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.
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!!
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!
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
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 ;)
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).
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
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.
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!
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.
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.
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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.
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.
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.
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 :)
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.
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).
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).
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"
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.
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.
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.
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.
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.
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.
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.
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.
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)
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.
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.
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.
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.
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''.
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.
So cool, really good video, I think you missed 2 points: 1- you explained stress and strain and have not include them in the video title 2- you missed using the symbols for both stress and strain which are sigma and epsilon respectively. Thanks
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
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?
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?
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?
When he was demonstrating with the Blu-Tack, all I did thoughout that whole video was pry the Blu-Tack off my desk and start squishing it! SO DISTRACTING! :D
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?
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.
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.
@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.
Great video. Only gripe for me was that you didn't define properties of materials like toughness and ductile which will probably come up on the exam (well at least on edexcel).
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?
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.
