If you're working on a material, the extension is directly proportional to the force up to a certain point, so proportionality limit. So there's a proportional relationship up to this point, and then there's an elastic limit. If you continue adding forces beyond this point, then the object won't go back to its original shape. Exceeds the elastic limit. And then we have something called the yield point. So things stretch and go back to their original shape. But if you go beyond the yield point, it suddenly gets longer. So the yield point is there. The extension increases fast for little increase in force as plastic deformation begins, plus the difference between elasstic Jackson and plastic. Elastic and plastic, I think elastic has elastic potential energy, but plastic maybe not. And what about deformation? If something is deformed plastically, what do we mean by that? Plastic maybe means they have less durable. Is that durable? Yeah, so with elastic deformation, I need to search it. Let me help you. Okay, so see this hairband. If I stretch, it itgo back to its original shape, so it's elastically deformed it with if it's elastic, it goes back to its original shape when the force is removed. But if I stretch as really big itnot, it's permanently deformed. Plastic deformation is when itstay deformed, it's gone beyond its elastic limit. And then the breaking force, and then the breaking point. So different materials have different profiles, so wires, springs, rubber bands will have slightly different shapes. So if we have a spring with a spring constant of 40 newtons per meter, it's extended by a load of five nusions. Calculate the extension which results on, hence the elastic strain energy stored in the stretch spring. So we know the force. We know the spring constant five over 40 is 0.125m. So the extension we can. Look at there. A light spring is subjected to a tensile force of six mutons, which extends the spring by 120 mm. Calculate the stiffness of the spring. So we want to find k, so we know the force, if we know the extension and we put it into meters. So six over point 12, we get the spring constant, a force of ten usions. It's now applied to this string spring. Find the new extension, assuming hooks 's law is obeyed. So the extension is the change in force over the spring constant ten over 50.2m. So we can stretch things. We can also compress them because if you think of it, buildings have to undergo compression as well as stretching. So there's squashing forces as well as pulling forces. So a force compression graph looks much the same as a force extension graph. Then we have elastic strarain energy. The area under a force extension graph will give us the energy stored in a stretch spring, so we find the area under the graph line. And if we have a curve, see, the line is slightly curved, you can still estimate it by drawing a triangle and getting the elastic potential energy by using that triangle. Explain the difference between the limit of proportionality and elastic limit of awar in tension. So what's the difference between the limit of proportionality and the elastic limit? What do you think? Think limit of proportionality is at a point between the limitation of elastic and Bricket is at the point if we, if we above the limit of proportionality, it will break this. For example, the ring. So the braking force, the wire, breaks here. So prothe limit of proportionality is this point. So at this, in this part of the graph, it obeys hooks 's law. So hoo's law is obeyed where force is proportional to extension. Whereas the elastic limit. Is there a maximum force that can be applied for the object to go back to its original shape? If you keep increasing the force beyond the elastic limit point, then you start to get permanently deformed structures, so they go beyond their limit of being able to go back to their original shape when the force is removed. Then two springs, one with a spring constant of 100 nusions per meter and one with stiffness of 200 nusions per meter. They're joined end to end. A load of 20 musions is suspended. So you rehave one spring. And another spring which is thicker. So this is the 200 nusions per meter and this is the 100 nusions per meter. So this is to suggest that this will be easier to stretch than this one because this is thicker. Calculate the total extension and the elastic strain. Energy stored in each spring. The bottom of the question got chopped off. So if we have a lighter spring attached end to end with a heavier, a higher spring, constant spring, what will be the total extension and the elastic strain energy stored in the spring? There's energy store in each spring and stiffness. So a lot of 20 newtons suspect calls to the extension and elastic strain. So end to end, one is 101 is 200 newtons per per meters. So a lot of 20 newtons suspect for this. 20 newtons, a lot of 20 newtons. I think that maybe 30m, that is a total extension extension. Yeah, not 13 shing meters but 0.3 of a. North Point three north meters because remember it's not 20 nutions. We need 200 nutions to stretch this spring, 1m. We need 100 newtons to stretch this one, 1m. But we only have 20. So if you do f equals kx for both of them. The first one is. 20 divided by 100. No point two and the other one is 20, divided by 200 is no point one. So if you add 0.2 vmeter and 0.1 of a meter, you get. Note point three note meters. Okay, so that springs and then the the elastic strain energy stored. So the elastic strain energy is a half f delta x. So in this system of the 100 mutions per meter and the 200 mutions or. What is the total energy stored in these stretch springs? If we have maybe total energy, maybe 40. So we have we have to do a half f times. Delta x. So the strain energy. In joules will be the half f delta x. So we note the total extension. We've just worked it out. The total extension delta x is 0.3. The force is 20 and then a half. So zero. Point three times. 20 times point five so we ash. No point three Jews. So. 20 times point, three times a half. Yeah that is not 20 35. Point 35. 20 times a half is ten times 0.3. So. This spring will store one jle of energy, this spring, spring will store two joules of energy, so the total energy stored is three jles. Okay, two plus one gives us three Jews. Okay, so. Witmeans, is that all divided by two? Is that this question is all divided by two? And that is 0.15 plus zero point. One and that is 0.25. So. E equals. Times f. Times delta x. So if we do the smaller spring. A half times 20 nusions times. How much did they? No point two measures, the lighter spring will stretch more. So this was stretch point 2m 20, divided by 100 nutrients per meter. So this, the first spring will stretch and store this amount of energy a half times, 20 times point two. So that gives us and. Ten times 0.2. Which is two jewels. The second spring, which is thicker, it has a spring constant of 200 nusions per meter. So 220 nusions divided by 200. It's stretch 0.1m. So if we do, the elastic energy is a half f to X A half times, 20 times. Note point one. N times point one gives us one. So the total energy stored will be two jles plus one joule. Okay, three Jews. Okay. My measure of this. Now your o modulus, sometimes you want to know the property of the material, but it can change in length or in diameter. So the way it behaves depends on the length of the material and the diameter of the material. So it should be harder to stretch a really thick piece of wire compared to a really thin piece of wire. It should be easier to stretch this one compared with this one. And it should be you should get more extension with more length and less extension with less length. So with Young modulus, the l nodulus is the property of the material, irrespective of its radius, its length. It's the property of the material. And that's useful for working out the strethe forces that they can withstand. So stress we've talked about, stress is force over area. And it's measured in the same units as pressure force over area. So stress is given the symbol sigma materials have a breaking stress, which is the force or uniicrosecarea that may be applied without the material breaking. So again, if you think of suspension bridges or people doing bungee jumps, this is important for them to know. So we have the stress is the force of the area. The strain is the extension over the length. Strain. So length over length, the units cancel each other. So strain has no units. So the Young modulus is the stress over the strain. It's a measure of the stiffness of the material and its stress over strain. So force over area. On the y axes against change in length. Over length. So f over a times delta x over x so. These cancel, so the units for Young modulus is also the same as pressure, its pascals. So this graph looks a bit like the hooks law graph, a stress against a strain graph. So you can work out a breaking stress. Using the Young modulus. So the Young modulus for steel is two by ten to the eleven passcals. Calculate the extension when a load of 15 nusions is applied to a wire of 2.5m length and a wire with a cross sexual area of four by ten to the -7m squared. So Young monchlus is force over area times original length over change in length. So we know the area, we know the force. We know the original length x, so the change in length is what we can find out by substituting. And we know we're given the Young modulus for steel, two by ten to the eleven pascals. So if we know this, this, this and this, we can find the extension. So rearranging our equation, swapping e with delta x, we have 50 nutions force, times length, 2.5m, divided by cross section tional area, times Young modulus two by ten to the eleven th. And when we work that out. We get an extension. Of. 1.6 by ten to the minus three of a metia. So that tells us that the wire will, the steel wire will stretch about nearly 2 mm. So there's different ways of measuring the Young modulus. You can use this equipment. Two lengths of wire to be tested are used. A is the reference rottwir and is kept in tension by a load. B is the why we're investigating. And you can use this scale. To see, as you add more load here, how much longer the length of this wire changes. Okay. So you can also stretch the wire across a bench and do the same experiment. Okay, so imagine you got a question like this, Jackson, a cable made of steel has a diameter of 18 mm. And length 15m. The Young nodulus for steel is 200 gigapascals, so 200x ten to the what's ts. How many pascals is gigar? Big 20 times ten to the six that would be maa so nine Yeah 200 by ten to the nine asscals. So we know e the Young modulus, so we know. Young modulus 200 by ten to the nine, or two by ten to the eleven, same as this one for steel. The cable is used to support a weight of ten kiln ussions, so we know the force. Find the tensile stress in the cable under this load. So stress. Stress is force over area. So we're not given the cross sectional area. We have to work it out. What will the stress speak? Stress is foresoarea. So it's. What's the diameter? Diameter is. Cable is a weight of ten kilo newtons, find the strength diameter. 18 mm, so that is 1.8 times ten to the -2m Times Square and times pi. Yes. So the tensile stress is. So area we have to work out pi R squared. And the force is ten killinesians, so ten I tend to the three. What do you get? Actually, I left the calculator upstairs. So. Ten by ten to the three. Divided by I times nine by ten to the minus three. Squage. So that gives me 39. I tend to the. 123456. Our spouls. Okay. The extension of the cable under this load. So the extension. E. Equals. So the strain. E equals stress over strain, which is horse over area. Over. What's the strain? Delta x. Over x. So we can simplify. This is force over area. And this inverts times x over delta x. So we're trying to find the extension of the cable. So we know the. 39 by ten to the six we know f over a. So that's equal to 39. I tend to the six. Times. The length. 15m. Age. 15 measures. Over. 200. Times ten to the minus or ten to the nine are scars. So I get. 2.94. Millimeters as the extension okay. The strain of the cable under this load. So again, we can do more questions like this. This is another way of measuring Young modulus. You stretch a wire, you put a marker with a ruler here, a scale here, and you stretch it with a different load, and you take the diameter along different points along the wire as you add the loads. So you can use a microrometer for measuring the thickness of the sprstring, the Suir, after you've added different loads. Okay, so these are more straightforward questions. But the thing is Jackson on, I can do these questions. We have to train you to do them and we have to train you to do them under exam conditions. So how are we going to help you do that? Do you want me to send you work and you do it before the next lesson and then we could go, we can go through it. Is that better? Yeah. Okay. So I'll copy this into your homework file and. Get you to do these questions. But these are these are good questions from a revision book for excel physics, okay? Because what you've got to do is to be able to do these without referring to a book quickly and under timed conditions. So I'll start sending you work. And if you put it, if you attach it a day before we have our next lesson, I can mark it and then we can spend some of the time reviewing it. Okay, Jackson, but for this, you should be able to do this, define tensile stress and explain why its units are the same as pressure units used for pressure. Anytime you're asked to define something, you can give a word equation. Good equation, okay stress strain tension tentensile strength equal to stress divided by strain. That's Young Marchus. Stress or restrain is Young modulus pensile stress is force. To find a by area. And their unuses are pascals. Pascal, because pressure Sher is also equal to force over area and it's measured in pascalals same thing. If you think if you're adding pressure, you're compressing something. And remember, if you're stretching it, it's under stress, tensile stretching stress too. So both are measured in pascals. Okay? So define, if you're asked in physics to define something, a word equation is good enough. Okay, define tensile strain. Tension tenstraing and explain western does not have any unit tension. Tension strin is stress divided by string. Is that this equation? No. The Young model, the Young moalist, that's the next question. Yes. Tenstring tencil. Is that a string now to and to strengthen initial initial strength in. Yeah it's it's something to do with the length. It's the change in length over the original length. So if these are measured in meters and these are measured in meters. Length at length they cancel out, don't they? So that cancels with that. So there's no units. So tensile stress is force over area, tensile strain is change in length or extension over length. Stress is measured in pascalstrahas no units. Hence, explain why Young modulus has the same units as stress. Some units are stress if string has no unit, so and the equation e equal to stress times string, so they have, so they have the same unit. That's stress. So stress is sigma, strain is epsilon. So this has no units. This has the same units as pressure. Yeah. So. F over a times. Length over change at length. And they're measured in pascals, okay? I'm going to send you these questions, and you're going to write them out in your own words. The Young modulus of copper is 120 gipasscals. A 3m length of copper wire of diameter that is subjected to a tensile force of ten usions determined a tensile stress in the wire. So. So what do we know? We know the Young modulus. So we know the Young modulus e. We know the length of the copper wire. We know the diameter, so we need that to work out the area. So. Sigma is the force. Yeah. So the force ten usions over the cross secual area. That should be by ten to the. Minus two b squared. Okay, so force over area. And that should give us. 1.3 mm, 1.3 by ten to the -3m. No, sorry. So. 2.5 by ten to the minus three squared times pi equals diviby ten. So that's a big number. 5.09 my tend to be. 12345. Pascals, remember, stress is measured in pascals, so determine the extension of the wire. So stress times length over extension gives us the change, change in length. So so five point Oh, nine, my ten to the five. Times the length. Three measures divide by. Extension. Maybe that is 15 point Oh, nine. It's the Young modulus. It's not the so it's the the Young modulus. This is he. They use x for extension 120 by ten to the nine pascare girls 120 by ten to the nine. Times three divifive divifive. So. 1.27. I tend to. Minus five. Hmm. The eagle stress of copper is 17 megapass as determine the mamaximum tensile force that can be applied to the wire before it starts to deform plastically. So. So copper is the wiwe're talking about. Force is stress. Times. Area. Remember, stress is forced, divided by area, so. If we know 70. So 70 by ten to the six. Times area, what's the area? So we know. Hi, sometimes. Ten 52I ten to the minus three. 70I tend to the six times I times 2.5 by ten to the minus three squared. Hmm. Yeah. That should be right. So I get 14 newtons. Let's check that, okay? And 70 by ten to the six times. I. Times 2.5x minus three. Yeah. Have you seen how to do these questions? I'll send you all this document. So this this is a summary. What I want you to do for next Wednesday is write answers for all these questions. Some of it is learning definitions, but these are what you need to know. Okay. And then do this question as well, because are you getting to do any lab work in your present school? Any experiments? Yeah. What sort of physics experiments do you get to do? Well, something about electricity and emf pd, variable resistance and something about force like the projectile and do the experiments about hunter and monkeys. Yeah, this Asian story. Okay, nice. Good, good. So the vertical component, you have acceleration, but constant speed horizontally. Good. Okay, so I' M Jackson. Bring your calculator to the next lesson. Okay, okay, yourself. Okay. Okay, I'll send you this work now. Bye, bye bye, miss.