Physics midterm question: comparing compression of rod in different orientations

Physics 205A Midterm 2, fall semester 2019
Cuesta College, San Luis Obispo, CA

A 0.40 m long copper rod with a square profile (0.10 m × 0.10 m) can be oriented standing up, or laid down on its side on a floor. If the same amount of downwards force is applied to the top surface in each case, discuss whether the standing-up rod or the laid-down rod will compress a greater ∆L amount (or if there will be a tie). Explain your reasoning using the properties of stress, strain, and Hooke's law.

Solution and grading rubric:

• p:
  Correct. Applies Hooke's law in a systematic manner by:
  1. recognizing that the applied force F and Young's modulus Y are the same for both rods; and
  2. as a result ΔL depends only on the original length L divided by cross-sectional area A; and
  3. since the standing-up rod has a longer original length (L = 0.40 m) and a smaller cross-sectional area (A = 0.010 m²), it will compress more than the laid-down rod with a shorter original length (L = 0.10 m) and a greater cross-sectional area (A = 0.040 m²).
• 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. Considers only difference in cross-sectional areas (neglecting the difference in original lengths), or vice versa; or recognizes both differences but somehow argues that the rods will still compress by the same amount.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least some systematic attempt at using Hooke's law quantities.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. Approach other than that of relating strain (force per unit area), Young's modulus, and strain using Hooke's law.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 70854, 70855
Exam code: midterm02sQm5
p: 18 students
r: 1 student
t: 28 students
v: 3 students
x: 2 students
y: 0 students
z: 0 students

A sample "p" response (from student 2586):
A sample "t" response (from student 6672), recognizing that the original length L changes with different orientation, but claims the cross-sectional area A is the same:
A sample "t" response (from student 2875), recognizing that the cross-sectional area A changes with different orientation, but claims the original length L is the same:

Physics quiz question: Young's modulus of steel

Physics 205A Quiz 6, fall semester 2019
Cuesta College, San Luis Obispo, CA

A sample of "#4" steel reinforcing bar has a length of 4.9 m and a cross-sectional area of 1.3×10^–4 m². A force of 1.1×10⁵ N is applied to stretch this steel bar by 0.020 m. The Young's modulus of steel is:
(A) 3.5×10⁶ N/m².
(B) 8.5×10⁸ N/m².
(C) 4.2×10¹⁰ N/m².
(D) 2.1×10¹¹ N/m².

[*] webcivil.com/usrcrebar.aspx.

Correct answer (highlight to unhide): (D)

Hooke's law is given by:

(F/A) = Y·(∆L/L),

such that the Young's modulus would be:

(F/A)·(L/∆L) = Y = ((1.1×10⁵ N)/(1.3×10^–4 m²))·((4.9 m)/(0.020 m)),

Y = 207,307,692,307.692 N/m²,

or to two significant figures, the Young's modulus for steel is: 2.1×10¹¹ N/m².

(Response (A) is (F/A)·(∆L/L); response (B) is F/A; response (C) is F/(A·∆L).)

Sections 70854, 70855
Exam code: quiz06co6O
(A) : 5 students
(B) : 2 students
(C) : 2 students
(D) : 43 students

Success level: 83%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.50

Online reading assignment: temperature

Physics 205A, fall semester 2019
Cuesta College, San Luis Obispo, CA

Students have a bi-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 temperature.


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.

"Temperature plays a big role in thermal stress with expansion or contraction. This can be used to our advantage or disadvantage."

"I understand that if the liquid expansion is greater than the container expansion, there will be overflow. Vice versa, there will be no overflow. Expansion occurs as a response to temperature change."

"Explaining a thermometer: temperature ultimately 'is' something greater than the feeling that something is hot or cold; rather, change in temperature is the expansion of materials. In the case of a thermometer, the red alcohol experiences a temperature increase expanding its volume filling up more of the glass indicating a temperature change."

"It totally didn't occur to me how objects expand depending on differences in temperature. It just isn't something that's on my mind daily, but now that I've read about it, it clearly makes sense. I understood the concept of the length of steel beams and how shorter beams would require a higher temperature to expand compared to longer ones."

"The more heat applied the greater an object will expand the size of the expansion is proportional to the size of the object. The same is true for chilling an object."

"That the forces needed to prevent a solid object from expanding must be strong enough to counteract any change in length that would occur due to a change in temperature. It makes sense to me that the change in forces can result in serious structural damage."

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.

"I do think I could use some extra examples covering linear thermal expansion and volume thermal expansion. These practice problems given were confusing to me."

"I had trouble understanding thermal stress and how it differs from normal stress. I was also confused by some of the equations for linear and volume thermal expansion."

"The linear and volume expansion formulas."

"I do not understand the concept behind why objects or fluids expand because of temperature change. Also, does heat mean expansion and cold mean shrink? Does it simply depend on the object?"

"I think I get the general concept of this, but I'm looking forward to the lecture and seeing how these equations will work out."

"Nothing was too crazy, just need to keep in mind how the equations work."

"The reading got more confusing as it went on. At the end, when it was discussing which time of day that the gas would be higher, I was not sure of the answer. "

For solids, what is the mathematical relationship between the coefficient of volume expansion β and the coefficient of linear expansion α?

"β = 3·α."

"The mathematical relationship between the coefficient of volume expansion and the coefficient of linear expansion is that the coefficient for volume expansion is three times as much as the coefficient of linear expansion."

To expand these two steel beams 1.0 cm from their original lengths, the longer beam will require __________ temperature increase compared to the shorter beam.

a smaller.	******************* [19]
the same.	**** [4]
a larger.	**** [4]
(Unsure/guessing/lost/help!)	* [1]

For a thermometer, the glass volume expansion coefficient 3α_glass is __________ the alcohol volume expansion coefficient β_alcohol.

less than.	************** [14]
equal to.	****** [6]
greater than.	****** [6]
(Unsure/guessing/lost/help!)	** [2]

For the water level in this plastic rainwater basin to lower as the temperature falls overnight, the plastic volume expansion coefficient 3α_plastic must be __________ the water volume expansion coefficient β_water.

less than.	*********** [11]
equal to.	***** [5]
greater than.	************************ [24]
(Unsure/guessing/lost/help!)	****** [6]

A certain fuel company will measure out a gallon of gasoline and sell it for the same price, whether it is cool or warm. Indicate the gallon of gasoline that has a greater:
(Only correct responses shown.)

mass: the cool gallon [35%]
density: the cool gallon [76%]

Briefly explain why a gallon of gasoline purchased when it is cool would be better than a gallon of gasoline purchased when it is warm. (In either case, the fuel company dispenses the same volume of exactly one "standard" gallon.)

"Colder gasoline is more dense than warmer gasoline, so a cold gallon of gas contains more energy than a warm gallon of gas, even though they might cost the same."

"Chemically, cooling down allows for the molecules to slow and move closer together, allowing for the density to increase."

"When the gas is cooler it becomes denser and you actually end up with more molecules of gas per gallon."

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"This class is going by so fast!"

"Just need to talk this over in class."

"I never knew they had to account for expansion when constructing sidewalks."

"I would love to go over the gasoline question a bit more."

"Why do objects expand and shrink with temperature change?" (The atoms and molecules inside move faster when hotter. But because of asymmetry of the spring-like interactions between the atoms and molecules, it is harder for them to move closer together (because of mutual repulsion) than it is for them to move farther apart, and so overall the object will expand.)

"Will we be experimenting with liquids during the next lab?" (Actually, we'll be finishing up with standing waves for the last lab.)

"Sad you didn't dress up as an astronaut again for Halloween this year :("

Online reading assignment: elasticity

Physics 205A, fall semester 2019
Cuesta College, San Luis Obispo, CA

Students have a bi-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 elasticity.


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.

"Tension is when you stretch something as opposed to compression when you squish something. Stress is the applying force to the object and strain is a measure of how the object/material responds."

"The two cases of elasticity, either with a tension force or a compression force. Tensile/compressive stress is the act of applying the force, whereas tensile/compressive strain is how the material behaves under tension/compression."

"When compressing a spring, or when it restores, the displacement of the spring is proportional to the force applied. Also, the tensile force is perpendicular to the area, and the shearing force is parallel with a surface."

"That k is the spring constant and x is the displacement of the spring from its unstrained length. The minus sign indicates that the restoring force always points in an opposite direction to the displacement of the spring from its length."

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.

"Nothing is too confusing to grasp from the text. Just a few equations that are used in certain circumstances."

"Hooke's law. I don't understand how materials with a material-dependent Young's modulus (in units of pascals) that characterizes the response of the material to these stresses."

"Using Hooke's law, and why exactly strain is unitless."

"From the presentation preview I was first confused about the tensile stress example but upon another glance I was able to understand it. The stress causes the object to stretch to a limit that does not cause it to break."

"Putting the complex theories into practical world applications and making the connection to conceptualizing while using the equations correctly."

"The elastic deformation equation is a little confusing because I'm not sure about all the components and variables."

"I don't understand hardly anything, I don't know what the variables stand for."

What is the SI (Système International) unit for stress?

"N/m²."

"Pa."

Explain why strain is a unitless quantity.

"Strain is unitless because it is a proportion of two quantities with the same dimensions."

"It's a unitless quantity because it deals with the fractional change of length or volume."

"I am not sure."

"I don't know."

What is the SI (Système International) unit for Young's modulus?

"N/m²."

"Pa."

The __________ lengths of vertical suspension bridge cable are stretched by a greater amount ∆L from their original lengths.

shorter.	***** [5]
longer.	**************************** [28]
(There is a tie.)	*** [3]
(Unsure/lost/guessing/help!)	***** [5]

The __________ columns of 2×4s support the least amount of force.

narrower (two 2×4s).	****************** [18]
wider (three 2×4s).	******** [8]
(There is a tie.)	********** [10]
(Unsure/lost/guessing/help!)	***** [5]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"Need some clearing up, book kind of went off the rails."

"Please go over these in class, I am confuuuuuused ):"

"I understand that Young's modulus is the ability of a material to withstand changes in length when under tension. Will this value always be provided for an individual material? Does it matter what the material is resting on... for example a piece of steel on concrete vs a wood table?" (Yes, the Young's modulus values will always be given for a problem (unless you need to solve for it); and no, it doesn't matter what the material (being tested) is resting on, provided that the supporting object is strong enough to handle whatever is being done to the material being tested.)

"Will we be doing a simple harmonic motion lab?" (Yes, for Lab 12.)

I don't have anything to say."

"Yay physics :)"

"I'm just enjoying the day."

"This irregular weather is killing me."

Physics midterm question: comparing Young's moduli of fishing lines

Physics 205A Midterm 2, fall semester 2018
Cuesta College, San Luis Obispo, CA

A long 1.00 m fishing line and a short 0.50 m fishing line (same cross-sectional area) are each strung horizontally over a pulley, and are attached to a 100 g mass and a 50 g mass, respectively. As a result both fishing lines stretch the same amount from their original lengths. It is not known if these fishing lines are made of the same material. Discuss which material has the greater Young's modulus value (or if there is a tie), and why. Explain your reasoning using the properties of stress, strain, and Hooke's law.

Solution and grading rubric:

• p:
  Correct. Applies Hooke's law in a systematic manner by:
  1. recognizing that they stretch the same amount ΔL and have the same cross-sectional area A; and
  2. the longer L fishing line has a greater tension force F applied to it than the shorter L fishing line with a lesser tension force F; and
  3. since Young's modulus Y = (F⋅L)/(A⋅ΔL), the longer L fishing line with the greater tension force F will have a larger Young's modulus (specifically four times larger) than the shorter fishing line with the lesser tension force.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. Typically has clerical errors (mislabeling "long" versus "short" labels), and so concludes that Young's modulus must be the same for both fishing lines.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. Typically only recognizes length L or tension force F has having an affect on Young's modulus Y; or has recognizes both quantities as having an affect on Y, but someone argues that these cancel each other out, such that the fishing lines have the same Y value.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least some systematic attempt at using Hooke's law quantities.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. Approach other than that of relating strain (force per unit area), Young's modulus, and strain using Hooke's law.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 70854, 70855
Exam code: midterm02r3iN
p: 37 students
r: 6 students
t: 11 students
v: 2 students
x: 0 students
y: 0 students
z: 1 student

A sample "p" response (from student 5683):
A sample "p" response (from student 8812):
A sample "p" response (from student 1113):

Physics quiz question: marshmallow compression

Physics 205A Quiz 6, fall semester 2018
Cuesta College, San Luis Obispo, CA

A marshmallow has a height of 3.8×10^–2 m, a circular cross-sectional area of 5.1×10^–4 m², and a Young's modulus of 2.9×10⁴ N/m².[*][**] A downwards force of 10 N is applied evenly onto the top of the marshmallow. As a result, the marshmallow is compressed by:
(A) 6.7×10^–9 m.
(B) 1.3×10^–5 m.
(C) 2.6×10^–2 m.
(D) 2.0×10⁴ m.

[*] amazon.com/ask/questions/Tx21SLNIPLG0WI4.
[**] physics.info/elasticity/.

Correct answer (highlight to unhide): (C)

Hooke's law is given by:

(F/A) = Y·(∆L/L),

such that the amount that the marshmallow would be compressed is:

∆L = (F·L)/(A·Y),

∆L = ((10 N)·(3.8×10^–2 m))/((5.1×10^–4 m²)·(2.9×10⁴ N/m²)),

∆L = 0.02569303584... m,

or to two significant figures, the marshmallow would compress by 2.6×10^–2 m.

(Response (A) is (F·L·A)/Y; response (B) is F·L/Y; response (D) is the stress F/A.)

Sections 70854, 70855
Exam code: quiz06POr7
(A) : 4 students
(B) : 3 students
(C) : 43 students
(D) : 2 students

Success level: 83%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.50

Online reading assignment: temperature

Physics 205A, fall semester 2018
Cuesta College, San Luis Obispo, CA

Students have a bi-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 temperature.


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.

"That the length of an object changes by an amount by a change in the amount of ΔL when the temperature changes by a ΔT. With linear expansion, when there is a hole in a piece of solid material, when heated the hole will expand along with the material."

"A shorter beam will require a greater increase in temperature to expand to the same of a longer beam based on the equation. If a liquid is in a container it may expand to a greater, less than, or equal to the coefficient of its container."

"The material-dependent linear expansion coefficient characterizes the response of the material to thermal stress. The shorter beam will require a greater increase in temperature to expand the same amount as the longer beam. If the liquid and the container both expand the same amount for the same increase in temperature then the liquid will still fill the container to the brim."

"The linear expansion of an object tells as how the object responds to thermal stress. I also learned that mercury and alcohol thermometers work because the volume of the liquids expand or contract as the temperature changes."

"The relationship between temperature and the effects it has on the molecules of materials. If the temperature increases, the molecules' vibrations speed up and the object/material expands. If the temperature decreases, then the molecules' vibrations slow down and the object/material shrinks."

"Thermal stress causes strain. Linear expansion and volume expansions are unitless."

"Temperature change is really just the measurement of the volume expansion of the liquid inside of a thermometer compared to the expansion of the thermometer."

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.

"I don't understand why the linear expansion coefficient is material dependent."

"Volume expansion--the water inside of a plastic bin. The water was at a lower level in the morning which means it contracted more than the plastic so I would assume it has a larger expansion coefficient?"

"The whole shorter beam needing more temperature change to increase the same length thing really messed me up for a second, because like shorter beam is less mass so like shouldn't it need less energy? But then somebody showed me the way that the equations work and it made sense."

"Volume expansion--I am not sure if it means that as the temperature rises, the volume increases of a substance. For instance, the alcohol in a thermostat rising as the temperature increases."

"How to understand when a coefficient for a solid is higher/lower than a liquid."

"How equations with ΔT can switch back and forth between Celsius and Kelvin units. That kind of tripped me up. I know that either can be used but I still found it a little confusing."

"I found the volume expansion kind of confusing when I first read about it. But after reading it over again I understand volume expansion and the equation for it."

"Everything makes sense."

"I did not get confused by any of this material."

For solids, what is the mathematical relationship between the coefficient of volume expansion β and the coefficient of linear expansion α?

"β = 3·α."

"Larger the linear expansion, the larger the volume expansion."

"Both coefficients are dependent on the type of material being measured. The coefficient of volumetric expansion is mathematically three times as much as the coefficient of linear expansion."

To expand these two steel beams 1.0 cm from their original lengths, the longer beam will require __________ temperature increase compared to the shorter beam.

a smaller.	***************************** [29]
the same.	**** [4]
a larger.	************ [12]
(Unsure/guessing/lost/help!)	*** [3]

For a thermometer, the glass volume expansion coefficient 3α_glass is __________ the alcohol volume expansion coefficient β_alcohol.

less than.	******************************* [31]
equal to.	*** [3]
greater than.	******* [7]
(Unsure/guessing/lost/help!)	******* [7]

For the water level in this plastic rainwater basin to lower as the temperature falls overnight, the plastic volume expansion coefficient 3α_plastic must be __________ the water volume expansion coefficient β_water.

less than.	************* [13]
equal to.	**** [4]
greater than.	************************ [24]
(Unsure/guessing/lost/help!)	******* [7]

A certain fuel company will measure out a gallon of gasoline and sell it for the same price, whether it is cool or warm. Indicate the gallon of gasoline that has a greater:
(Only correct responses shown.)

mass: the cool gallon [25%]
density: the cool gallon [70%]

Briefly explain why a gallon of gasoline purchased when it is cool would be better than a gallon of gasoline purchased when it is warm. (In either case, the fuel company dispenses the same volume of exactly one "standard" gallon.)

"Colder gasoline is more dense than warmer gasoline, so another way to look at it is that a cold gallon of gas contains more energy than a warm gallon of gas."

"It's better to purchase a gallon of gasoline cool than when it is warm because gas is more dense when it is cool. Denser fluids have more mass so essentially when you fill your tank with cool gas you get more product for the same price per gallon."

"The hotter it is the more space between molecules. When cool the molecules move slowly when hot they move faster."

"I don't know--HELP!"

"If you buy gas when it is hot out you won't be able to put as much in your tank to make it full because it is hot and expanded. When it cools down, it will condense back its smaller form and you will have the same amount of gas but your tank won't be full?"

"I honestly don’t understand why it's better."

"Isn't mass and density the same?"

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"Is the next midterm has only five questions?" (Yes, just like the previous midterm.)

"Please help with the gasoline question! thank you!"

"Please go over volume expansion coefficients."

"No questions today; this material seems to make sense."

"Would you rather live in an unexplored cave or in a treehouse in a remote forest?" (I choose treehouse.)

"How can fuel companies compensate for temperature-dependent volume changes of gas?" (They typically don't; so let the buyer beware.)

"I've been too focused on other classes and this totally slipped my mind."

Online reading assignment: elasticity

Physics 205A, fall semester 2018
Cuesta College, San Luis Obispo, CA

Students have a bi-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 elasticity.


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.

"Tension is when you stretch something and compresion is when you squish something."

"Hooke's law can show how the material will respond to stress being applied to it."

"Stress is the application of a force, while strain is the measure of how the material responds."

"Tension is the stretching of something while compression is the squishing of something."

"Stress is defined as the force per unit area of a material. Stress = force/cross-sectional area. Strain is defined as extension per unit length. Strain = extension/original length."

"I understand the concept of restorative force applied by a spring when you stretch or compress it. The spring is always going to 'want' to return to its original length."

"Most of it was confusing."

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.

"I'm not quite understanding how these variables such as tension, stress, and strain are all connected, is it just through Hooke's law or is there something else that will connect them?"

"Well I could use a run-through on Hooke's law and how we solve it. as well what each of the symbols represent in-depth."

"The whole section on Hooke's law confused me. I just really didnt understand what was being put into the equations, except for the moduli for differing materials."

"Everything in this reading actually made perfect sense to me, there really wasn't anything that I kind of found confusing. Maybe Hooke's law, but I read it over a couple times and it makes sense now."

"I didn't find much confusing since I feel like this chapter is pretty straightforward."

What is the SI (Système International) unit for stress?

"Pa."

"N/m²."

Explain why strain is a unitless quantity.

"strain is dimensionless and have no units."

"It's the ratio of two lengths."

"Because its a fractional change?"

"Strain is unitless because it is a fraction of the change in length over a length so the units cancel out. "

"I'm not sure."

"Not sure, I just know it is."

What is the SI (Système International) unit for Young's modulus?

"Pa."

"N/m²."

The __________ lengths of vertical suspension bridge cable are stretched by a greater amount ∆L from their original lengths.

shorter.	****** [6]
longer.	******************** [20]
(There is a tie.)	***** [5]
(Unsure/lost/guessing/help!)	******** [8]

The __________ columns of 2×4s support the least amount of force.

narrower (two 2×4s).	****************** [18]
wider (three 2×4s).	***** [5]
(There is a tie.)	******* [7]
(Unsure/lost/guessing/help!)	********* [9]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"For collisions, the definition of an elastic collision is that all energy is conserved, and there is no permanent damage. So why is that that there's permanent damage here if it's called elastic deformation?" (Actually, it's only called elastic deformation as long as when you let the material relax, it can still return (unharmed) to its original, undamaged state. If you do stretch or squish the material such that you irreversibly damage it, then you've exceeded its "elastic limit" (cf. p. 279 from the textbook).)

"How do we set up and work through these type of problems?"

"I would like to go over some practice problems in this section."

Physics midterm question: comparing the stretching of fishing lines

Physics 205A Midterm 2, fall semester 2017
Cuesta College, San Luis Obispo, CA

A long, thin fishing line and a short, thick fishing line (both made of the same material) are strung horizontally over a pulley, and attached to a 100 g mass and a 50 g mass, respectively. Discuss why the thin fishing line will stretch a greater amount than the thick fishing line. Explain your reasoning using the properties of stress, strain, and Hooke's law.

Solution and grading rubric:

• p:
  Correct. Applies Hooke's law in a systematic manner by:
  1. recognizing that the Young's modulus (Y) is the same for both fishing lines ("made of the same material"); and
  2. applying Hooke's law to show that the long, thin fishing line will stretch a greater amount ΔL = (F⋅L)/(A⋅Y) due to the combined contribution of three separate factors:
     1. a greater force F applied to it (which increases ΔL); and
     2. a smaller cross-sectional area A (which increases ΔL); and
     3. a longer, original unstretched length L (which increases ΔL).
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. Typically missing one of the three factors (a)-(c) above, but correctly discusses the effect of the two remaining factors.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. Typically missing or misinterprets one of the three factors (a)-(c) above, but does not explicitly discuss how these factors affect ΔL in Hooke's law.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least some systematic attempt at using Hooke's law quantities. Typically missing two of three factors (a)-(c) above, and does not explicitly discuss how these factors affect ΔL in Hooke's law.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. Approach other than that of relating strain (force per unit area), Young's modulus, and strain using Hooke's law.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 70854, 70855
Exam code: midterm02bu2Z
p: 15 students
r: 12 students
t: 2 students
v: 3 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 4532):

Physics quiz question: concrete sample compression

Physics 205A Quiz 6, fall semester 2017
Cuesta College, San Luis Obispo, CA

A concrete sample was (non-destructively) tested by compressing it with a stress of 9.9×10⁶ N/m²[*]. The Young's modulus of this concrete is 2.8×10¹⁰ N/m²[**]. If the concrete sample started with a height of 0.305 m, during testing it was compressed by:
(A) 1.1×10^–11 m.
(B) 1.1×10^–4 m.
(C) 3.5×10^–4 m.
(D) 5.5×10^–3 m.

[*] youtu.be/iCWsDHhbi9g.
[**] engineeringtoolbox.com/concrete-properties-d_1223.html.

Correct answer (highlight to unhide): (B)

Hooke's law is given by:

(F/A) = Y·(∆L/L),

where the compressive stress (F/A) is given as 9.9×10⁶ N/m². The amount that sample would be compressed by will be:

∆L = (F/A)·(L/Y),

∆L = (9.9×10⁶ N/m²)·((0.305 m)/(2.8×10¹⁰ N/m²)),

∆L = 0.0001078392857 m,

or to two significant figures, the concrete sample would compress by 1.1×10^–4 m.

(Response (A) is L/Y; response (C) is the strain (∆L/L) = (F/A)/Y; response (D) is the volume of the concrete cylinder, which cannot be determined from the values given above.)

Sections 70854, 70855
Exam code: quiz06Ho0k
(A) : 4 students
(B) : 40 students
(C) : 1 student
(D) : 0 students

Success level: 89%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.27

Online reading assignment: temperature

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

Students have a bi-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 temperature.


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.

"The increase in any one dimension of a solid is called linear expansion. The volume of a normal material also increases as temperature increases, this is known as volume thermal expansion."

"The material-dependent linear expansion coefficient characterizes the response of the material to thermal stress."

"The material in the section relate to experiences in real life, such as liquid expanding when it is cooled and metals cooling and expanding."

"Solids and liquids expand with changes in temperature. A shorter length rod will expand less than a longer length when made of the same material and same change in temperature. ∆L is the change in length due to temperature."

"Thermal stress causes strain. A shorter beam will require a greater change in temperature to expand/contract the same distance as a longer beam."

"I learned that I need cooler gas to save money at the pump."

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.

"I don't fully understand volume expansion and feel that in some of the equations I would go go back and forth on what increases or decreases in volume."

"I found thermal stress and strain confusing. I could use further explanation on the equation."

"How you would calculate the amount of expansion that a metal undergoes by given the original length and the temperature?"

"I do not know how all of the equations relate to each other. I think I will have to review more before next class."

"Not as confusing as the last few subjects. Which is a relief for the end of semester. Still, I skimmed it because I'm studying for the quiz."

"Could you go over thermal stress? Maybe do an example problem, the one in the book was a little confusing."

"I didn't understand why the shorter beam will require a greater increase in temperature to expand the same amount as the longer beam."

"Thankfully due to my chemistry class this wasn't very confusing."

"I found most everything confusing from this reading and would benefit greatly from in class examples."

"I haven't gotten much into the reading yet, so it's all a little confusing right now."

"Nothing."

For solids, what is the mathematical relationship between the coefficient of volume expansion β and the coefficient of linear expansion α?

"β = 3·α."

"They have the same units, K^–1."

"No idea."

To expand these two steel beams 1.0 cm from their original lengths, the longer beam will require __________ temperature increase compared to the shorter beam.

a smaller.	*********************** [23]
the same.	**** [4]
a larger.	****** [6]
(Unsure/guessing/lost/help!)	* [1]

For a thermometer, the glass volume expansion coefficient 3α_glass is __________ the alcohol volume expansion coefficient β_alcohol.

less than.	********************** [22]
equal to.	***** [5]
greater than.	***** [5]
(Unsure/guessing/lost/help!)	** [2]

For the water level in this plastic rainwater basin to lower as the temperature falls overnight, the plastic volume expansion coefficient 3α_plastic must be __________ the water volume expansion coefficient β_water.

less than.	************* [13]
equal to.	**** [4]
greater than.	************ [12]
(Unsure/guessing/lost/help!)	***** [5]

A certain fuel company will measure out a gallon of gasoline and sell it for the same price, whether it is cool or warm. Indicate the gallon of gasoline that has a greater:
(Only correct responses shown.)

mass: the cool gallon [38%]
density: the cool gallon [68%]

Briefly explain why a gallon of gasoline purchased when it is cool would be better than a gallon of gasoline purchased when it is warm. (In either case, the fuel company dispenses the same volume of exactly one "standard" gallon.)

"I don't know. Is it easier to handle? Maybe cheaper to move."

"The cooler gallon of gasoline would have more density and therefore should have more energy based in that gallon of gasoline."

"Because it has a greater density so the amount of energy within that gallon of gasoline is greater."

"The gasoline is more dense when it is cold and there for the volume is smaller. Although when it is warm the volume is bigger due to it being less dense. The volume might be more but the amount is still the same. Gas stations measure by volume therefore it is better to get gas when it is cold."

"Gasoline (and nearly all objects) expand and become less dense due to heat. Because of this it is more dense during a cool day. Since its density increases and since gas is bought in volume, you get more 'bang for your buck' when you buy on a cooler day."

"How can we figure out the gasoline question? We weren't given the properties of gasoline and how reactive it is at different temperatures."

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"Thank you for applying concepts to real-life situations."

"Does heat by itself change the atomic structure in solids?" (The space between atoms increases as atoms vibrate more at higher temperatures, because atoms repel each other at close distances, they will spend more time farther apart than closer together as they vibrate more.)

"We will soon be fluent in Greek." (Graecum est; non legitur.)

"Still really enjoying the class."