hello everyone welcome back to zed physics today we are going to be doing a revision lesson on materials so let's get started the first thing that we need to revise is actually the definition of tensile and compressive forces so remember tensile forces actually produce extension so that means that we're essentially trying to stretch an object for instance if i was to apply a tensile force onto this material over here this would stretch under the tensile force a compressive force would tend to reduce the length of the material it would in other words shorten it or compress it like so so this over here would be an example of a compressive force and this leads us up to hooke's law which is the next point in the elo physics specification so hooke's law says that the applied force is directly proportional to the extension in this case f stands for the applied force so we can just write this down this over here is the applied force which is measured in newton's x is our extension like so remember extension would be found by subtracting the final length from the initial length uh i can just write this down maybe here length final minus length initial and k is the spring constant which is also often called the force constant so let me just write this down like so so this over here will be the force constant now what are the units of the force constant k will be f divided by x so f is measured in newtons and x is measured in meters therefore k will have units of newtons per meter now let's have a look at an experiment in order to demonstrate hooke's law and hopefully find the spring constant the or the force constant of a spring so we have the following setup over here we have a stand which is connected to a spring with some masses attached to it that we are going to vary we're also going to attach just behind the actual stand probably with a with a boss and a clamp a ruler just next to the spring because we're going to have some masses attached to the stand it's also much safer to use a g-clamp to attach the stand to our desks now the first thing that we need to do is as we said suspend some masses from the actual spring in the following experiment we are going to be varying the mass and we're going to be recording the extension remember in order to find the extension all we need to do is to subtract the original length of the spring from the extended length we're going to find the force for each of those masses using f is equal to mg and then we're going to plot a graph of the force against extension in order to make our readings as accurate as possible we need to make sure that we take all readings at eye level in order to reduce the parallax error in this experiment if hooke's law is indeed correct we expect our results to produce a straight line through the origin we can actually compare this with the equation of a straight line we can just do this over here so f is equal to kx this is hooke's law y is equal to mx plus c we can see that our intercept is zero x is on surprise surprise the x-axis f is on the y-axis and this means that our gradient is equal to the spring constant so in a force against extension graph the gradient is equal to the force constant k now what about the area underneath the curve in order to find the area we need to find the area of this triangle in order to do so we're going to be multiplying force by extension so that means that we're going to have force times distance which so once again the area will be equal to half f x now this will have units of newton meters so that means that our area will actually be the work done intuitively this also makes sense because in order to find the work done we need to multiply the force by the displacement that's been traveled in the direction of the force so we can say that the area underneath the curve is equal to the work done like so which is also equal to the amount of energy like so this energy in particular is known as elastic potential energy and it has the following two formulas so let's just write this down so elastic potential energy is the area underneath the curve which is a half what's happening here let's fix that a half f x but because of hulk's law we know that f is equal to kx like so so what i'm going to do is i'm just going to sub that back into the original equation and what i'm going to get is that elastic potential energy is going to equal to a half kx times x which is equal to a half kx squared those are the two formulas that we know for elastic potential energy remember in an f against x graph the gradient is equal to a spring constant and the area underneath the curve is equal to the work done or the elastic potential energy let's have a look at stress and strain first of all the stress which is given this symbol sigma over here is defined as the amount of force that has been applied divided by the cross sectional area that means that the stress which is very very similar to pressure will have units of newtons per meter squared or you can also measure it in pascals as well for the units strain on the other hand which is a known as in particular the tensile strain which is applied to stretch really an object is defined as extension divided by the original length so let me just write this down so strain which is given the symbol epsilon like so is our extension x divided by the original length just to avoid in confusion i'm going to just label those so x in this case is the extension and l is our original length like so because it's going to have units of meter over meter strain is actually unitless it is often given as a percentage by the way for instance for our original length was let's say one meter and then it stretched let's say 0.1 hour our strain will actually be 10 so [Music] we can convert that to a percentage which is approximately equal to 10 so don't get confused if you come across in a question the stream being given as a percentage we should be fairly confident just converting those numbers from percentage to um to a fraction and vice versa and there's one more quantity that we definitely need to know for our exams and this is the ultimate tensile strength now this is the greatest amount of stress i'm just going to underline this because that's really important that material can withstand before reaching its breaking point quite a common misconception is to just write down or think that it's the greatest amount of force but remember if that force is spread over a large surface area it doesn't really matter it's the stress which really affects the material so once again the ultimate tensile strength is the greatest amount of stress that a material can withstand before reaching breaking point we can combine those two quantities stress and strain into a quantity which is known as young's modulus which is given the symbol e in your formula booklet if you're doing ocr physics and this quantity young's modulus is stress or in particular tensile stress this could be important so let's just write this down so this will be equal to tensile stress like so divided by tensile strain so tensile strain mathematically this would be just equal to essentially stress like so divided by strain now remember our stress is force over area then we're going to be dividing that by the strain which is extension over original length if i am dividing by a fraction this is the same as multiplying by the inverse so this means that jung's modulus will be equal to f divided by a times the original length divided by the extension okay guys now let's have a look at an experiment that we can do in order to determine young's modulus of a metal wire the first thing that we need is a table or a desk of some sort and we're going to clamp a wire which is given in this blue color which is running along the desk with a pulley on the end the reason why we use a pulley because this way we can keep this part of the wire purely horizontal then we can attach a mass at the end of the wire we we are going to be varying this mass m like so we're going to put a marker on the actual wire with a ruler underneath it by seeing how much the marker moves we'll be able to determine the amount of extension in the wire remember f is equal to mg which is our force so we'll be able to determine our young's modulus which is stress over strain remember the force this will just be equal to mg for the area of a wire we can use a micrometer screw gauge to determine the diameter and then just use pi d over two squared our extension we'll be able to determine with this setup with the marker and the ruler underneath it and our original length of the piece of wire we can just determine with a ruler note that often the extension of a metal wire can be very very tiny so we may have to use a traveling microscope if the extension is quite small so maybe in brackets over here i'm just going to add this that we may have to use a traveling microscope like so in this experiment we are going to be varying the force f by essentially adding progressively more more mass onto the end of the wine we're going to be measuring the extension x in terms of measurements we're going to be first of all we'll need to measure the diameter d of the wire with a micrometer we'll take several readings along the length of the wire in order to ensure that the wire has a consistent diameter all the way along its length and then we're going to average we're going to use this to calculate the cross-sectional area a and for that we're just going to use the cross-sectional area formula which is just pi r squared which means that this equal to pi d over 2 squared which is equal to pi d squared divided by 4. we're also going to be measuring the original length with a ruler we are also going to be measuring the extension x with a with this marker over here and a ruler or if the extension is smaller than a couple of millimeters we're going to be using a traveling microscope in order to be really accurate and reduce the percentage uncertainty in our measurements so just to summarize uh we have the force f over here that we're going to measure just using mg l over here will be our original length that we're going to measure with a ruler a is our cross sectional area we're going to measure the diameter with a micrometer and x over here is our extension that we're going to be measuring with this setup over here after we have taken all of these measurements what we need to do is to plot a graph of the force that's been applied against the extension x if we remember what we did with the formulae for young's modulus which is equal to stress over strain which is equal to force divided by cross sectional area divided by extension which is then divided by the original length this will be equal to f over a multiplied by l over x because dividing by a fraction is the same as multiplying by the inverse and what we can do is then compare this equation with the equation of a straight line remember if f is on the y axis what we need to do is rearrange for this so what i'm going to say is that f will be equal to young's modulus e times the cross-sectional area a times the extension x and we'll also need to divide by the length like so so let's just divide by the length and we can compare this with the equation of a straight line remember y is equal to mx plus c i'm just going to add a plus 0 because i can and we can see that the graph should be a straight line through the origin additionally we can see that f is on the y axis and x is on surprise surprise the x axis so our gradient we can use a different color for this uh where actually be equal to this expression so uh let's write this over here on the side that our gradient m will be equal to young's modulus times the cross-sectional area divided by the original length which means that our young's modulus which is what we're looking for in this case will be equal to the value of a gradient multiplied by the original length of the wire divided by the cross sectional area okay folks so hopefully this experiment makes sense now okay guys now before we have a look at stress and strain graphs uh let's define a couple of very important definitions first of all what is a ductile material so this is a material which can easily be drawn into wires additionally we need to define elastic deformation and for instance we apply a tensile stress onto this material over here if the material returns to its original shape after the force is removed then this material is elastic so we can just make sure to underline this because this is really important on the other hand in plastic deformation the material does not return to its original shape or original length after the force is removed okay now let's have a look at some stress and strain graphs okay guys now let's have a look at the stress again strain graph for a ductile material first of all up to point p in this first region over here we can see the stress is proportional to strain most of the time the material would actually obey hooke's law up to point p which is known as the limit of proportionality at point e permanent deformation occurs so that means that up to point e which is known as the elastic limit the material will exhibit or will experience elastic deformation if you go beyond point e plastic deformation occurs so that means the material is permanently deformed when the force is removed the highest amount of of of stress that a material can withstand is known as the ultimate tensile strength and this is this point uh over here this over here is our ultimate tensile strength and eventually if we keep going we're going to reach the breaking point of the material so this over here is the stress again strain graph for a ductile material let's have a look at the behavior of a brittle material as an example of brittle material for instance it could be something like glass for instance okay anyway so if you pull out a graph of stress against strain for a brittle material we're going to see that the graph will be a straight line through the origin all the way up to the breaking point now in practice this means that stress is proportional to strain and that hooke's law is obeyed now notice that elastic deformation occurs all the way up to the breaking point and remember elastic deformation means the material will return to its original length after the force is removed finally we are going to have a look at polymeric materials which are materials which are made from these long chains of molecules an example for instance is rubber now notice that this has a very distinctive shape for instance if we are trying to stretch the object from applying a tensile strength the curve will be like so however if we apply a compressive uh stress the um curve will be like so now notice that this will have elastic behavior this means that the material will return to its original shape after the force that's been applied has now been removed in general as well hooke's law is not obeyed we can see that this graph is not a straight line through georgia notice that some energy will be lost as well in the process normally as heat in terms of polythene which is an example of a polymeric material which exhibits plastic behavior the stress and strain graph initially starts being proportional and some of them may initially obey hooke's law however quickly you reach a point at which plastic behavior occurs and the material no longer will return to its original shape after the applied force has been removed okay folks so this was the hall of materials any questions uh please drop a comment down below thank you very much for watching if you found this video useful please give it a like and a subscribe thanks again see you soon for the next video