Physics 205B Quiz 7, Spring Semester 2011
Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 26.45
If electrons had a Lorentz factor γ = 2.00, how fast would they be traveling?
(A) 0.414c.
(B) 0.500c.
(C) 0.866c.
(D) 1.41c.
Correct answer: (C)
Inverting the Lorentz factor equation γ = 1/sqrt(1 - (v/c)^2)) to solve for v results in:
v = c*sqrt(1 - 1/(γ^2)),
such that with γ = 2.00, v = 0.886c. Response (A) is 1 - c*sqrt(2*(γ - 1)); response (B) is c*sqrt(1/(γ^2)); response (D) is c*sqrt(2*(γ - 1)), which results in an implausible result.
Section 30882
Exam code: quiz07t0LO
(A) : 0 students
(B) : 1 student
(C) : 5 students
(D) : 2 students
"Success level": 75%
Discrimination index (Aubrecht & Aubrecht, 1983): -0.50
Compare to an older version of this question from Fall 2010.
Showing posts with label special relativity. Show all posts
Showing posts with label special relativity. Show all posts
20110601
Physics quiz archive: radioactive decay, special relativity
Physics 205B Quiz 7, Spring Semester 2011
Cuesta College, San Luis Obispo, CA
Section 30882, version 1
Section 30882 results
Exam code: quiz07t0LO
Cuesta College, San Luis Obispo, CA
Section 30882, version 1
Section 30882 results
Exam code: quiz07t0LO
0- 6 :
7-12 :
13-18 : ** [low = 18]
19-24 : ***** [mean = 22.5 +/- 3.6]
25-30 : ** [high = 27]
20110104
Physics final exam problem: relativistic RHEED speeds
Physics 205B Final Exam, Fall Semester 2010
Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 26.55
[20 points.] Reflection high-energy electron diffraction2 is a technique where electrons with a kinetic energy of up to 100,000 eV probe the atomic structure of crystalline surfaces. How fast do these electrons travel, as measured from a stationary reference frame? Express your answer as a factor of c. Show your work and explain your reasoning.
Solution and grading rubric:
Grading distribution:
Section 70856
p: 6 students
r: 1 students
t: 0 students
v: 2 students
x: 0 students
y: 0 students
z: 1 student
A sample "p" response (from student 1010), although the final result is expressed as a factor of c, "m/s" units are inserted:
Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 26.55
[20 points.] Reflection high-energy electron diffraction2 is a technique where electrons with a kinetic energy of up to 100,000 eV probe the atomic structure of crystalline surfaces. How fast do these electrons travel, as measured from a stationary reference frame? Express your answer as a factor of c. Show your work and explain your reasoning.
Solution and grading rubric:
- p = 20/20:
Correct. - 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. - v = 8/20:
Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. - 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:
Section 70856
p: 6 students
r: 1 students
t: 0 students
v: 2 students
x: 0 students
y: 0 students
z: 1 student
A sample "p" response (from student 1010), although the final result is expressed as a factor of c, "m/s" units are inserted:
20101220
Physics quiz question: comparing light speeds
Physics 205B Quiz 7, Fall Semester 2010
Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 26.3.
A Physics 205B is moving at a constant velocity to the right. Two lights are simultaneously trigged to flash (in the rest frame of the lights) when student is midway between them. According to the Physics 205B student, the speed of the flash from the right light is __________ the flash from the left light.
(A) faster than.
(B) slower than.
(C) the same as.
(D) (Not enough information is given.)
Correct answer: (C)
From Einstein's second postulate of special relativity, the speed of light is invariant and independent of the relative motion of the observer and source.
Student responses
Section 70856
(A) : 3 students
(B) : 0 students
(C) : 8 students
(D) : 0 students
Success level: 72%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.33
Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 26.3.
A Physics 205B is moving at a constant velocity to the right. Two lights are simultaneously trigged to flash (in the rest frame of the lights) when student is midway between them. According to the Physics 205B student, the speed of the flash from the right light is __________ the flash from the left light. (A) faster than.
(B) slower than.
(C) the same as.
(D) (Not enough information is given.)
Correct answer: (C)
From Einstein's second postulate of special relativity, the speed of light is invariant and independent of the relative motion of the observer and source.
Student responses
Section 70856
(A) : 3 students
(B) : 0 students
(C) : 8 students
(D) : 0 students
Success level: 72%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.33
20101219
Physics quiz question: time dilated pulse
Physics 205B Quiz 7, Fall Semester 2010
Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Multiple-Choice Question 26.5, Problem 26.5.
A Physics 205B student has a resting pulse of 1 second per beat. She then takes a ride aboard a spacecraft traveling at a constant velocity of 0.100c away from Earth. While the spacecraft is moving, the resting pulse of the Physics 205B student is __________ 1 second per beat, according to Earth observers.
(A) longer than.
(B) shorter than.
(C) exactly equal to.
(D) (Not enough information is given.)
Correct answer: (A)
The relevant time interval is the pulse of the Physics 205B student. The proper time interval delta(t_0) for her pulse is 1 second, as measured in her own reference frame (the spacecraft). The observed time interval delta(t) for her pulse is measured from Earth, which is at rest outside of the reference frame of the spacecraft. Then the relation between the two time intervals is given by:
delta(t) = gamma*delta(t_0);
and since gamma = 1/sqrt(1 - (v/c)^2) = 1/sqrt(1 - (0.100c/c)^2) = 1/sqrt(1 - 0.0100) = 1/sqrt(0.9900) = 1/0.9950 = 1.005, then:
delta(t) = 1.005*(1 second/pulse) = 1.005 seconds/pulse.
Student responses
Section 70856
(A) : 8 students
(B) : 2 students
(C) : 1 student
(D) : 0 students
Success level: 72%
Discrimination index (Aubrecht & Aubrecht, 1983): -0.33
Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Multiple-Choice Question 26.5, Problem 26.5.
A Physics 205B student has a resting pulse of 1 second per beat. She then takes a ride aboard a spacecraft traveling at a constant velocity of 0.100c away from Earth. While the spacecraft is moving, the resting pulse of the Physics 205B student is __________ 1 second per beat, according to Earth observers.
(A) longer than.
(B) shorter than.
(C) exactly equal to.
(D) (Not enough information is given.)
Correct answer: (A)
The relevant time interval is the pulse of the Physics 205B student. The proper time interval delta(t_0) for her pulse is 1 second, as measured in her own reference frame (the spacecraft). The observed time interval delta(t) for her pulse is measured from Earth, which is at rest outside of the reference frame of the spacecraft. Then the relation between the two time intervals is given by:
delta(t) = gamma*delta(t_0);
and since gamma = 1/sqrt(1 - (v/c)^2) = 1/sqrt(1 - (0.100c/c)^2) = 1/sqrt(1 - 0.0100) = 1/sqrt(0.9900) = 1/0.9950 = 1.005, then:
delta(t) = 1.005*(1 second/pulse) = 1.005 seconds/pulse.
Student responses
Section 70856
(A) : 8 students
(B) : 2 students
(C) : 1 student
(D) : 0 students
Success level: 72%
Discrimination index (Aubrecht & Aubrecht, 1983): -0.33
20101218
Physics quiz question: CERN protons
Physics 205B Quiz 7, Fall Semester 2010
Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 26.7.
The CERN Large Hadron Collider in Switzerland accelerates protons up to a speed corresponding to a Lorentz factor gamma of 3.000e3, as measured from a stationary reference frame (http://faculty.tamu-commerce.edu/cbertulani/cab/papers/7420.pdf). What is the speed of each proton?
(A) 0.9996667c.
(B) 0.9998333c.
(C) 0.9999998889c.
(D) 0.9999999444c.
Correct answer: (D)
The Lorentz factor gamma, in terms of the speed v is given by:
gamma = sqrt(1/(1 - (v/c)^2));
which can be algebraically manipulated to express v in terms of gamma:
gamma^2 = 1/(1 - (v/c)^2);
1 - (v/c)^2 = 1/(gamma^2);
(v/c)^2 = 1 - 1/(gamma^2);
v = c*sqrt(1 - 1/(gamma^2));
such that with gamma = 3.000e3;
v = c*sqrt(1 - 1/(3.000e3)^2) = c*sqrt(1 - 0.0000001111) = c*sqrt(0.9999998889) = 0.9999999444*c.
Response (A) is 1-(1/gamma); response (B) is sqrt(1-(1/gamma)); response (C) is 1-(1/gamma^2).
Student responses
Section 70856
(A) : 1 student
(B) : 1 student
(C) : 3 students
(D) : 6 students
Success level: 54%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.67
Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 26.7.
The CERN Large Hadron Collider in Switzerland accelerates protons up to a speed corresponding to a Lorentz factor gamma of 3.000e3, as measured from a stationary reference frame (http://faculty.tamu-commerce.edu/cbertulani/cab/papers/7420.pdf). What is the speed of each proton?
(A) 0.9996667c.
(B) 0.9998333c.
(C) 0.9999998889c.
(D) 0.9999999444c.
Correct answer: (D)
The Lorentz factor gamma, in terms of the speed v is given by:
gamma = sqrt(1/(1 - (v/c)^2));
which can be algebraically manipulated to express v in terms of gamma:
gamma^2 = 1/(1 - (v/c)^2);
1 - (v/c)^2 = 1/(gamma^2);
(v/c)^2 = 1 - 1/(gamma^2);
v = c*sqrt(1 - 1/(gamma^2));
such that with gamma = 3.000e3;
v = c*sqrt(1 - 1/(3.000e3)^2) = c*sqrt(1 - 0.0000001111) = c*sqrt(0.9999998889) = 0.9999999444*c.
Response (A) is 1-(1/gamma); response (B) is sqrt(1-(1/gamma)); response (C) is 1-(1/gamma^2).
Student responses
Section 70856
(A) : 1 student
(B) : 1 student
(C) : 3 students
(D) : 6 students
Success level: 54%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.67
20100521
Physics quiz question: CERN proton Lorentz factor
Physics 205B Quiz 7, Spring Semester 2010
Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 26.55(a)
The CERN Proton Synchrotron Booster in Switzerland (http://cdsmedia.cern.ch/img/CERN-Brochure-2008-001-Eng.pdf) is able to accelerate protons up to a speed of 0.916c, as measured from a stationary reference frame. What is the Lorentz factor γ for protons at this speed?
(A) 1.09.
(B) 1.19.
(C) 2.49.
(D) 3.45.
Correct answer: (C)
The Lorentz factor is given by:
γ = 1/sqrt(1 - (v/c)^2) = 1/sqrt(1 - (0.916c/c)^2) = 2.49.
Response (A) is 1/(v/c); response (B) is 1/(v/c)^2; response (D) is 1/sqrt(1 - (v/c)).
Student responses
Section 31988
(A) : 2 students
(B) : 3 students
(C) : 7 students
(D) : 0 students
Success level: 58%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.80
Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 26.55(a)
The CERN Proton Synchrotron Booster in Switzerland (http://cdsmedia.cern.ch/img/CERN-Brochure-2008-001-Eng.pdf) is able to accelerate protons up to a speed of 0.916c, as measured from a stationary reference frame. What is the Lorentz factor γ for protons at this speed?
(A) 1.09.
(B) 1.19.
(C) 2.49.
(D) 3.45.
Correct answer: (C)
The Lorentz factor is given by:
γ = 1/sqrt(1 - (v/c)^2) = 1/sqrt(1 - (0.916c/c)^2) = 2.49.
Response (A) is 1/(v/c); response (B) is 1/(v/c)^2; response (D) is 1/sqrt(1 - (v/c)).
Student responses
Section 31988
(A) : 2 students
(B) : 3 students
(C) : 7 students
(D) : 0 students
Success level: 58%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.80
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