Tiêu đề 9.Mechanical Properties of Solids-F.pdf ✅

1 | P a g e NEET-2022 Ultimate Crash Course PHYSICS Mechanical Properties of Solids
2 | P a g e POINTS TO REMEMBER 1. Y is a measure of stiffness of a solid material 2. Y is typically used to characterise a rod or a wire stressed under either tension or compression 3. Y is of great importance in engineering as its value is one of the pieces of information which must be known to calculate accurately the deformations that will occur in a loaded structure or its parts. 4. Bulk modulus (B) of a material measures its tendency to recover its original volume, i.e., it is a measure of Incompressibility of the body. 5. The reciprocal of bulk modulus, i.e., 1 B is called the compressibility of the body, i.e., compressibility 1 /  = = −  V V B P Thus, compressibility is defined as the fractional decrease in volume per unit increase in pressure. 6. In case of gases, B is of two types isothermal elasticity (or isothermal bulk modulus), Bi and adiabatic elasticity an adiabatic bulk modulus) B a . Further, B P i = and B P a =  . Here, P is the pressure of the gas and 7 is the ratio of the two specific heats of a gas. Clearly, = a i B B  . We shall learn in that it is B a which controls the speed of sound in a gaseous medium. 7. A solid opposes both change of shape and volume and as such it possesses both volume elasticity (B) and elasticity of shape (  ). Solids also possess elasticity in length (Y) since they have the ability to resist longitudinal elongation and compression. Thus, solids possess all the three moduli of elasticity. 8. A liquid offers no permanent resistance to shear stress but offers great resistance to forces tending to decrease its volume. Accordingly, it possesses only volume elasticity (B). 9. A gas, like a liquid, offers no permanent resistance to shear stress but offers only a small resistance to forces tending to decrease its volume. Accordingly, it possesses only volume elasticity (B) and that too to a very small extent. 10. Gases are least elastic and solids are the most elastic while the elasticity of liquids is in between the two. 11. It should be noted that the three elastic moduli (Y, K and  ) are not independent. When one analyses a wave travelling through an elastic media,  is a convenient parameter to relate these three moduli. 12. The relations between Y, K,  and  are as follows. (i) Y = + 2 1   ( ) (ii) Y K = − 3 1 2 (  ) (iii) 9 3 = + K Y K   (iv) 3 2 6 2 − = + K K    13. (a) If Hooke's law is obeyed (that is the proportional limit is not reached), the material is said to deform elastically. The energy stored is recovered on removing the load. In this case, the strain is typically less than 0.5% for metals. (b) In plastic deformation, the energy is converted into heat. 14. Ductile materials show a large amount of plastic deformation. 15. Brittle materials fracture at low strains, close to their elastic limits. 16. Metals and glass have high Young's modulus and low elastic strain. 17. Plastics have lower Young modulus (less stiff), large elongation and do not obey Hooke's law like metals do. 18. The behaviour described by Hooke's law makes it possible for deformed bodies to vibrate with SHM. 19. Loss of strength by a material due to repeated stresses is called elastic fatigue. 20. Young's modulus of a material is numerically equal to the stress required to double the length of a wire of this material. 21. Longitudinal strain (L L/ ) can often be measured conveniently with a strain gauge which can be attached to an operating machinery. 22. Although Y may be almost the same for both tension and compression, the ultimate strength may be different for the two cases. For example, concrete is very strong in compression but so weak in tension that it is almost never used in this way in engineering, practice. 23. With the rise in temperature, Y. B and  all decrease.
3 | P a g e •11- 24. The compressibilities of solids are extremely small (of the order of 11 1 10− − Pa ). 25. A material is easily compressed if it has a small bulk modulus. 26. (a) Bulk modulus corresponds to change of pressure and it involves change of size but not shape. (b) Shear modulus corresponds to tangential (shear stress) and involves change of shape but not size. (c) Young's modulus corresponds to tensile or compressive stress and usually involves both change in size and shape. 27. For a rigid body,  =  = L V 0, 0,  (angle of strain) = 0 and accordingly Y = B =  = , which implies that the elasticity of a rigid body is infinite. 28. Shear stresses play a critical role in shafts that rotate under load, in bone fracture caused by Misting and in springs. 29. Whereas Y and  exist only for solids, B exists for all the three states of matter. Y and  do not exist for fluids since these can neither be deformed in one dimension (i.e., cannot sustain tensile stress) nor can sustain shearing stress. 30. Whereas 1/B is called compressibility, 1/  is called shear coefficient. 31. Poisson's ratio is not a modulus of elasticity as it is the ratio of two strains and not of a stress to a strain. All the four (Y, B, or  ) are collectively referred to as the elastic constants. 32. As Y = + 2 1   ( ) and a is of the order of unity, the quantities Y and g have approximately the same order of magnitude. SOME IMPORTANT FORMULAE 1.  = L L longitudinal strain where  L represents the change in length and L is the original length 2.  = V V volume strain where  V is the change in volume and V is the original volume 3.  = = x L  shearing strain where  is the angle through which a line originally perpendicular to the body turns when it is sheared, x is the horizontal distance the sheared face moves and L is the height of the body. 4. = F A stress where F is the force acting on an area A. 5. stress E strain = where E is called the coefficient or modulus of elasticity. 6. F / A FL Y L / L A L = =   where Y is the Young's modulus of elasticity of a wire (or a rod), F/ A represents tensile stress and L / L is the longitudinal strain 7. P P.V B V / V V   = = −  where B is the bulk modulus of elasticity, P is change pressure and V / V is the corresponding volume strain 8. / / = = =   T F A FL x L A x   where  is the shear modulus or modulus of rigidity, T is the tangential stress and  is the corresponding shed strain. 9. / / − =  D D L L 
4 | P a g e where a is the Poisson's ratio, D D/ and L L/ denote lateral strain and longitudinal strain respectively 10. ( ) ( ) ( )( )( ) 2 1 1 / / 2 2 2  = =   =  YA L U F L F A L L AL L ( ) ( ) ( ) 1 stress F / A strain L / L volume V 2 =     where U is the elastic potential enemy of a wire of length L and cross-sectional area A which undergoes an extension L when subjected to a force F. 11. U 1 u stress strain V 2 = =  ; Where u is the elastic potential energy density. Topic-wise analysis of NEET 2014-2021 Topic name/ year 2014 2015 2016 2017 2018 2019 2019 (Orissa) 2020 2020 (covid-19) 2021 T1: Hooke's Law and Young's Modulus 1 1 1 1 1 T2 : Bulk & Rigidit y Modulus and Work Done in Stretching a Wire 1 1 1 1 NEET Previous Years at a Glance 1. Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by  on applying a force F, how much force is needed to stretch the second wire by the same amount? [2018] (a) 9 F (b) 6 F (c) F (d) 4 F 2. The bulk modulus of a spherical object is 'B'. If it is subjected to uniform pressure 'p', the fractional decrease in radius is [2017] (a) B 3p (b) 3p B (c) p 3B (d) p B 3. The approximate depth of an ocean is 2700 m. The compressibility of water is 45.4 × 10–11 Pa–1 and density of water is 103 kg/m3 .What fractional compression of water will be obtained at the bottom of the ocean ? [2015] (a) 1.0 × 10–2 (b) 1.2 × 10–2 (c) 1.4 × 10–2 (d) 0.8 × 10–2 4. The Young's modulus of steel is twice that of brass. Two wires of same length and of same area of cross section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weights added to the steel and brass wires must be in the ratio of : [2015] (a) 2 : 1 (b) 4 : 1 (c) 1 : 1 (d) 1 : 2 5. Copper of fixed volume ‘V; is drawn into wire of length ‘l’. When this wire is subjected to a constant force ‘F’, the extension produced in the wire is ‘Dl’. Which of the following graphs is a straight line? [2014] (a) l versus 1 l (b) l versus 2 l (c) l versus 2 1 l (d) l versus l 6. When a block of mass M is suspended by a long wire of length L, the length of the wire become (L+l). The elastic potential energy stored in the extended wire is :- [NEET–2019] (1) Mgl (2) MgL (3) 1 2 Mgl (4) 1 2 MgL 7. An object kept in a large room having air temperature of 25°C takes 12 minutes to cool from 80°C to 70°C. The time taken to cool for the same object from 70°C to 60°C would be nearly :- [NEET – 2019 ODISSA] (1) 10 min (2) 12 min (3) 20 min (4) 15 min