PROPERTIES OF BULK MATTERS

SOLIDS:  In order to meet our daily requirements , It becomes necessary to have a study of the materials around as such as steel,Alloys , Ceramics etc. eg why springs are made of steels , Mugs are made of clay and cooking utensils are made of alloys ? Thus we require a study of materials of which solids are made .

ELASTICITY: Whenever a force is applied to change the shape of a body , if the distance between any  two particles of it remains unchanged , the body is called a rigid body  . No  body is perfectly rigid if the deforming force is large enough. Bodies are either Elastic or Plastic  The property of a body by virtue of which the body regains its original shape after the removal of deforming force is called Elasticity. The bodies which shows the property of elasticity  are called Elastic bodies . example are rubber, steel , glass , etc . The nearest approach to elastic body is quartz .
The property of a body by virtue of which the body doesnot regains its original shape after the removal  of the deforming force is called Plasticity . The bodies which shows the property are called plastic bodies . Nearest approach to a plastic body is putty .

STRESS:  When a deforming force acts on a body , relative displacement of it force occurs . Due to elastic forces among the molecules of the solid , the body has a tendancy to regain its original state . this internal or restoring force per unit area , set up inside the body is called Stress . It is equal and opposite to the deforming force and is measured in terms of external force . Thus Stress = F/A

 F = force in newtons (N)
A = cross-sectional area in m²

SI Unit   =  Nm^-2 or pascals (Pa)

        It is of four types : 

1. Tensile stress : It is the restoring force per unit area of the deforming body when the length of the body increases in the direction of deforming force. This is also called Longitudinal Stress .
2. Compressional Stress ; It is the restoring force per unit area of the deformed body when the length of the body increases in the direction of applied force . 
3. Tangential  or Shearing Stress : If the deforming force acts tangentially over a certain area , then the body gets sheared through a certain angle , such a stress is called Shearing or Tangential Stress . 
4. Hydro-static Stress : If the body is subjected to a uniform deformation from all sides . then the stress is called Hydro-static Stress .  

STRAIN:  It is measured as the ratio of change produced in some measure or configuration . It is denoted by E (Read as Epsilon ) . It is just a ratio and has no units . It is of three types :

1. Tensile :/Longitudinal / Linear Strain:  It is produced when the deforming force producing change in length . It is defined as ratio of change in length to the original length L .
   
2. Bulk/Volumetric Strain :  It is defined as the ratio of change in volume to the total volume . Thus E= 🔺V/V .
3. Shearing Strain : It is defined as the ratio of the relative displacement of one of its plane to its distance from the fixed plane or it is defined as the angle through which the line originally perpendicular  to the fixed force has turned . This is also called angle of shear .

MODULUS OR COEFFICIENT OF ELASTICITY :   The ratio of stress to strain is called coefficient of elasticity . Pertaining to three types of strains , there are three types of elasticity .

1. Longitudinal or Young's Modulus Of Elasticity  : It is the ratio of tensile stress to the longitudinal strain .Consider a wire of length L and having an area of cross - section A . Let the wire be elongated by length 🔺L  , when stretched by a force F . Thus Tensile stress F.L/A.🔺L 
2.  Volume / Bulk Modulus of Elasticity : It is defined as the ratio of stress to the volumetric strain . Consider  a cube ( or a sphere ) of volume V and Let a force F acts normal to each face . Let 🔺v be the change in volume . Thus Stress = F/A where A is the area of the surface on which force F acts . Volumetric strain = F.V/🔺V. A .     The reciprocal of the Bulk Modulus is called Compressibility K . 
3. Shear Modulus or Modulus of Rigidity : It  is the ratio of Tangential stress to shearing strain . Consider a cube with its lower face fixed on a surface . Apply a force F  Tangential to the vertical face such that each face of cube gets sheared / shifted parallel toward its base . thus the Modulus of The Rigidity = F.L/A.🔺L . 

HOOKS LAW  : "Within elastic limits , Extension is proportional to tension " It means that the change in length as a result of the deforming force is directly proportional to  the deforming force . This Law is true if the Deformation produced is less . The law is true for streching , Compression , Bending , Twisting , etc .

FLUIDS : Pressure exerted by Liquid column : - Consider a liquid contained in  a vessel up-to  height h . Let  ρ be the density of liquid and A be the area of cross section at the base .  Thus Pressure exerted by the liquid column at the base = Force / Area = mg/A = Ah ρ g /A   = P= hg ρ 

PASCAL'S LAW  : Whenever pressure is applied to the free surface of a liquid , it gets transmitted equally in all directions , provided the effect of gravity is neglected or it states that " Idf the effect of Gravity is neglected , then the pressure at every part of the liquid in static equation is same . 

proof : Consider a right circular cylinder BC of area  of cross section A lying inside a vessel containing a liquid . The liquid inside the cylinder is in Equilibrium inside the action of force exerted liquid outside the cylinder . These forces are acting Everywhere normal to the surface of the cylinder . if F1 & F2 are the forces  acting on the faces B and C and P1 and P2  are the pressure . 

Exerted on the faces respectively then F1 = P1A and F2 = P2A
since the liquid is in equilibrium F1=F2
P1A = P2A   = P1 = P2 .

Application of Pascal's law : 

1. Hydraulic lift 
2. Hydraulic brakes 
3. Hydraulic press