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

Physics quiz archive: simple harmonic motion, waves

Physics 205A Quiz 6, fall semester 2019
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855 version 1
Exam code: quiz06co6O



Sections 70854, 70855 results

0- 6 :	* [low = 3]
7-12 :	****
13-18 :	*************
19-24 :	**************** [mean = 22.1 +/- 6.1]
25-30 :	****************** [high = 30]

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

Physics quiz archive: simple harmonic motion, waves

Physics 205A Quiz 6, fall semester 2018
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855 version 1
Exam code: quiz06POr7



Sections 70854, 70855 results

0- 6 :
7-12 :	**** [low = 9]
13-18 :	********
19-24 :	********************* [mean = 23.3 +/- 5.6]
25-30 :	******************** [high = 30]

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

Physics quiz archive: simple harmonic motion, waves

Physics 205A Quiz 6, fall semester 2017
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855 version 1
Exam code: quiz06Ho0k


Sections 70854, 70855 results

0- 6 :	* [low = 6]
7-12 :	*
13-18 :	*********
19-24 :	************* [mean = 23.3 +/- 5.8]
25-30 :	********************* [high = 30]

Online reading assignment: elasticity

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 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.

"Strain, tension and Young's modulus and what they represent. Tension is stretching something out while compression is bringing stuff together."

"Tension is a pulling force, with tension stress being a pulling force applied to a material, while tension strain is how the material reacts. Compression is a squishing force, similarly with compressive stress peing a pressing force to a material and compressive strain being how the material reacts."

"Elasticity is the nondestructive stretching or squishing. The tension in stretching, compression is squishing."

"Elasticity is a material's ability to cope with stress/strain or tension/compression. These variables are balanced in Hooke's law, where the energy from stress is equal to the material's strain and its Young modulus."

"Force applied along the x axis is equal to x displacement times a proportionality constant k. Pressure is expressed as P equal to force F on a perpendicular surface divided by area A."

"The use of tensile stress and compression stress seem pretty simple. Tensile is applying a force to 'stretch' something and compression is applying a force to 'squish' something."

"A material is considered elastic when it can be bowed (whether squished or stretched), but returns to its original state after. Tension is when such material is stretched whereas compression is when it is squished. There are two types of stress and strain: tensile and compressive. Tensile stress is when you apply force to a cross-section sample to stretch it, but tensile strain is how the material responds. Compressive stress is when you apply force to a cross-section sample to squish it, but compressive strain is how the material responds."

"The restoring force of an ideal spring is: F_x = k·x. Where k is the spring constant and x being the displacement."

"The larger the k value, the more force it takes to stretch or compress a spring."

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 a little bit confused by Hooke's law. I don't really get what it is or what it is used for."

"I could definitely use help with Hooke's law and applying the concepts to the equations."

"Hooke's law was a bit confusing. I just don't know how to use it."

"Describe Hooke's law a bit more."

"Stress and strain are a little confusing to me and would need some clarification on that along with Hooke's law."

"I would need more examples on how to use and comprehend Hooke's law better. The formula is pretty clear but I am scared to be confused on some cases."

"It was all very straightforward. Again, the only challenge I seem to encounter is becoming familiar with the new equations being presented."

"Nothing too confusing."

"Nothing really which is good."

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

"Pa."

"N/m² = Pascals."

Explain why strain is a unitless quantity.

"Because it's change in length over length."

"Strain is the change in length divided by the initial length. Since both quantities have the dimensions of length, the resulting quantity in unitless."

"Because it is a fractional length change."

"I am not entirely sure."

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

"Pa, the same as stress."

"N/m²."

"Y?"

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

shorter.	******** [8]
longer.	*************************** [27]
(There is a tie.)	*** [3]
(Unsure/lost/guessing/help!)	** [2]

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

narrower (two 2×4s).	******************** [20]
wider (three 2×4s).	************ [12]
(There is a tie.)	****** [6]
(Unsure/lost/guessing/help!)	** [2]

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

"More elaboration on Hooke's law."

"I would love it if you could quickly go over the answer to the bridge cable question on this assignment. Thank you!"

"Can you go over the question with the 2×4s?"

"This is probably easier than I think, I just didn’t have too much time to go into it."

"Thank you for changing your lecture times next semester! You rock!"

Online reading assignment: elasticity

Physics 205A, fall semester 2016
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.

"Compression is a squeezing force, tension is a stretching force, and tensile stress is force applied to the center of a strip of material perpendicularly."

"To compress or stretch a spring, a force must be applied to it, by newtons third law the springs also applies an opposite force of the same magnitude. The reaction force is applied to the object attached to the spring."

"Hooke's law of restoring force of an ideal spring is F_x = –k·x."

"Compression and tension. Compression is squishing something and tension is when you stretch something."

"The difference between tension and compression. I also understand how those forces cause strain."

"How elastic deformation in a spring is non-permanent and reversible while plastic deformation of a spring undergoes permanent deformation and is non-reversible. Hooke's law can be used to find the tension force, the length or extension of the spring, and/or the value of the spring constant."

"This section was on elasticity. Tension is when you stretch something and compression is when you squish something. Tensile stress is applying a force to a certain cross-section sample to stretch it, while tensile strain is a measure of how the material responds. Hooke's law is used to calculate tensile/compressive stress. Stress is exerted in Pa, and the strain is unitless in the equation."

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 really understand where ∆L comes from. I don't know 'what change in L' means (especially in the context of the 2×4 problem)."

"I am confused by some of the variables for the equations from the reading. So, I would like to go over those and to also apply it to situations to make the subjects more relatable."

"I don't understand how to balance the hooke's law equation for two different lengths of material. If one side of the equation remains constant doesn't that mean the whole equation remains unchanged?"

"I didn't really find anything confusing."

"I found the Hooke's law to be a little confusing in the blog. The Y variable is throwing me off."

"I don't understand some of the textbook problems that they worked out. I feel like they were mixing up ∆L and L but I know it must be my mistake."

"I found the whole strain thing a little confusing, kinda had me overall 'confuzzled.'"

"I don't understand why the forces between atoms act like springs. How were the values for Young's modulus of solid materials derived?"

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

"Pa."

"Pascals."

"N/m², aka Pascals (Pa)."

Explain why strain is a unitless quantity.

"Is it because the units cancel out?"

"Because length is both in the numerator and denominator so they cancel out."

"Change in length divided by original length. Since both the 'change in length' and 'original length' have the same units, strain is a unit-less quantity."

"Because strain is how the material responds?"

"It depends on the material and how it responds to stress?"

"Because of the infinite ways to represent it in different scenarios. It depends on the cross-sectional area, the material, etc.?"

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

"Pa."

"Pascals."

"N/m²."

"It is named after the French polymath Blaise Pascal."

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

shorter.	*********** [11]
longer.	*************** [15]
(There is a tie.)	******* [7]
(Unsure/lost/guessing/help!)	***** [5]

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

narrower (two 2×4s).	*************** [15]
wider (three 2×4s).	****** [6]
(There is a tie.)	********** [10]
(Unsure/lost/guessing/help!)	******* [7]

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

"Did not get a chance to read this section yet. Cramming for an exam in another class I forgot until now."

"I don't fully understand what Young's modulus represents."

"How does cross-sectional area apply to Hooke's law?"

"I am not sure about these last two questions. Can we go over them in class?"

"If a suspension bridge's max load was reached, evenly displaced, which wire would snap first?" (Assuming that they all carry the same stress, and are designed to stretch the same ∆L amount, then the wire that experiences the most strain would probably snap first--which would be the shortest one.)

Physics quiz question: femur compression

Physics 205A Quiz 6, fall semester 2015
Cuesta College, San Luis Obispo, CA

An average femur bone (Young's modulus 9.4×10⁹ N/m²) has a length of 0.48 m and an approximate cross-sectional area of 1.72×10^–3 m², and reportedly can support a maximum 2.4×10⁴ N of force.[*][**] When this force is applied, the femur would compress by:
(A) 2.1×10^–9 m.
(B) 9.1×10^–9 m.
(C) 7.2×10^–8 m.
(D) 7.1×10^–4 m.

[*] "30 times the weight of an adult," orthopaedicsone.com/display/Review/Femur.
[**] "Weight of average adult: 178 lbs," wolfr.am/8dc2Ohi7.

Correct answer (highlight to unhide): (D)

Hooke's law is given by:

(F/A) = Y·(∆L/L),

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

∆L = (F·L)/(A·Y),

∆L = ((2.4×10⁴ N)·(0.48 m))/((1.72×10^–3 m²)·(9.4×10⁹ N/m²)),

∆L = 0.0007125185552 m,

or to two significant figures, the femur would compress by 7.1×10^–4 m.

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

Sections 70854, 70855, 73320
Exam code: quiz06m45S
(A) : 3 students
(B) : 0 students
(C) : 3 students
(D) : 67 students

Success level: 92%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.17

Online reading assignment: elasticity

Physics 205A, fall semester 2015
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.

"Stress is applying a force to stretch something while strain is how the object responds to the stress."

"Tensile stress is applying a force to a certain cross section sample to stretch it. A compressive stress is an applying force to a certain cross section sample to squish it. Both tensile strain and compressive strain, measures how the material responds."

"Tension is stretching stuff thinner, compression is squishing stuff. Tensile stress is applying a force to stretch stuff and compressive stress is a force squishing stuff. Hooke's law gives the relationship of this stress (F/A), causing a strain (∆L/L) of a given material (Y)."

"Compressive stress is force applied on a cross section. Compressive strain is how the cross section responds to to the stress/ force applied."

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 found Hooke's Law tough to apply to real-life examples."

"Everything from your blog made sense, but the textbook confused me more than helped me honestly. They're are a few conceptional questions that I have that we will probably go over in class."

"Using the elastic deformation equation with Young's modulus."

"I have a hard time understanding Hooks law and how it works, it may be because I don't have a handle for what it actually is."

"The manipulation of different equations can be challenging when I am trying to conceptualize the problem."

"I understand most of it"

"I found nothing confusing--I am a genius."

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

"Pa."

"N/m²."

"It does not have a unit."

"Newtons."

Explain why strain is a unitless quantity.

"When dividing a quantity of a particular unit by another quantity of the same units, the units cancel out and only a numerical value (the quotient of the quantities) remains."

"It is a measure of deformation--change in length divided by initial length cancels out the units."

"The fractional length change cause the units for length to cancel out, thus giving strain a unitless quantity--it is a relative change in shape."

"I don't know...please explain in class."

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

"Pa."

"N/m²."

"Young's modulus is the ratio of stress (which has units of pressure) to strain (which is dimensionless), and so Young's modulus has units of pressure. Its SI unit is therefore the pascal."

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

shorter.	********* [9]
longer.	******************************* [31]
(There is a tie.)	**************** [16]
(Unsure/lost/guessing/help!)	***** [5]

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

narrower (two 2×4s).	************************** [26]
wider (three 2×4s).	**************** [16]
(There is a tie.)	*************** [15]
(Unsure/lost/guessing/help!)	**** [4]

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

"Is the material going to get easier or harder at this point in the semester?" (I think the only difference in the material from now on is that it is very compartmentalized, and does not critically rely on previous chapters for full understanding. After the build-up in the motion-forces-Newton's laws chapter sequence, this should be a good thing.)

The homework problems for the book are orders of magnitude more difficult than the rest of the coursework, I NEVER know how to do them and it makes me sad."

"The A in Hooke's law stands for area, right?" (Uh, yes.)

"Why is the notation '∆L' used for both tension and compression? Confusing." (If you start with a given length L, then ∆L represents how the length changes from that original amount, whether it gets slightly longer (due to stretching), or slightly shorter (due to squishing).)

"I'm going to get my cartilage pierced." (So, your cartilage will have a certain amount of stress applied to it, which will respond with...OW.)

Physics quiz question: stretching fishing lines

Physics 205A Quiz 6, fall semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e Conceptual Question 11.4, Problems 11.1, 11.3

"Untitled"
Eileen Delhi
flic.kr/p/fGR8Fi

Trilene® XL Super Strong fishing line (Young's modulus 2.0×10⁹ N/m²) and Eagle Claw® Sportfisher fishing line (Young's modulus 3.1×10⁹ N/m²) have the same 10.0 m length [*]. The Trilene® fishing line has a cross-sectional area 1.8 times that of the Eagle Claw®. Both fishing lines are stretched with a tension force of 98 N. The __________ fishing line will stretch more.
(A) Trilene®.
(B) Eagle Claw®.
(C) (There is a tie.)
(D) (Not enough information is given.)

[*] S. Ottolini, G. Halpin, P. LaBruzzo, "Tensile Strength of Fishing Line," santarosa.edu/~yataiiya/E45/PROJECTS/Tensile%20Strength%20of%20Fishing%20Line%20Power%20Point.ppt.

Correct answer (highlight to unhide): (B)

Hooke's law for the Trilene® and Eagle Claw® fishing lines are given by:

(F/A_Tri) = Y_Tri·(∆L_Tri/L),
(F/A_Eagle) = Y_Eagle·(∆L_Eagle/L),

where tension F and the original, unstretched length L are the same for both fishing lines. The Trilene® fishing line has a cross-sectional area 1.8× that of the Eagle Claw® fishing line:

A_Tri = 1.8·A_Eagle.

The amount that the Trilene® fishing line will be stretched is given by:

∆L_Tri = (F·L)/(A_Tri·Y_Tri),

∆L_Tri = ((98 N)·(10.0 m))/((1.8·A_Eagle)·(2.0×10⁹ N/m²)),

∆L_Tri = (2.7×10^–7 m³)/A_Eagle.

Similarly, the amount that the Eagle Claw® fishing line will be stretched is given by:

∆L_Eagle = (F·L)/(A_Eagle·Y_Eagle),

∆L_Eagle = ((98 N)·(10.0 m))/((A_Eagle)·(3.1×10⁹ N/m²)),

∆L_Eagle = (3.1×10^–7 m³)/A_Eagle.

Thus this sample of Eagle Claw® fishing line will stretch more than the Trilene® fishing line sample.

Sections 70854, 70855, 73320
Exam code: quiz06eAg7
(A) : 13 students
(B) : 49 students
(C) : 2 students
(D) : 0 students

Success level: 77%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.46

Online reading assignment: elasticity

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 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.

"Strain is the ratio of the change in length to the length when a tensile force is applied. Stress is the ratio of the tensile force to the cross-sectional area."

"Tensile force stretches something, which results in strain. Compressive force squishes something, which results in strain."

"Four things to consider with elasticity are tension, compression, stress, and strain. Tension is when you stretch something whereas compression is when you squish something. Both tensile stress and compressive stress cause strain. Hooke's law is the quantitative relation between tensile/compressive stress (force exerted per unit area, in N/m², or Pa), and strain (given as a fractional length change, unitless), with a material-dependent Young's modulus (in units of Pa) that characterizes the response of the material to these stresses."

"Didn't read it yet."

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 stress. I don't understand all the variables being used."

"I don't understand how Y can be independent of the length and cross section of an area? Is the object like a really solid metal that has no give?"

"I'm still trying to figure out why strain is a unitless measure. Possibly because any change it makes is so minuscule that it cannot be measured?"

"Pretty intuitive, really."

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

"N/m² or Pa."

"idk."

"N times m-squared."

"F/A."

Explain why strain is a unitless quantity.

"Strain is measured in proportion to what is being strained, so instead of being strained by say 2 meters, it is strained by 10%, which is a unitless value that is only related to the object being strained."

"It is defined as change in length, divided by initial length, but since these quantities both have dimensions of length, the result is a dimensionless quantity."

"Because it is a measurement of deformation."

"I'm not sure."

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

"N/m² or Pa."

"k times N times meters-squared."

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

shorter.	********* [9]
longer.	******************************* [31]
(There is a tie.)	********** [10]
(Unsure/lost/guessing/help!)	****** [6]

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

narrower (two 2×4s).	******************** [20]
wider (three 2×4s).	************ [12]
(There is a tie.)	************* [13]
(Unsure/lost/guessing/help!)	*********** [11]

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

"I didn't find anything in this section too confusing, but I always appreciate examples in class."

"Will we be given Young's modulus values? Does it just describe how strong materials are?" (Yes, unless it is being solved for. Yes, large Young's modulus materials don't show much strain when stress is applied, given that thickness and lengths are equal.)

"What exactly is the cross-sectional area for cables?" (The area of their circular shape at either end.)

"The string we used in the last lab had a high Young's modulus and low tensile strength. I hope the bond Measure 'L' that just passed for Cuesta College goes into providing strings that don't break so easily." (I would be more concerned with using bond measure funds for the construction of new buildings that don't break easily. #Lyeah)