20141024

Physics presentation: rotational dynamics

¡Adios, Sapito! In this iconic cinematic moment from Raiders of the Lost Ark (Lucasfilm, Paramount Pictures, 1981), Indiana Jones outruns a gigantic round boulder. Somehow I don't think the principle of energy conservation was on his mind at the moment, but it ought to have been.

Regardless of Dr. Jones having majored in archaeology instead of physics, we'll be pondering the inclusion of rotational motion into energy conservation.

First, let's define some rotational parameters.

Angular speed (denoted by lower-case Greek letter ω) measures how fast an object rotates, using units of radians per second, where there are 2π radians per revolution. If an object is fixed such that rotates in place, then this is the only parameter necessary to describe its motion.

If an object rolls along a surface without slipping, then it will simultaneously travel with a translational speed v while rotating with an angular speed ω.

A rolling object's translational speed v and angular speed ω are constrained via the "rolling without slipping" condition v = r·ω, so an object with a radius r that has a slow or fast translational speed must also be rolling with a corresponding slow or fast angular speed. (Note the peculiar nature of the radians unit, where it conveniently disappears such that r and ω result in units of meters per second.)

Here two objects with different radii have the same translational speed v, but from the v = r·ω condition, the larger radius object has a slower angular speed as it rolls, while the smaller radius object has a faster angular speed in order to keep up.

Similar to how translational speed v and angular speed ω are related, there is a relationship between the mass M and the rotational inertia I of an object. Whereas an object's mass is a measure of how easy or difficult it is to change its translational motion, an object's "rotational inertia" measures the distribution of mass about its axis that makes it easy or difficult to change its rotational motion. The rotational inertia depends on the mass, size, and configuration of the object, and the appropriate expressions for rotational inertia should be used for each type of rotating object.

The simplest rotating object is a point mass M swung around in a circle of radius R; its moment of inertia is given by Ipoint mass = M·R2. (Video link: "2010 Asian Games - Men's Hammer Throw Final.")

The moment of inertia of a more complicated set of poi balls (two oil-soaked bundles at ends of chains) is simply twice the moment of inertia of a single point mass. This is the idea behind finding the moment of inertia of complex objects--merely the sum of the individual moment of inertia for its components. (Video link: "Ronan McLoughlin Fire Poi Slow motion (HD).")

Likewise for a uniform rod of mass M and length L that is swung around at one end, its moment of inertia is given by Irod, at end = (1/3)·M·R2. (The numerical factor of (1/3) for this object comes from calculus, but for the purposes of this course these numerical factors are merely to be looked up for each different type of object as needed.) (Video link: "2013 MLB Home Run Derby Extreme Slow Motion Swings.")

The moment of inertia of a three-bladed wind turbine--which can be thought of as a set of three uniform rods swung at their ends--is merely three times the individual moment of inertia of a single uniform rod. You can always look up the moment of inertia of simple objects, and for more complex objects merely add together the moment of inertia of each of its components. (Video link: "Enercon wind energy turbines in action.")

Second, incorporating rotational motion into energy conservation.

Rotational kinetic energy Krot is the energy of rotational motion. Rotational kinetic energy depends on the rotational inertia I and the square of the angular speed ω of the object, and the resulting units of kg·m2/s2 are also expressed as joules (once the peculiar units of rad2 disappear). A object that is not rotating has no rotational kinetic energy, and the faster an object rotates, the more rotational kinetic energy it has.

Instead of finding out how much rotational kinetic energy Krot an object has, often we are more concerned with its initial-to-final change Krot, which is the final amount of rotational kinetic energy minus the initial amount of rotational kinetic energy. Notice how the common factors of (1/2) and rotational inertia I (which is presumed to be constant) are pulled out, leaving a "difference of squares" for the final and initial angular speeds in the parenthesis.

For an object with both translational motion and rotational motion, it will have both translational kinetic energy and rotational kinetic energy. For the rider on this Solowheel®, the translational kinetic energy Ktr will be given by (1/2)·(Mrider + mwheelv2, and the rotational kinetic energy Krot will be given by (1/2)·Iwheel·ω2. (Video link: "Riding the Solowheel to work - every days obstacle course.")

Note that the two kinetic energy expressions are not unrelated as the Solowheel® rolls without slipping, such that the constraint v = r·ω can be used to connect the translational speed v in the translational kinetic energy expression with the angular speed ω in the rotational kinetic energy expression. We'll demonstrate this connection in some examples of objects that roll without slipping during lecture.

Now let's incorporate rotational kinetic energy into the total energy conservation equation, which shows how the transfer of energy (as work is done by non-conservative forces acting on or against the motion of the object) causes changes in any or all of the four known mechanical energy forms on the right-hand side of the equation.

As discussed previously, in the idealized case that there are no non-conservative forces (such as friction, drag, or from external sources), then the left-hand size of this equation would be zero. Then the individual energy terms on the right-hand side of this equation can then trade and balance amongst themselves, instead of with the outside world.

So now let's see how this more comprehensive transfer/balance equation can be applied to idealized situations where friction and drag are negligible.

A tire is released from rest at the top of a ramp, and it rolls without slipping to reach the bottom of the ramp, where it then travels upwards off of a smaller ramp, where it reaches the top of its trajectory at a height lower than its initial starting point. And this was done for science. And must-see television. And now endures as a pervasive internet meme. (Video link: "Tire ski jump.")

For the first part of this stunt, from starting at the top of the ramp to the bottom of the ramp, does the tire's translational kinetic energy increase or decrease? Does its rotational kinetic energy increase or decrease? Does its gravitational potential energy increase or decrease?

Assuming that there is no friction/drag (such that we can neglect non-conservative work), which energy system experienced a greater amount of change (whether increase or decrease): translational kinetic energy, rotational kinetic energy, or gravitational potential energy?

For the subsequent part of this stunt, from starting at the bottom of the second ramp to reaching the top of its trajectory, does the tire's translational kinetic energy increase or decrease? Does its rotational kinetic energy increase or decrease? Does its gravitational potential energy increase or decrease?

Assuming that there is no friction/drag (such that we can neglect non-conservative work), which energy system experienced a greater amount of change (whether increase or decrease): translational kinetic energy, rotational kinetic energy, or gravitational potential energy?

Astronomy current events question: audience vote on Pluto as a planet

Astronomy 210L, fall semester 2014
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!)
David A. Aguilar, Christine Pulliam, "Is Pluto a Planet? The Votes Are In," (September 22, 2014)
http://www.cfa.harvard.edu/news/2014-25
After presentations from three planetary scientists at the Harvard-Smithsonian Center for Astrophysics, __________ audience members voted on a definition for Pluto being a planet.
(A) NASA.
(B) International Astronomical Union.
(C) general public.
(D) preschool and kindergarten.
(E) Nobel Prize winner.

Correct answer: (C)

Student responses
Sections 70178, 70186
(A) : 4 students
(B) : 12 students
(C) : 22 students
(D) : 1 student
(E) : 0 students

Astronomy current events question: WASP-94 "cousin" planets

Astronomy 210L, fall semester 2014
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!)
waspplanets@gmail.com, "WASP-94: 'Cousin' Planets Around Twin Stars," (September 30, 2014)
http://wasp-planets.net/2014/09/30/wasp-94-cousin-planets-around-twin-stars/
The Wide-Angle Search for Planets telescopes discovered that binary system stars WASP-94A and WASP-94B are each orbited by a Jupiter-sized extrasolar planet, by observing these planets:
(A) wobbling their stars.
(B) colliding with each other.
(C) being torn apart by tidal forces.
(D) passing in front of their stars.
(E) emitting infrared light.

Correct answer: (D)

Student responses
Sections 70178, 70186
(A) : 3 students
(B) : 2 students
(C) : 3 students
(D) : 25 students
(E) : 6 students

Astronomy current events question: Titan's south pole cloud

Astronomy 210L, fall semester 2014
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!)
Preston Dyches, "Swirling Cloud at Titan's Pole is Cold and Toxic," (October 1, 2014)
http://www.nasa.gov/jpl/cassini/swirling-cloud-at-titans-pole-is-cold-and-toxic/index.html
NASA's Cassini mission observations of __________ revealed the temperature and chemical composition of the south pole cloud of Saturn's largest moon, Titan.
(A) a comet impact.
(B) radio interference.
(C) reflected sunlight.
(D) auroral lights.
(E) lightning storms.

Correct answer: (C)

Student responses
Sections 70178, 70186
(A) : 1 student
(B) : 5 students
(C) : 16 students
(D) : 6 students
(E) : 11 students

20141022

Online reading assignment: stellar parameters (SLO campus)

Astronomy 210, fall semester 2014
Cuesta College, San Luis Obispo, CA

Students have a weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing presentations on parallax, distance, apparent magnitude, absolute magnitude, Wien's law and the Stefan-Boltzmann law.


Selected/edited responses are given below.

Describe something you found interesting from the assigned textbook reading or presentation preview, and explain why this was personally interesting for you.
"That we are able to find out the size of a star based upon its luminosity and temperature."

"Wien's law is neat because you can tell how hot a star is by just looking at what color it is."

"The H-R diagram--because this gives you an idea of how big, how hot, and how other stars are related to the sun."

"White hot stars are hotter than the red ones."

"I never knew that there was this much information on stars. I'm totally interested but I'm totally confused at the same time."

Describe something you found confusing from the assigned textbook reading or presentation preview, and explain why this was personally confusing for you.
"Pretty much everything."

"The differences between apparent and absolute magnitude."

"How to calculate distance and brightness! Oh my gosh, help!"

"The S-B Law because I just don't understand how it works."

"The stars and all of their classifications! After the video [Wonders of the Universe: Stardust] last week, I became aware of how much there is to know about stars and I was blown away. And I knew this was going to trip me up. So just all the information and keeping it straight is the hardest part."

Explain how apparent magnitude and the absolute magnitude are defined differently.
"Apparent magnitude is how bright a star looks like from the naked eye and absolute magnitude is how bright a star really is (once the distance of the star is accounted for)."

"Apparent magnitude is how bright we see a star, regardless of its distance from the earth. Absolute magnitude is how bright a star would appear if we put it at 32.616 light-years [10 parsecs] away."

"I'm unsure."

"Apparent is a guesstimate, and absolute is exact."

Suppose the sun was moved to a distance of 10 parsecs away. As a result, its __________ magnitude would become dimmer.
absolute.  ********* [9]
apparent.  ******************* [19]
(Both of the above choices.)  ***** [5]
(Neither of the above choices.)  [0]
(Unsure/guessing/lost/help!)  **** [4]

Rank the temperatures of these stars (1 = hottest, 4 = coolest; there are no ties).
(Only correct responses shown.)
Hottest: blue main sequence star [81%]
Second hottest: white main sequence star [76%]
Third hottest: yellow main sequence star [84%]
Coolest: red main sequence star [92%]

Rank the temperatures of these stars (1 = hottest, 4 = coolest; there are no ties).
(Only correct responses shown.)
Hottest: blue supergiant [78%]
Second hottest: white dwarf [51%]
Third hottest: yellow supergiant [64%]
Coolest: red dwarf [87%]

Two stars (equally far away) have the same temperature, but one star is dimmer, and the other star is brighter. The __________ star will be larger in size.
dimmer.  ****** [6]
brighter.  **************************** [28]
(These stars would be the same size.)  [0]
(Unsure/guessing/lost/help!)  *** [3]

Two stars (equally far away) have the same brightness, but one star is cooler, and the other star is hotter. The __________ star will be larger in size.
cooler.  ********************* [21]
hotter.  ********* [9]
(These stars would be the same size.)  **** [4]
(Unsure/guessing/lost/help!)  *** [3]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.
"More examples and charts would be good. Please go over the distance of the stars and what is cooler/hotter and dimmer/brighter." (Yes.)

"Parsecs (pc) are better than light-years (ly)!" (Yes.)

"Do we need to memorize all of these equations?" (What equations? More seriously, you do need to "memorize" the logical reasoning behind the mathematics we'll be learning this week in order to apply it to quiz and exam questions.)

"What are you going to be for Halloween?" (Come to Madonnaween at the Madonna Inn the Monday before Halloween, and find out. I'm not dressing up as a DJ, but I am DJing!))

Online reading assignment: torque and rotations

Physics 205A, fall semester 2014
Cuesta College, San Luis Obispo, CA

Students have a weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing a presentation on torque and rotations.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.
"Torque is the twisting by a force that tends to cause rotation."

"Torque is the product of force (N) and the length of the perpendicular lever arm (m). The force vector (line of action) is perpendicular to the perpendicular lever arm."

"N1 applies to torque when the object is in equilibrium. N2 applies when the object is starting to rotate."

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.
"Net torque."

"How an object can have a net force of zero while the torque is nonzero. I also do not get how if its torque was nonzero and net force was zero, how such an object could have a nonzero angular acceleration."

"I am not 100% on drawing out a diagram for torque."

"Line of action for a force."

"The lever arm, and how it was drawn/what function it serves."

What is the SI (Système International) unit for torque?
"N·m."

"Tau."

"Newtons."

Briefly describe how the line of action should be drawn for a given force.
"The line of action should extend along the force vector direction."

"I have no idea."

"With a dashed line."

When a lever arm (or moment arm) is drawn, briefly explain where it starts, and how it should intersect the line of action for a force.
"The lever arm starts at the rotation axis and is perpendicular to the line of action."

"I have no clue. Sorry."

For the stuck wrench (assuming that it is rigid and not flexing), Newton's rotational __________ law applies, and the clockwise torques and counterclockwise torques acting on the wrench are __________.
first; balanced.   ************************************************* [49]
second; unbalanced.   ********* [9]
(Unsure/lost/guessing/help!)   ***** [5]

For the crane, Newton's rotational __________ law applies, and the clockwise torques and counterclockwise torques acting on the crane are __________.
first; balanced.   ******** [8]
second; unbalanced.   ************************************************* [49]
(Unsure/lost/guessing/help!)   ****** [6]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.
"I once broke a torque wrench trying to loosen the lug nuts on a Lexus. They must have been torqued up to 200 ft·lbs. Apparently, they don't want you to do anything to their cars at all." (Unless you had a Nutcracker®.)

"Can you go over how to draw diagrams for these problems? Can you please go over the 'line of action?'" (Yes, and yes.)

"I apologize for turning in such a shameful assignment. I will definitely read the material before class, so I can follow what is going on."

"Does the extra credit from lab count as a part of the total extra credit for the class?"(No, lab points are capped at a 100 points maximum.)

"Would it be possible to do a really good review for the upcoming quiz?" (Let's see how well you can rock the sample quiz from last year.)

"Didn't think it could get any harder. You must be mad smart."

"I think I am going to like this section."

20141021

Physics midterm question: water-filled bucket twirled in a vertical circle

Physics 205A Midterm 1, fall semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 5.39

Water is poured into a bucket attached to an ideal string, and is then twirled around in a circle. The speed of the bucket is momentarily constant at the bottom of its circular path. Discuss why the magnitude of the normal force of the bucket on the water is greater than the magnitude of the weight force of Earth on the water. Explain your reasoning by using a free-body diagram, the properties of forces and Newton's laws.

Solution and grading rubric:
  • p:
    Correct. Recognizes that Newton's second law applies to uniform circular motion (constant speed but continuously changing direction) where the (non-zero) net force on the water must point inwards (upwards), thus the upwards normal force of the bucket on the water is greater in magnitude than the downwards weight force of Earth on the water.
  • r:
    Nearly correct, but includes minor math errors. Some attempt at applying Newton's laws to a free-body diagram, but may have a centrifugal or centripetal "m·v/r2" force in addition to the normal and weight forces.
  • t:
    Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Problematic attempt at applying Newton's laws (N1 or N3) to a free-body diagram (with extraneous or missing forces, or inconsistent with Newton's laws).
  • v:
    Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Effectively only has a substantive attempt at a free-body diagram, or only a substantive attempt at discussing Newton's laws.
  • x:
    Implementation of ideas, but credit given for effort rather than merit. Approach other than that of applying Newton's laws to a free-body diagram.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
    Blank.
Grading distribution:
Sections 70854, 70855, 73320
Exam code: midterm01m0oU
p: 8 students
r: 24 students
t: 28 students
v: 13 students
x: 0 students
y: 0 students
z: 1 student

A sample "p" response (from student 0203):

Another sample "p" response (from student 1828):

A sample "r" response (from student 1914), with an additional centripetal force on the free-body diagram:

A sample "v" response (from student 3474):

Online reading assignment: stellar parameters (NC campus)

Astronomy 210, fall semester 2014
Cuesta College, San Luis Obispo, CA

Students have a weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing presentations on parallax, distance, apparent magnitude, absolute magnitude, Wien's law and the Stefan-Boltzmann law.


Selected/edited responses are given below.

Describe something you found interesting from the assigned textbook reading or presentation preview, and explain why this was personally interesting for you.
"That astronomers use triangulation to calculate the distance of a star. It is nice to see this practical application of trigonometry which, interestingly, can be compared to how surveyors calculate distance as well."

"I found the whole chapter pretty interesting, especially how the color really shows the temperature of the star. This is mostly due to the fact that we usually see blue and white as cool colours, so when it turns out that they're in fact indicators of the hottest suns it seems somewhat counter intuitive. Even though I know blue flames are hotter than red flames, it still seems so odd."

"The Stefan-Boltzamann law, because I was trying to figure out all the concepts (luminosity, temperature, and size) how they all come together to determine different things about the stars."

"How bigger stars aren't necessarily hotter."

"That you can tell which star has the most luminosity based on it's color and size. This is interesting because I didn't know it was so simple as this."

"The charts for determining the luminosity of stars was cool. I didn't think it would be that easy, but it makes sense and is really quick to do!"

"It's cool to know that I'm not crazy or seeing things when I see a star as having a red color."

Describe something you found confusing from the assigned textbook reading or presentation preview, and explain why this was personally confusing for you.
"How can we measure the distances to stars?"

"The Stefan-Boltzamann law because I feel I still need examples to understand it completely and be able to use it."

"Apparent magnitude and absolute magnitude. It's hard to conceptualize."

"I was confused about what I found to be interesting. That is, why we don't see stars of all colors of the rainbow."

"Light-years and parsecs. I get that they ares a units of measure but why did we choose them? What would be an examples of them?"

Explain how apparent magnitude and the absolute magnitude are defined differently.
"Apparent magnitude is what we see from Earth. Absolute is what the actual brightness is."

Suppose the sun was moved to a distance of 10 parsecs away. As a result, its __________ magnitude would become dimmer.
absolute.  *** [3]
apparent.  ****************** [18]
(Both of the above choices.)  ** [2]
(Neither of the above choices.)  ** [2]
(Unsure/guessing/lost/help!)  **** [4]

Rank the temperatures of these stars (1 = hottest, 4 = coolest; there are no ties).
(Only correct responses shown.)
Hottest: blue main sequence star [70%]
Second hottest: white main sequence star [59%]
Third hottest: yellow main sequence star [83%]
Coolest: red main sequence star [90%]

Rank the temperatures of these stars (1 = hottest, 4 = coolest; there are no ties).
(Only correct responses shown.)
Hottest: blue supergiant [83%]
Second hottest: white dwarf [59%]
Third hottest: yellow supergiant [72%]
Coolest: red dwarf [93%]

Two stars (equally far away) have the same temperature, but one star is dimmer, and the other star is brighter. The __________ star will be larger in size.
dimmer.  *** [3]
brighter.  ************************** [26]
(These stars would be the same size.)  [0]
(Unsure/guessing/lost/help!)  [0]

Two stars (equally far away) have the same brightness, but one star is cooler, and the other star is hotter. The __________ star will be larger in size.
cooler.  ************** [14]
hotter.  ************** [14]
(These stars would be the same size.)  [0]
(Unsure/guessing/lost/help!)  * [1]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.
"How do they know the temperature of a star?" (By looking at its color.)

"Could we please briefly discuss in class the relationship between a star's color and its temperature?"(Yes.)

"What's up with your hearing aid?" (I had Sudden Sensorineural Hearing Loss (SSHL) a few years ago, when your hearing disappears overnight--and no one really knows what causes it. But FWIW I'm now the world's deafest swing DJ. #fml #strongthanhearingloss)

20141020

Online reading assignment: collisions

Physics 205A, fall semester 2014
Cuesta College, San Luis Obispo, CA

Students have a weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing a presentation on collisions.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.
"I understand the different types of collisions. I also understand how to use the conservation law equations."

"Total momentum is a sum total of momenta of objects in a system. Internal interactions do not change total momentum, external interactions might change it. Reading also touches on what a collision is."

"A perfectly inelastic collision occurs when two objects stick together. Inelastic occurs when one object pushes the other away and there's visible damage. Finally, an elastic collision occurs when one object completely pushes another and there is no visible damage."

"I assumed that two objects stuck together wouldn't lose lots of energy, but after reading more about it, they can lose lots of kinetic energy."

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.
"The relative velocity kinetic energy conservation equation just is not clicking for me. A brief explanation of why that equation is what it is would help greatly."

"You lost me at the concept of momentum."

Explain the difference between a (partially) inelastic collision and a perfectly inelastic collision.
"If two cars hit each other and do not stick to each other , but are crushed or bent, then the collision is partially inelastic. If two cars collide and are stuck together, the collision is perfectly inelastic."

"In an inelastic collision both objects bounce off each other and there is visible damage, in a perfectly inelastic collision, however, both objects are stuck together in addition to visible damage."

Explain why drag, friction, and other external forces do not matter during sufficiently "brief" collisions, in order for momentum to be conserved.
"We're limiting it to the initial state just before the collision and the final state just after the collision. The external forces have negligible impulses in the short time span."

"The system needs to be isolated from all external factors, because if it isn't then momentum is not conserved. To put it into context, external forces will always be a factor, but the forces involved within a collision are so large that any external forces can be safely ignored, for they do not alter the final result in a significant way."

For the Nissan Altima and Nissan Rogue crash test, classify the type of collision. (Neglect drag/friction/external forces during this "brief" collision.)
Perfectly inelastic (kinetic energy not conserved).   ** [2]
(Partially) inelastic (kinetic energy not conserved).   **************************************** [40]
Elastic (kinetic energy conserved).   ***** [5]
(Unsure/lost/guessing/help!)   ******** [8]

For the Ford Explorer and Ford Taurus crash test, classify the type of collision. (Neglect drag/friction/external forces during this "brief" collision.)
Perfectly inelastic (kinetic energy not conserved).   ******** [8]
(Partially) inelastic (kinetic energy not conserved).   ****** [6]
Elastic (kinetic energy conserved).   ********************************* [33]
(Unsure/lost/guessing/help!)   ******** [8]

For the train and minivan crash, classify the type of collision. (Neglect drag/friction/external forces during this "brief" collision.)
Perfectly inelastic (kinetic energy not conserved).   ******************************* [31]
(Partially) inelastic (kinetic energy not conserved).   ******* [7]
Elastic (kinetic energy conserved).   ***** [5]
(Unsure/lost/guessing/help!)   ************ [12]

For the bullet burrowing through and back out of the baseball, classify the type of collision. (Neglect drag/friction/external forces during this "brief" collision.)
Perfectly inelastic (kinetic energy not conserved).   *** [3]
(Partially) inelastic (kinetic energy not conserved).   **************************** [28]
Elastic (kinetic energy conserved).   ************ [12]
(Unsure/lost/guessing/help!)   ************ [12]

For the bullet shot out of this gun, classify the type of collision. (Neglect drag/friction/external forces during this "brief" collision.)
Perfectly inelastic (kinetic energy not conserved).   *** [3]
(Partially) inelastic (kinetic energy not conserved).   ****************** [18]
Elastic (kinetic energy conserved).   ******************** [20]
(Unsure/lost/guessing/help!)   ************** [14]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.
"I am having some trouble understanding elastic, partially inelastic, and perfectly inelastic collisions, and momentum conservation and kinetic energy conservation equations. Would you be able to go over some examples in class please? Could you also go over kinetic energy being conserved or not being conserved?" (Yes. And if time allows, you'll get to solve an example as well.)

"How do you tell the difference between perfectly inelastic and partially inelastic collisions? Is it just the sticking (or not)?" (Yes, for a perfectly inelastic collision, the objects are stuck-together after the collision. It's actually quite common in automobile accidents.)

"What would it be if two objects collided, stuck together, and did not have deformation?" (If there is not visible deformation, then translational kinetic energy was dissipated into other forms, such as sound, heat, etc.)

"Can you go over the last question on the midterm?" (It's discussed on the blog, along with samples of student solutions.)

"Do you celebrate Halloween?" (My people celebrate something called "Madonnaween.")

20141019

Physics midterm problem: Apollo 14 golf swing

Physics 205A Midterm 1, fall semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 3.49

"Golf on the Moon (NASA)"
John Gizis (Creative Commons Attribution License 2.5)
http://youtu.be/KZLl3XwlAIE

In February 1971, Apollo 14 astronaut Alan Shepard used a make-shift golf club to hit a golf ball on the moon, and described it as traveling "miles and miles and miles."[*] An online message board[**] discussed reasonable parameters for a golf ball hit by an average golfer:
I am informed by a mathematician, also a keen golfer, that assuming a speed off the club of 37 m/s, which is average, and an elevation of 40°, which is usual for a 6-iron, then a distance [less than one mile] could be expected.
Based on these parameters, determine whether Shepard's "miles and miles and miles" claim or the online "less than one mile" claim is more plausible. The magnitude of the gravitational constant on the moon is gmoon = 1.62 m/s2, and use the approximation 1 mi = 1,600 m. Neglect air resistance. Show your work and explain your reasoning using properties of projectile motion.

[*] Eric M. Jones, "EVA-2 Closeout and the Golf Shots," http://history.nasa.gov/alsj/a14/a14.clsout2.html.
[**] moorouge, "Topic: How far did Alan Shepard's golf ball go?" http://www.collectspace.com/ubb/Forum29/HTML/001181.html.

Solution and grading rubric:
  • p:
    Correct. Finds x- and y-components of the initial velocity vector, then applies projectile motion equations in a methodical manner and determines which claim is more plausible using one of these (or other) approaches:
    • finds Δt for the golf ball to reach the ground, then uses this time to determine the horizontal displacement Δx of the ball, which is less than 1,600 m;
    • finds Δt for the golf ball to theoretically travel a horizontal distance Δx = 1,600 m, then uses this time to determine the vertical displacement Δy of the golf ball, and concludes that since Δy is negative, then the golf ball traveled less than 1,600 m.
  • r:
    Nearly correct, but includes minor math errors. May have the wrong sign on the gravitational acceleration constant, or simple arithmetic errors, but makes a sound argument based on the numerical values resulting from these errors.
  • t:
    Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least enough steps are shown that would theoretically result in a complete answer, multiple errors notwithstanding.
  • v:
    Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner.
  • x:
    Implementation of ideas, but credit given for effort rather than merit.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
    Blank.
Grading distribution:
Sections 70854, 70855, 73320
Exam code: midterm01m0oU
p: 23 students
r: 15 students
t: 8 students
v: 8 students
x: 14 students
y: 5 students
z: 1 student

A sample "p" response (from student 3560), calculating the time for the golf ball to hit the ground, and finding that the horizontal distance traveled during that time would be less than a mile:

Another sample "p" response (from student 0123), calculating the time for the golf ball to travel one mile horizontally, then determining that the golf ball would need to be vertically well below the ground in order to travel that horizontal distance:

Another sample "p" response (from student 1263), calculating the time for the golf ball to reach its highest height, then multiplying that by two to get the total flight time, and rinding that the horizontal distance traveled during that total flight time would be less than a mile:

A sample "y" response (from student 9693), speculating that the golf ball would travel farther than a mile on Earth because of the weaker gravitational constant on the moon.