm of water. The top of the water level is exposed to atmospheric pressure (Patm = 101.3 kPa). The density of water is ρwater = 1.00×103 kg/m3. The water pressure at the bottom of graduated cylinder is:
(A) 1.0×102 Pa.
(B) 9.8×102 Pa.
(C) 1.003×105 Pa.
(D) 1.023×105 Pa.

Correct answer (highlight to unhide): (D)

For static fluids, the energy density relation between pressure and changes in elevation is given by:

0 = ∆P + ρ·g·∆y,

0 = (PbottomPtop) + ρwater·g·(ybottomytop),

where the air pressure at the water surface at the top of the graduated cylinder is 101.3 kPa = 1.013×105 Pa, such that:

Pbottom = Ptop – ρwater·g·(ybottomytop),

Pbottom = 1.013×105 Pa – (1.00×103 kg/m3)·(9.80 m/s2)·((–0.10 m) – (0 m)),

Pbottom = 1.013×105 Pa – 0.0098×105 Pa = 1.023×105 Pa.

(Response (A) is ρwater·∆y; response (B) is ρwater·g·∆y, which is the relative pressure difference between the top and bottom of the water in the graduated cylinder; response (C) is Ptop + ρwater·g·(ybottomytop).)

Sections 70854, 70855
Exam code: quiz05nWaW
(A) : 2 students
(B) : 11 students
(C) : 15 students
(D) : 21 students

Success level: 43%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.28

Physics quiz question: weights of comparable floaters

Physics 205A Quiz 5, fall semester 2017
Cuesta College, San Luis Obispo, CA

Two solid objects of different sizes both float with 75% of their volumes below water. It is 
not known whether these objects are made of the same material. The __________ object has a greater weight.
(A) smaller.
(B) larger.
(C) (There is a tie.)
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (A)

The magnitude of the buoyant force is given by:

FB = ρfluid·g·(Volume submerged),

where the density ρ is of the surrounding fluid (water) and the gravitational constant g = 9.80 m/s2. Since the volume of water displaced by the smaller object is less than the volume of water displaced by the larger object, then the smaller object has a smaller magnitude buoyant force exerted on it.

Newton's first law applies to both objects, as they are stationary, and thus the forces acting on either object must sum to zero.
Since the smaller object has a small upwards buoyant force acting on it, then it must have a correspondingly small downwards weight force acting on it. Similarly, the larger object has a larger buoyant force and a larger weight force acting on it. Thus the larger object has a greater weight than the smaller object.

Sections 70854, 70855
Exam code: quiz05nWaW
(A) : 1 student
(B) : 32 students
(C) : 4 students
(D) : 12 students

Success level: 65%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.17

Physics quiz question: speed, pressure changes in horizontal, narrowing pipe

Physics 205A Quiz 5, fall semester 2017
Cuesta College, San Luis Obispo, CA

Water as it moves horizontally from [1]→[2] through a pipe with decreasing cross-sectional area. The radius of the pipe at point [1] is 0.10 m, and water enters point [1] with a speed of 0.25 m/s. Assume ideal fluid flow. As water flows from [1]→[2], the speed __________; while the pressure __________.
(A) remains constant; remains constant.
(B) remains constant; changes.
(C) changes; remains constant.
(D) changes; changes.

Correct answer (highlight to unhide): (D)

From applying the continuity equation:

A1·v1 = A2·v2,

because the diameter of the pipe narrows as it flows from [1]→[2], the cross-sectional area decreases (A1 > A2), such that the speed of the water increases:

v1 < v2.

Then from Bernoulli's equation:

0 = ∆P + (1/2)·ρ·∆(v2) + ρ·g·∆y,

the third term on the right-hand side is zero because there is no change in elevation (y1 = y2), while the second term on the right-hand side increases (as the speed increases along the pipe), thus the pressure must decrease. Thus both speed and pressure change as water flows from [1]→[2] through this pipe.

Sections 70854, 70855
Exam code: quiz05nWaW
(A) : 0 students
(B) : 6 students
(C) : 6 students
(D) : 36 students

Success level: 73%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.29

Astronomy current events question: dendritic furrow formation on Mars

Astronomy 210L, fall semester 2017
Cuesta College, San Luis Obispo, CA

Students are assigned to read online articles on current astronomy events, and take a short current events quiz during the first 10 minutes of lab. (This motivates students to show up promptly to lab, as the time cut-off for the quiz is strictly enforced!)
Thomas Deane, "Winters on Mars Are Shaping the Red Planet's Landscape" (October 27, 2017)
tcd.ie/news_events/articles/winters-on-mars-are-shaping-the-red-planet-s-landscape/8305
Researchers proposed that carbon dioxide rapidly changing from solid to vapor causes various sand dune features on Mars, based on:
(A) laboratory experiments.
(B) reflected infrared light.
(C) analysis of released gases.
(D) similar features in the Mojave desert.
(E) computer simulations.

Correct answer: (A)

Student responses
Sections 70178, 70186
(A) : 23 students
(B) : 1 student
(C) : 6 students
(D) : 7 students
(E) : 5 students

Astronomy current events question: Proxima Centauri's cold dust belt

Astronomy 210L, fall semester 2017
Cuesta College, San Luis Obispo, CA

Students are assigned to read online articles on current astronomy events, and take a short current events quiz during the first 10 minutes of lab. (This motivates students to show up promptly to lab, as the time cut-off for the quiz is strictly enforced!)
Guillem Anglada, Pedro J. Amado, Antxon Alberdi, Enrique Macias, Itziar de Gregorio-Monsalvo, and Richard Hook, "ALMA Discovers Cold Dust Around Nearest Star" (November 3, 2017)
eso.org/public/news/eso1735/
The Atacama Large Millimeter/submillimeter Array Observatory detected a dust belt surrounding the star Proxima Centauri, which may indicate the presence of:
(A) gravitational waves.
(B) cold dark matter.
(C) a white dwarf.
(D) multiple planets.
(E) artificial asteroids.

Correct answer: (D)

Student responses
Sections 70178, 70186
(A) : 1 student
(B) : 7 students
(C) : 2 students
(D) : 28 students
(E) : 4 students

Astronomy current events question: comet orbiting star KIC 3542116

Astronomy 210L, fall semester 2017
Cuesta College, San Luis Obispo, CA

Students are assigned to read online articles on current astronomy events, and take a short current events quiz during the first 10 minutes of lab. (This motivates students to show up promptly to lab, as the time cut-off for the quiz is strictly enforced!)
Abby Abazorius, Alyssa Drake, Robert Massey, Rebecca Johnson, and Michele Johnson, "Citizen Scientist Spots Comet Tails Streaking Past Distant Star" (October 30, 2017)
ras.org.uk/news-and-press/3061-citizen-scientist-spots-comet-tails-streaking-past-distant-star
A comet orbiting the star KIC 3542116 was discovered by an online volunteer noticing slight decreases in light as it __________ its star.
(A) gravitationally pulled.
(B) escaped from.
(C) collided with.
(D) passed in front of.
(E) reflects light from.

Correct answer: (D)

Student responses
Sections 70178, 70186
(A) : 2 students
(B) : 0 students
(C) : 1 student
(D) : 37 students
(E) : 2 students

20171116

Astronomy quiz question: star cluster with white dwarfs

Astronomy 210 Quiz 6, fall semester 2017
Cuesta College, San Luis Obispo, CA

A star cluster with white dwarfs would also have __________ at the same time.
(A) massive protostars.
(B) medium-mass main sequence stars.
(C) red dwarfs.
(D) giants.

Correct answer (highlight to unhide): (C)

All stars in a star cluster are born at the same time, but undergo stellar evolution at different rates depending on their masses. Medium-mass stars start out as protostars, then reach their main sequence stage, and subsequently become giants, planetary nebulae, and then white dwarfs. So a star cluster with medium-mass stars in their terminal white dwarf stage would not have the earlier stages of medium-mass stars: main-sequence nor giants.

Since massive stars evolve from protostars much faster than medium-mass stars to reach their main-sequence stage, and then to become supergiants that explode as type II supernovae, none of them will be in their protostar stage in a star cluster where the medium-mass stars have already long ended their main-sequence lifetimes.

Low-mass stars evolve from protostars much slower than medium-mass stars to reach their main-sequence stage to become red dwarfs, and since these low-mass stars have such long main-sequence lifetimes (there have been no red dwarfs that have left the main-sequence since the universe began), and so low-mass red dwarfs can be found in an old star cluster where the medium-mass stars have reached their terminal white dwarf stage.

Section 70158
Exam code: quiz06sSu3
(A) : 5 students
(B) : 19 students
(C) : 9 students
(D) : 10 students

Success level: 25% (including partial credit for multiple-choice)
Discrimination index (Aubrecht & Aubrecht, 1983): 0.31

Astronomy quiz archive: stellar evolution

Astronomy 210 Quiz 6, fall semester 2017
Cuesta College, San Luis Obispo, CA

Section 70158, version 1
Exam code: quiz06sSu3


Section 70158
0- 8.0 :   *** [low = 7.5]
8.5-16.0 :   ****************
16.5-24.0 :   ************ [mean = 19.3 +/- 8.0]
24.5-32.0 :   ******
32.5-40.0 :   **** [high = 36.5]


Section 70160, version 1
Exam code: quiz06nMuE


Section 70160
0- 8.0 :   * [low = 8.0]
8.5-16.0 :   ********
16.5-24.0 :   ******
24.5-32.0 :   ********* [mean = 23.7 +/- 9.0]
32.5-40.0 :   ********* [high = 36.5]