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## Class 11 Physics (India)

# Bulk stress and strain

Let's explore the concept of bulk stress and bulk strain. Created by Mahesh Shenoy.

## Want to join the conversation?

- Bulk stress is F/(initial area) or F/(area after compression)?(2 votes)
- The surface area is the same before and after compression when under hydraulic pressure, material is not 'magically' formed or destroyed once compressed.

But, this depends on the material's tensile stress and strain. Consider a balloon's surface area, it will increase when blowing it up because of the material's elasticity or tensile strain (proportional to tensile stress), as you blow into it, the material stretches.

If wrong, lemme know,

hope this helps,

onward!(1 vote)

- when pressure is applied on to the stone underwater does the stone get permanently deformed or is it temporary and when the stone is taken out it regains its original shape ?(2 votes)
- so at "2:30" are we considering only the magnitude of the forces,because force is vector quantity right? so, the bulk stress cannot be eqaul to the pressure because they are completely opposite to each other(1 vote)
- I guess we're considering the forces as vectors here, wherever there is an external force acting per unit area,

there will be deformation(however small), there will be a restorative force developed over that area,

the external force = -restorative force

as net force = 0 as a = 0 (equal in mag. opp. in direction)(Newton's 1st law of motion) when in**EQUILIBRIUM**

try drawing a free body dia, resolve the (couple)forces into their components, you will find they cancel.

And one more thing,**bulk stress, and pressure are scalar quantities**.

hope this helps,

if wrong let me know,

Onward!(1 vote)

- Let's say we have a balloon immersed in water, it exerts pressure due to compression (bulk stress), so, there is a (net) force exerted by the balloon downwards other than its weight => loss in weight is lesser than if object is not compressed, right?

(note that the pressure exerted by water/Liq.∝Bulk Stress is greater on the bottom than the top)

Now, consider Archimedes' principle, wouldn't the weight of displaced water < change in weight of the object?(1 vote) - so unlike the earlier strains(longitudinal strain & shear strain ) this one(bulk strain) is different right? because here instead of taking the difference of change, we are taking changed volume..so that's why we are adding minus here....am i right?(1 vote)
- sir will there be any change in area during compression of volume(1 vote)

## Video transcript

if you take a store and put it inside a container with water then you may already know that this water will start pushing on that stone in all directions like this and if you calculate this total force per unit area how much force is acting per unit area then we call this quantity we call this quantity as pressure pressure and in this video we're going to understand the effects of this pressure on materials all right so let's begin now instead of a stone if we imagine there was a balloon over here and was being compressed in all directions then I hope you'll agree with me that the balloon would just shrink in size well guess what our stone will do something very similar because of this force in all directions that stone is going to get compressed it's gonna shrink in size and of course the shrinking is going to be very microscopic and as a result of that we can't see with our naked eyes but it will be there so we could imagine that this stone shrinks in size like this as a result of this pressure now of course I've exaggerated over here in reality would be very tiny but it's there and now to resist this deformation our material is going to generate material is going to generate a restoring force which will oppose this so a restoring force will be produced in the opposite direction and if you calculate this total restoring force per unit area we'll call that as the bulk stress so the quantity over here is bulk stress and we've spoken about stress before in previous videos and we always define stress as the restoring force some kind of restoring force per unit area and we've spoken about this stress a lot in previous videos so if you need a refresher it would be great idea to go back and watch those videos first and then come back over here but we always define stress as some restoring force per unit area and if that restoring force acts in all the directions all the directions then we use the word bulk stress now when this is in equilibrium the restoring force the force from inside must be the same as the force from the outside right otherwise the material would never come in equilibrium and so we could say in equilibrium that both stress must be equal to pressure to pressure and as a result of this pressure notice the volume the volume of this material has decreased and so we are going to define another quantity called as bulk stream bulk stream and again as discussed before strain is a quantity which is usually defined as some change in dimension per unit dimension that's how we usually define stream and so over here since the wall you miss changing we could call this as the change in volume per unit volume per unit volume and now naturally if you increase this pressure more and more then the store will compress more and more and as a result the bulk strain would increase and the bulk stress would keep increasing so there must be a correlation between the bulk stress and the bulk strain right and that correlation is given by Hookes law Hookes law says that the BOK stress which is the same as pressure is proportional to bulk strain is proportional to bulk strain and we can now get rid of this proportionality and we'll say it's equal to I'm gonna put a constant here and that constant is the modulus of elasticity and the modulus of elasticity over here is called as be the bulk modulus so we call this as bulk modulus and notice since under pressure the volume of the stone is decreasing the Delta V is a negative number because the final volume is smaller than the initial volume and just to represent that usually we'll put a negative sign over here just telling us that the volume decreases when you put this stone under pressure all right let's talk a little bit more about this bulk modulus now let's start with its units notice just like any strain the bulk strain also is unitless which means the modulus B must have the same units as pressure and the units of pressure is Newton's per meter square or Pascal's so the bulk modulus also has the same units as Pascal's the next thing is what is bulk modulus tell us well if bulk modulus is very high the notice for the same strain a higher pressure is needed in other words higher the bulk modulus more difficulties or harder it is to compress that material so if you look at some examples from say this table we have some material over here and we have its bulk model I on the right hand side notice that steel has the very high bulk modulus compared to water and air steel B is being solid we would expect solids to have high bulk modulus because very hard to compress them on the other hand note is liquid has a little bit lower bulk modulus but still pretty high to Giga Pascal's Giga is 10 to the power 9 is still pretty high but not as high as solids but notice air which is a gas has a very low bulk modulus which means a much lower pressure is needed to compress air air is easily compressible it is also quite intuitive because if you take for example a plastic bottle which has just air inside it no water then it's very easy to crush that because air has a very low bulk modulus so notice lower the bulk modulus easier it is to compress something and therefore I hope you can see that the compressibility factor or how easy it is to compress something is actually immerse Li related to bulk modulus and it's for that reason we actually define something called compressibility come press ability and the name itself tells you what it is it's a number that tells you how easy it is to compress something and we define that as the reciprocal of the bulk modulus and so from that from the compressive three point of view air has a high value of compressibility and steel for example has a low value of compressibility now one material that usually pops to my head when we talk about bulk bulk stress and compressing is sponge right I mean think about it sponge they are very easily compressible in yet their solids I mean think about that solids usually have a high bulk modulus or low compressibility but sponge is an exception right I mean it's a solid and yet it can be easily compressed so it has a very very high compressibility why do you think that is well it turns out that sponge has a lot of holes so it has a lot of air pockets in between and it's because air is highly compressible this whole sponge ends up being highly compressible so the reason for that is it has a lot of trapped air inside