Hooke's Law and Young's Modulus - A Level Physics

[@PhysicsOnline]

Very clear descriptions here that have really helped the students I teach. Thanks.

[@Sibasish07]

A Level Physics Online lol u copy him?

[@mikeoxlong2077]

it is rare to see one legend commenting on the video of another

[@eyeris292]

Probably one of the best videos I've seen regarding the topic of stress-strain, springs, etc. not only from a practical standpoint but from an experimental standpoint as well. DrPhysics, thank you for supplying the community with multi-faceted ways of thinking that is applicable not only to students but also to potential real-world applications in a work environment as well.

[@sarkiesarkie4918]

wow, what a teacher. at 63 im still learning stuff. been a welder for many years and this explanation has helped enormously. Many thanks.

[@kenhooke6297]

Hooke's Law so clearly explained, and the associated physics too. Thank you. Always interested in Hooke's Law. Robert Hooke is part of our family tree!!

[@sonamdixit4121]

ohh really

[@jaan735]

👌🏻😂😂

[@Homeworlder]

I've spent 6 weeks with my teacher rabbiting on at me about Young's Modulus but she never once said what it actually is. Thanks to this I finally understand how simple it is! This is an excellent video, thank you!

[@Shalie7506]

It's 11 years later, how are you now

[@Homeworlder]

@@Shalie7506 would you believe it, I took a career in teaching myself

[@DrPhysicsA]

Young's Modulus will apply to anything where stress is proportional to strain. So if the proportionate extension is related to the pressure or stress (force over area).

[@DrPhysicsA]

Well work done is the area under the curve. If the curve is regular then you might have a formula you can use. Otherwise its a case of adding up the squares (if its plotted on graph paper).

[@DrPhysicsA]

j lee - these videos are designed for the syllabuses of AQA, OCR, Edexcel and CIE. Not all of them will be relevant for each course.

[@mp923]

DrPhysicsA you should make a patreon!

[@azaneenurarif2102]

DrPhysicsA

[@pushpamahadevan7242]

DrPhysicsA-S/TG

[@DrPhysicsA]

Thanks for kind comment. Young's modulus is defined as stress over strain which is pressure (F/A) divided by strain (extension over original length). So E = F/A / x/l which can be rearranged to E = Fl/Ax

[@DrPhysicsA]

Yes. The SI units use kg, m and sec. So if a measurement is in mm you need to convert it to m.

[@DrPhysicsA]

In the case of a spring, the extension (x) is the distance between the mean position and the extended position. Force = kx where k is the spring constant. But if you consider a spring oscillating then the force is constantly varying since it is proportional to the extension which itself is constantly varying.

[@DrPhysicsA]

It will certainly distort if you crush it. Not sure if that is "crossing the elastic limit" since that term is usually reserved for over-stretching the spring.

[@RyanSeeRolyPoly]

You are a ledge, I have been studying this in science for weeks and my teacher does not explain shit all, I've just learned how to do this in a quarter of an hour. Cheers pal, have a nice day ;)

[@DrPhysicsA]

You find the cross-sectional area by measuring it using a device which measures the circumference accurately. The tension will usually just be the weight applied to the wire which you will usually determined.

[@DrPhysicsA]

K is the spring constant such that F = KX, where F is the force and X is the extension. Stress is force over area. Strain is extension over original length. From that you should be able to derive an equation for K.

[@SUONIndustry]

thank you very very much,sir.I am the best physic student in my class right now.I'm truly appreciate your work.

[@DrPhysicsA]

Sorry - don't know. My vids are intended to cover the broad A level material of the main A Level courses.

[@DrPhysicsA]

Well I assume that the "bar" you refer to is capable of being stretched - so is in the form of a wire. Measure length of wire and diameter (from which cross sectional area can be calculated). Suspend wire from a suitable fixed point. Hang weights on the wire and measure the extension for each weight (but dont go beyond elastic limit). Plot Force/Area against extension/ original length. The slope is Young's Modulus (ie F/A / x/l)

[@DrPhysicsA]

You are right that the limit of proportionality comes first and is usually closely followed by the elastic limit. Hooke's law still applies at the limit of P, but if you go beyond the elastic limit then the material will be permanently stretched/deformed. There is some material on Work, Energy and Power at the back end of the vid on "Classical Mechanics - A Level Physics"

[@DrPhysicsA]

Hi. Hooke's Law doesn't apply on an atomic scale because of Heisenberg's uncertainty principle. At the atomic scale all measurements are uncertain. But atomic vibrations can be thought of as similar to the simple harmonic vibrations of a spring as in my videos on SHM.

[@yaredaddis484]

Thanks for your tutorials. You are helping people all over the world.your tutorials are clear and easily to understand.

[@donnertang9319]

00:00 Hooke's law F=kx 06:23 Stress and Strain Stress(tensile strength)=F/A Strain=x/l W=1/2 Fx= (kx^2)/2 12:53 Young's Modulus E=Stress/Strain=Fx/lA Energy in stressed material = 1/2 (stress)* strain or the area under the stress to strain graph

[@turicaederynmab5343]

I love learning more about math and physics! I struggle with other topics so focussing on my passions in my spare time will help me become a better phycisist in future.

[@andrepedersen1147]

Continuously amazed over your brilliance in both explaining and teaching. There come few great teachers these days, but you're surely one of the better ones. Been watching your videoes during my whole bachelor's degree. Few teach subjects as easy and clear as you do. Thanks! Keep up the good work!

[@sudheesh882]

the simplest explanation I have ever see about tensile..... all can understand... you are amazing sir

[@DrPhysicsA]

The practical aspects determine whether a material will be malleable and ductile or whether it is brittle or plastic.

[@DrPhysicsA]

Stress = f/a will always be true but in the case of a spring it is very complicated and not much use. In the case of a wire hanging vertically with a weight F=mg on the end, then the relevant area is the cross sectional area of the wire. But for a spring the wire is coiled and it would be difficult to assess the cross sectional area to which the force applied.

[@DrPhysicsA]

I guess the point they were making is that if the material returns to its original state then the material was being stretched within its elastic limit. ie it had not gone beyond that point in which case it would not have done so. A spring can be loaded and unloaded and still obey F=kx as long as you always keep within the elastic limit. But if the spring gets deformed with too heavy a load then the F=kx rule will no longer apply.

[@chriswang1381]

Man your amazing at teaching physics, your videos always helped me and friends a lot !!!!

[@DrPhysicsA]

Well you could watch my 44 A Level Physics revision videos (assuming you are doing A levels or equivalent exams) but they are really only revision videos and can't replace the original tuition. Good luck with the exam.

[@trobe5219]

your videos are pulling through my a-levels, keep it up!

[@DrPhysicsA]

My A level playlist covers material for OCR A and B, AQA and Edexcel, with some CIE as well. I can't really tell you how to convert a C to an A other than to go thro the material thoroughly and perhaps practice exam questions, examples of which you can find online. All good wishes for the exam.

[@MCmontageX]

Hi there, this was a very clear and informative video although i would like to add that you could use searle's apparatus to measure the young modulus of a wire. This involves adding a second wire parallel to the test wire, the second wire acts as a control wire where by any changes in temperature do not affect the end results due to the addition of the second wire. Also a vernier scale could be installed between the two wires which you use to gauge how far the test wire has extended as opposed to the control. Also i think that you need to explain the fact that the young modulus which can be calculate graphically only applies to the straight portion of the stress/strain graph. Young modulus can only be measured within the limits of proportionality. Thanks for making the video, i just wanted to add a little of my knowledge just to clarify a few things.

[@DrPhysicsA]

I am no expert on this but it is to do with molecular structures. During the elastic stretching the molecular bonds are stretched but the structure remains in tact. The yield point arises when the bonds start to break and the material cannot then return to its original state.

[@goliath3577]

I cannot thank you enough for this video, you explain the concepts so well.

[@DrPhysicsA]

I think you've answered your own question. Wk = Fx when the force is constant. If the force varies (as it does with Hooke's law) then you have to integrate each element of F dx to find total work done. So Wk = Integral F dx. In the case of Hooke's law for, say, a spring the force varies linearly with x (since F=kx). So you get a straight line relationship between F and x. The integral in this case is just the area of the triangle under that curve, which is half the base times the height ie Fx/2.

[@DrPhysicsA]

At 13:55, as I indicated in my reply to an earlier comment, I was actually just establishing the dimensionality. E = stress/strain = F/A / x/L = FL/Ax = units of work/energy / units of volume - hence energy per unit volume. The graph at 15:30 better sets out your point. The energy per unit volume stored in a stretched wire is 0.5 x stress x strain = 0.5 (F/A) (x/L).

[@MrHellworth]

QUESTION: why does the yield point (the point at which the material stretches with constant or reduced load) occur?

[@DrPhysicsA]

You can't calculate tensile strength from info in this video. Tensile strength is the maximum stress that a material can withstand while being stretched or pulled before deforming. It is usually found by performing a tensile test and recording the stress versus strain. Tensile strength is defined as a stress, which is measured as force per unit area.

[@DrPhysicsA]

Well the modulus of elasticity is usually the same as Young's modulus which is stress/strain. Stress is F/A and strain is x/L. So E = F/A / x/L = FL/xA. So F/A = Ex/L. That means that T in your equation must equate to Stress.

[@squablywablly]

this is so convenient! the teaching is good and you can rewind and pause. Its very helpful.

[@DrPhysicsA]

Strictly it is Energy per unit volume = 1/2 * stress * strain. On your second point I was actually establishing the dimensionality. E = stress/strain = F/A / x/L = FL/Ax = units of work/energy / units of volume - hence energy per unit volume.

[@DrPhysicsA]

Elastic - a stretched material will return to original shape cos atoms can be pulled apart up to a limit and the move back to equilibrium position when load removed. Plastic - stretch leads to permanent deformation - atoms dont return to original position. You may need to look up how atoms are organised in metals, ceramics, polymers and combinations.

[@NebulaeCat]

Wow you've helped me A LOT. My script at university is absolutely terrible comparing to this :) saved me for today's lab, as I was really struggling to get it all :)

[@FatMonkey1395]

How I wish you were here in January of 2012, but hey, Thank you so much, I'll finally be acing physics2 this time around!

[@Daniel-jd4wz]

4:30 - wouldn't it be better to describe it as the limit of proportionality rather than elastic limit? The material still exhibits elastic properties at the limit of proportionality - the only difference being that force exerted doesn't equal the extension. I've always learnt them as two different points, but I might be wrong. Thought I'd make a point of it. Thanks.

[@DrPhysicsA]

Wk is Fx/2 But F is kx by Hookes Law So E = Wk = kx2/2

[@DrPhysicsA]

Not uniquely. The material in the A Level Physics playlist covers the main material in the Edexcel, AQA A/B and OCR A/B courses except for some biophysics which I have not covered.

[@DrPhysicsA]

Stress is proportional to strain.

[@DrPhysicsA]

The units of Young's Modulus are indeed N/m^2 (ie the units of pressure).

[@DrPhysicsA]

Well for A Level physics its probably sufficient to say that the bonds within the crystal structure are atomic or molecular. But at an engineering level it all gets much more complex. It's not something I've studied at that level.

[@abdoali2088]

simple,clear amazing videos,very useful for the beginner, thnks you.

[@alvinsu8740]

@Dr.PhysicsA,Do have a video for the Analysing Forces in Equilibrium? I need you teach how me how to form a diagram to make it easier so that I can know which SIN,COS or TAN I need to applied.

[@mahmoudm451]

I didn't understand why we take the average force?

[@chriswinnard7739]

Mahmoud Matar force*distance = work done in general when moving something, or in this case stretching/compressing. Here force isn't constant so less work will be done each moment when you start to stretch something compared to when its almost fully stretched. the power (work done per second) changes so average amount of energy transfer is needed to give an overall value. that probably doesn't help but its kind of hard to explain

[@mahmoudm451]

Shon Wuls Oh I think I got what you mean, if the force is constant, at that time work=force*distance, but if the force is varying throughout the stretch/compression, then we take the average force isn't it?

[@chriswinnard7739]

Mahmoud Matar yeah, but force will always be varying because more force is required each moment when extension is longer as F=kx

[@mahmoudm451]

Shon Wuls that means that the more it strerches, the more force you need to apply to stretch it more, and that's principally the reason why the force varies?

[@chriswinnard7739]

Mahmoud Matar exactly that

[@anilhatiboglu4534]

if i didn't understand wrong, young's modulus is actually the work done to per unit volume which is streching . But if i think of a spring, what is the volume? spring would have a free space inside the helix shape unlike a wire. is it still consistent?

[@shekharbhattarai9262]

Since,the change in length(strain)depends upon the force(stress),wouldn't it be more appropriate to choose stress along x-axis and strain along y-axis?

[@DrPhysicsA]

I hope I said that Young's modulus E was the gradient of the graph; that is stress is divided by strain.

[@simplisticirony5896]

Your videos are brilliant, mate. Thank you!

[@DrPhysicsA]

Thanks.

[@FatMonkey1395]

You helped me loads on my way to an A overall in physics and an A* in physics5!!! Got into university :D:D:D

[@HotzFred]

Very good educational video, but at 15:50 isn't that supposed to be the Energy per unit volume, (Not the Energy). Since Energy = 1/2 Fx , and 1/2 Stress x Strain = 1/2 F x X / A x l = Energy/Volume . Please correct me if I'm wrong, Thank You

[@DrPhysicsA]

Yes and I have added an annotation to that effect. Thanks.

[@teslatesla5285]

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[@DrPhysicsA]

Congratulations. Have a great time at uni.

[@mikeygargaro174]

Great Video, what exam board(s) do you cover?

[@mahmoudm451]

You said that the young modulus is the work done per stretched volume, and work done is equal to the energy transformed, so basically the energy per stretched volume is equal to the gradient of the stress vs strain graph, so why are we taking the area?

[@kitbattarbee8184]

Hi, when I learned this I was taught that when you do an experiment to plot a stress-strain graph, the area does change (particularly during plastic deformation when the material starts to neck). I don't really fully understand this so I could be wrong.

[@johnbyrne7083]

Hi. Lots of great stuff here. Forgive me if someone has already mentioned. You make a quick reference to the Youngs Modulus equaling Work per unit Volume. I am not sure if this is correct. Is not the area under a stress-strain graph (not the gradient) equal to the Strain energy per unit volume? I think your annotation mentions this, but doesn't correct the final part of the formula above. Thanks for any clarification.

[@DWolf16]

Hi, I understand completly these operations and concepts. However, what I seem not to find/understand is how can I calculate the Young's Modulus if my input data has many times given Tensile Strength values and Tensile Elongation (in %) Would these "Strangth and Elongation" be considered "Stress" and "Strain" respectively? I am confused and don't know if i am doing it right.

[@Crehan.]

sorry at 15:43 you say the area under the graph is elastic potential energy stored in the string, but surely it couldn't be, as the unit of stressXstrain would be the same as Stress/strain as strain has no unit? Also if its you have the time would you mind explaining to me hysteresis? Thank you.

[@DrPhysicsA]

Yes you are right. It is of course the energy per unit volume. I have added an annotation to that effect.

[@kevinbeckenham3872]

We need good educational Films on youtube like these films,because it is revision for me. My thanks go's to the lecturer & person who produced the films and also youtube.''Thank's''.

[@lucaciurares5606]

I have an elastic tube, and inside the tube i put wather uder diffrent pression to observe deformation of the tube. How can i compute Young modulus, knowing the pressures and the deformation of tube.

[@badshabz1]

When you talking about bonds being brocken when the matial is streched beyond limit of proportionality are you refering to intermolecular bonding?

[@masudkamali4109]

Dr.PhysicsA can you tell me how i can find out the cross sectional area and tension in the wire in young modules. if you have a video can you please put the link on the message board.

[@alanchapman370]

Hi, excellent videos, I follow all your work. Small point, (~16.29) I don't think the area under a stress strain graph gives you stored energy. The units will be wrong. Only the area under a force extension graph give you the energy stored. Let me know what you think.

[@DrPhysicsA]

You are right. It's actually the strain energy per unit volume.

[@Noxxiie]

why are you even watching this?

[@Noxxiie]

***** not you...

[@rowanmusic1556]

Hello, firstly can I just thanks for putting up these videos. They've helped me enormously with AS Physics so far. At 4:28 you call the point illustrated with an arrow the elastic limit. Isn't this the limit of proportionality? I thought the elastic limit came after the limit of proportionality. On another note, are you planning to publish any videos on work,energy and power? Cheers.

[@Osama_Alkadomi]

how to find the cross sectional area of the wire/do we need to know how to do it

[@osheensingh6079]

thanks a lot sir........u are just brilliant sir,u r doing a great job for students like us....thanks once again sir

[@hatatske]

Thank you very much! My GCE physics unit two exam is today. I'm feeling more confident on this topic now!

[@james5604]

DrPhysicsA, shouldn't E=Stress*Strain, rather than Stress/Strain? You mentioned that the area under the curve was the potential area, so I figured that would result from a product equation rather than a ratio.

[@bepositive1559]

Your explanation and video is really good...how do you record this

[@johnvalerkossi8809]

Very Very Interesting fact about Young modulus = Work/volume. I did learn something new. thank you .

[@donnertang9319]

Is there is a connection between the elastic potential energy and kinetic energy? I noticed that one is given in (1/2)(kx^2) and the other(1/2)(mv^2), they look similar with m and k both being constants and v with x being variable

[@DrPhysicsA]

Good. Hope the exam went well.

[@lamaalnajjar3292]

You're just amazing !!! . But I'm wondering about calculating the extension of group of springs in parallel or in series . Could you makeup a video on that ?

[@masudurrahman8265]

If force,F is applied on both end of wire what will be the equation of young's modules?

[@gagangahir5976]

does the spring constant K equals to the gradient on the force and extension graph??? @drphysicsA

[@george10618]

fantastic video as it covers the course perfectly keep it up but can u help me with the part, what would the springs constant be if we used two wires in series and the same for parallel

[@emanaref8170]

Is there any other example for young's modules ?

[@alfonsoantonio4202]

can you have a video about pressure, and bulks modulus?

[@aidanmarshall558]

@DrPhysicsA i am doing kevlar for a physics project and was wandering how to explain the fact the kevlar has a youngs modulus yet its is flexible. I thought that this would be contradictory due to youngs modulus being a measure of stiffness. Any help would be greatly appreciated thanks.

[@mahmoudm451]

does that mean that the area under the F against x graph, will give us the work done?

[@feitan5052]

Yeah, you could say the elastic potential energy stored in the spring.

[@howtomakeanything9031]

Isn't it possible to extend something to infinity and it aquaere it's original position

[@rikk9391]

please please do a detailed video on superconductivity and the property associated with it.

[@gregorycawthorne]

Hello! I am a bit confused as to why there are two equations for work done? I got wk=F*x. But then you said that the average wk = (F/2)*x. Now again this sort of makes sense to me, in that the average force would be F/2 if the force was gradually increased on a period of time from 0 to max F. But I guess what I'm asking is what is the significance of each of the two and what applications would you have to use and and not the other? Thanks :).

[@abdullahkabbani8123]

Straight away subscribed you. Great teaching, thanks!

[@0113slimshady]

How would you calculate the work done from a Force vs. Extension graph if the graph was curved.

[@ali-bb7so]

Could you tell me the difference between elastic limit and yield point

[@DrPhysicsA]

Elastic limit is when the material stops behaving elastically and begins behaving plastically - from here onwards it would no longer return to it's original length. Yield point is when the material suddenly starts to stretch without any extra load.

[@rohitgupta1975]

@DrPhysicsA: Dr, in the end you say that energy stored = half * stress * strain . But that has the units of Pascals. So it's not dimensionally correct. I also didn't understand how you substituted FL with Wk in the equation for Young's modulus. F is not moving through a distance L; L is fixed.

[@Mech.Masters]

How do we come to know the exact value of yield stress of a material??? Because it is difficult to find the actual point when the yielding starts???

[@ihtishammiraj770]

Hey DoctorPhysics :) Thannk you soo much for these videos, theyve been a reaaal help Can u tell me though which yeard did a physics practical in stress in springs come out for the cambridge a-level exams? wud be real helpful thanking u in advance

[@Svajok]

And lastly, how could I apply this knowledge to practical situations? Could you give an example please? Thanks a lot!