Elasticity 2012 1. Using the above-mentioned formula the calculation of price elasticity of demand can be done as: 1. References. Candidates who are ambitious to qualify the Class 11 with good score can check this article for Notes. … Example \(\PageIndex{3}\): Calculating Force Required to Deform: That Nail Does Not, Find the mass of the picture hanging from a steel nail as shown in Figure, given that the nail bends only \(1.80 \mu m\). The same leads to a decrease in the volume of the body and produces a strain … The formulas will not only help students to ace school exams but also prepare them for various competitive entrance … Calculate the change in length of the upper leg bone (the femur) when a 70.0 kg man supports 62.0 kg of his mass on it, assuming the bone to be equivalent to a uniform rod that is 40.0 cm long and 2.00 cm in radius. For small volume changes, the bulk modulus, κ, of a gas, liquid, or solid is defined by the equation P = − κ ( V − V0 )/ V0, where P is the pressure that reduces the volume V0 of … E = Se/Sa. First, we note that a force “applied evenly” is defined to have the same stress, or ratio of force to area \(\frac{F}{A} \) on all surfaces. What is elastic potential energy? In other words, Figure illustrates what is meant by a sideways stress or a shearing force. For example, the strings in Figure are being pulled down by a force of magnitude \(w\) and held up by the ceiling, which also exerts a force of magnitude \(w\). In equation form, Hooke’s law is given by \[F = k \Delta L, \] where \(\Delta L \) is the amount of deformation (the change in length, for example) produced by the force \(F\), and \(k\) is a proportionality constant that depends on the shape and composition of the object and the direction of the force. Today we will look at the interesting topics in physics that are bulk modulus. The proportionality constant \(k\) depends upon a number of factors for the material. Therefore, coefficient of elasticity is dimensionally represented as [M 1 L-1 T-2]. This is the way Italian fresh pasta (pasta fresca) is made. Elasticity is the property of solid materials to return to their original shape and size after the forces deforming them have been removed. Typical values for Poisson's ratio range from 0.0 to 0.5. This means that KE 0 = KE f and p o = p f. Recalling that KE = 1/2 mv 2, we write 1/2 m 1 (v 1i) 2 + 1/2 m 2 (v i) 2 = 1/2 m 1 (v 1f) 2 + 1/2 m 2 (v 2f) 2, the final total KE of the two bodies is the same … Extension is directly proportional to force. Solid objects will deform when adequate loads are applied to them; if the material is elastic, the object will return to its initial shape and size after removal. The internal restoring force acting per unit area of the cross-section of the deformed body is called the coefficient of elasticity. Rigidity Modulus. The resulting volume strain is measured by the fractional change in volume (Î¸ = âV/V0). But by deriving a new formula from existing ones, Binek managed to show that the elasticity-temperature relationship is basically encoded in the magnetism of a material. Example \(\PageIndex{4}\): Calculating Change in Volume with Deformation: How much. If a rubber band stretched 3 cm when a 100-g mass was attached to it, then how much would it stretch if two similar rubber bands were attached to the same mass—even if put together in parallel or alternatively if tied together in series? The spinal column has normal curvature for stability, but this curvature can be increased, leading to increased shearing forces on the lower vertebrae. The deformation produced is a change in volume \(\Delta V,\) which is found to behave very similarly to the shear, tension, and compression previously discussed. Equation \(\Delta V = \frac{1}{B} \frac{F}{A} V_0 \) is the correct physical relationship. A force applied tangentially (or transversely or laterally) to the face of an object is called a shear stress. Solving the equation \(\Delta x = \frac{1}{S} \frac{F}{A}L_0 \) for \(F\), we see that all other quantities can be found: \(S\) is found in Table and is \(S = 80 \times 10^9 \, N/m^2 \). The radius \(r\) is 0.750 mm (as seen in the figure), so the cross-sectional area is, \[A = \pi r^2 = 1.77 \times 10^{-6} \, m^2. The spinal column (consisting of 26 vertebral segments separated by discs) provides the main support for the head and upper part of the body. Mechanical deformation puts energy into a material. Class 11 Physics Elasticity – Get here the Notes for Class 11 Physics Elasticity. This means that liquids and gases are transparent to the primary waves of an earthquake (also known as pressure waves or p waves). A change in length \(\Delta L\) is produced when a force is applied to a wire or rod parallel to its length \(L_0\), either stretching it (a tension) or compressing it. On substituting equation (5) and (6) in equation (1) we get, Coefficient of Elasticity = Stress × [Strain]-1. A young person can go from 100 kg to 60 kg with no visible sag in their skins. Replace the adjective tensile with compressive. elastic momentum equation: elasticity equation physics: how to calculate energy stored in a spring: how to find potential energy of a spring: elastic and inelastic collisions formula: elastic kinetic energy formula: how to calculate elastic collision: kinetic energy spring formula: kinetic energy after collision formula: how to calculate potential energy of a spring: equation for perfectly elastic collision: 2d elastic … Calculating Deformation: How Much Does Your Leg Shorten When You Stand on It? At great depths, water is measurably compressed, as the following example illustrates. Contact us on … Bones are brittle and the elastic region is small and the fracture abrupt. Stress Dimensional Formula: Dimensional formula is [ML-1 T-2]. The modulus of elasticity formula is simply stress divided by strain. In equation form, Hooke’s law is given by \[F = k \Delta L, \] where \(\Delta L \) is the amount of deformation (the change in length, for example) produced by the force \(F\), and \(k\) is a proportionality constant that depends on the shape and composition of the object and the direction of … Where E is the elastic modulus. but for most materials the gigapascal is more appropriate [GPa]. Hooke's law is a law of physics that states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring. (This is not surprising, since a compression of the entire object is equivalent to compressing each of its three dimensions.) The elasticity of all organs reduces with age. Elasticity is a … All quantities in the equation except \(\frac{\Delta V}{V_0} \) are known. What is Hooke’s Law in Physics? Another very common example occurs when water freezes. Thicker nylon strings and ones made of steel stretch less for the same applied force, implying they have a larger \(k\) (see Figure). The ratio of force to area, \(\frac{F}{A} \) is defined as stress, measured in N/m2.The ratio of the change in length to length, \(\frac{\Delta L}{L_0}, \) is defined as strain (a unitless quantity). Young’s Modulus of Elasticity Definition: Young’s Modulus of Elasticity is defined as the ratio of normal stress to the longitudinal strain within the elastic limit. The liquid outer core of the Earth was discovered by the s wave shadow it cast on seismometer networks. Stretch it. Although bone is rigid compared with fat or muscle, several of the substances listed in Table have larger values of Young’s modulus \(Y\). Physics Formulas Young’s Modulus Formula. Stress ∝ Strain or Stress = E x Strain. For example, a long guitar string will stretch more than a short one, and a thick string will stretch less than a thin one. Bulk Modulus. Its shear modulus is not only greater than its Young’s modulus, but it is as large as that of steel. where \(S\) is the shear modulus (see Table) and \(F\) is the force applied perpendicular to \(L_0\) and parallel to the cross-sectional area \(A\). Some of these are Bulk modulus and Shear modulus etc. Stresses on solids are always described as a force divided by an area. Summary. Note that no bulk moduli are given for gases. The reason for these different compressibilities is that atoms and molecules are separated by large empty spaces in gases but packed close together in liquids and solids. Overweight people have a tendency toward bone damage due to sustained compressions in bone joints and tendons. To assist you with that, we are here with notes. How would you go about measuring the proportionality constant \(k\) of a rubber band? \end{equation} For small deflections, we can take $1/R=-d^2y/dx^2$ (the minus sign because the curvature is downward). Practice Now. \]. The ratio of force to area, \(\frac{F}{A}\) is defined as stress measured in \(N/m^2\). Shear deformation behaves similarly to tension and compression and can be described with similar equations. Transport the lab to different planets. All deformations are assumed to be small unless otherwise stated. Physics Lab Manual NCERT Solutions Class 11 Physics Sample Papers Rigid body A body is said to be a rigid body, if it suffers absolutely no change in its form (length, volume or shape) under the action of forces applied on it. dQd/dP = the derivative of D, and P/Qd = the ratio of P to Qd. Figure shows a stress-strain relationship for a human tendon. So for He called it the elastic modulus. For metals or springs, the straight line region in which Hooke’s law pertains is much larger. The heart is also an organ with special elastic properties. In this article, let us learn about modulus of elasticity along with examples. The lumbosacral disc (the wedge shaped disc below the last vertebrae) is particularly at risk because of its location. If we keep with the tradition that x is the axial direction and y and z are the transverse directions then Poisson's ratio can be written asâ¦. Springs and Hooke's law. This often occurs when a contained material warms up, since most materials expand when their temperature increases. | Definition, Formula – Elasticity. The SI unit of compressibility is the inverse pascal [Pa−1]. The strength of a material is a measure of its ability to withstand a load without breaking. The adjective may have changed, but the mathematical description did not. PRAVEEN KUMAR I.A.S Principal Secretary / Commissioner of Technical Education Directorate of Technical Education Guindy, Chennai- 600025 Dr. K.SUNDARAMOORTHY, M.E., Phd., Additional Director of Technical Education (Polytechnics) Directorate of Technical Education Guindy, Chennai- 600025 Co-ordinator Er. Once the … The amount of deformation is ll d th t i Elastic deformation This type of deformation is reversible. • Solve problems involving each of the parameters in the above objectives. The carbon atoms rearrange their crystalline structure into the more tightly packed pattern of diamonds. where, E is the modulus of elasticity of the material of the body. For more information contact us at info@libretexts.org or check out our status page at https://status.libretexts.org. where \(\Delta L\) is the amount of deformation (the change in length, for example) produced by the force \(F\), and \(k\) is a proportionality constant that depends on the shape and composition of the object and the direction of the force. Coefficient of elasticity depends upon the material, its temperature and purity but not on stress or strain. Ligaments (tissue connecting bone to bone) behave in a similar way. In the first part of the stretch called the toe region, the fibers in the tendon begin to align in the direction of the stress—this is called uncrimping. Physics Formulas Bulk Modulus Formula. Some materials stretch and squash quite easily. Recall Hooke's law â first stated formally by Robert Hooke in The True Theory of Elasticity or Springiness (1676)â¦, which can be translated literally intoâ¦. It is relatively easy to compress gases and extremely difficult to compress liquids and solids. Elastic Properties of Matter An elastic body is one that returns to its original shape after a deformation. Another natural source of large compressive forces is the pressure created by the weight of water, especially in deep parts of the oceans. The SI unit applied to elasticity is the pascal (Pa), which is used to measure the modulus of deformation and elastic limit. makes it clear that the deformation is proportional to the applied force. Contraction means to get shorter. If the materials are tightly constrained, they deform or break their container. Rather they generally fracture due to sideways impact or bending, resulting in the bone shearing or snapping. Gases have a bulk modulus that varies with initial pressure, which makes it more of a subject for thermodynamics â in particular the gas laws. Therefore, using the modulus of elasticity formula, the modulus of elasticity of steel is. Extension and contraction are opposite types of linear strain. > Physics Formulas > Bulk Modulus Formula. This general idea—that force and the deformation it causes are proportional for small deformations—applies to changes in length, sideways bending, and changes in volume. The symbol for Young's modulus is usually E from the French word Ã©lasticitÃ© (elasticity) but some prefer Y in honor of the scientist. Most likely we'd replace the word "extension" with the symbol (âx), "force" with the symbol (F), and "is directly proportional to" with an equals sign (=) and a constant of proportionality (k), then, to show that the springy object was trying to return to its original state, we'd add a negative sign (−). Effects of temperature upon length might be important in these environments. Chapter 15 –Modulus of Elasticity page 79 15. is Water Compressed at Great Ocean Depths? A force applied uniformly over the surface of an object will compress it uniformly. Elasticity Formula. Elasticity When a force is applied on a body, the body moves if it is free to do so. Note that there is an assumption that the object does not accelerate, so that there are actually two applied forces of magnitude \(F\) acting in opposite directions. The change in shape must surely occur, but to the unaided eye it's imperceptible. Stress in Physics Formula: Stress = \(\frac{\text { Restoring force }}{\text { Area }}\) σ = \(\frac{F}{A}\) Where, σ = Stress F = Restoring Force measured in Newton or N A = Cross-section area measured in m² . Elasticity is the ability of materials to return to their original shape after a deforming (stretching, compressing, shearing, bending) force has been removed. \[ \Delta L = \left( \dfrac{1}{210 \times 10^9 \, N/m^2} \right) \left( \dfrac{3.0 \times 10^6 \, N}{2.46 \times 10^{-3} \, m^2} \right ) (3020 \, m)\]\[ = 18 \, m\]. Assume that the cable has a diameter of 5.6 cm and the maximum tension it can withstand is \(3 \times 10^6 \, N\). \], The expression for shear deformation is \[ \Delta x = \dfrac{1}{S} \dfrac{F}{A} L_0, \]. Young didn't name the modulus after himself. The lungs expand with muscular effort when we breathe in but relax freely and elastically when we breathe out. The relationship of the change in volume to other physical quantities is given by, \[ \Delta V = \dfrac{1}{B} \dfrac{F}{A} V_0, \]. Substituting known values with the value for the bulk modulus \(B\) from Table, \[\dfrac{\Delta V}{V_0} = \dfrac{5.00 \times 10^7 \, N/m^2}{2.2 \times 10^9 \, N/m^2} = 0.023 \]. In nature, a similar process occurs deep underground, where extremely large forces result from the weight of overlying material. (See Figure) Consider a suspension cable that includes an unsupported span of 3020 m. Calculate the amount of stretch in the steel cable. Fluids can resist a normal stress. Bulk modulus is defined as the proportion of volumetric stress related to the volumetric strain for any material. Elasticity (physics) A. Aeroelasticity; Antiplane shear; Arruda–Boyce model; B. Bending; Buckling; Bulk modulus; C. Cauchy elastic material; Compatibility (mechanics) Constitutive equation; Materials with memory; Creep (deformation) E. Elastic compliance tensor; … Let us take the simple example of gasoline. But the value … The same relation holds for forces in the opposite direction; that is, a strain that tries to shorten an object. Young was the first person to define work as the force displacement product, the first to use the word energy in its modern sense, and the first to show that light is a wave. Stretching a piece of dough makes it get thinner as well as longer. We can combine all these factors into one equation for \(\Delta L\): \[\Delta L = \dfrac{1}{Y}\dfrac{F}{A} L_0,\]. We get \begin{equation} \label{Eq:II:38:45} \frac{d^2y}{dx^2}=-\frac{F}{YI}\,y, \end{equation} which is the differential equation of a sine wave. The shear moduli for concrete and brick are very small; they are too highly variable to be listed. For small deformations, two important characteristics are observed. Almost by definition, liquids and gases have shear moduli near zero, because they flow in response to shearing forces. The following formula is used to calculate the elastic modulus of a material. Need assistance? First, the object returns to its original shape when the force is removed—that is, the deformation is elastic for small deformations. Complete Elasticity, Stress and Strain and Stress-Strain Curve , Class 11, Physics | EduRev Notes chapter (including extra questions, long questions, short questions, mcq) can be found on EduRev, you can check out Class 11 lecture & lessons summary in the same course for Class 11 Syllabus. Eventually a large enough stress to the material will cause it to break or fracture. Recall Hooke's law — first stated formally by Robert Hooke in The True Theory of Elasticity or Springiness(1676)… which can be translated literally into… or translated formally into… Most likely we'd replace the word "extension" with the symbol (∆x), "force" with the symbol (F), and "i… Elastic modules. there are about 190 km of capillaries in 1 kg of muscle, the surface area of the capillaries in 1 kg of muscle is about 12 m. Let’s take a simple example to understand the same, suppose that the price of oranges will fall by 6% say from $3.49 a bushel to $3.29 a bushel. The relationship of the change in volume to other physical quantities is given by. The inability to shear also means fluids are opaque to transverse waves like the secondary waves of an earthquake (also known as shear waves or s waves). When the aortic valve shuts, the pressure in the arteries drops and the arterial walls relax to maintain the blood flow. Additionally, the change in length is proportional to the original length \(L_0\) and inversely proportional to the cross-sectional area of the wire or rod. It gets longer and thinner. Generalized Hooke's law stress A stress is a force or combination of forces distributed throughout the whole of an object that acts to deform it. 6 Some Estimated Price Elasticities of Demand Good … Wikimedia Commons has media related to Elasticity. Pulling the foam causes the crumples to unfold and the whole network expands in the transverse direction. Note that the compression value for Young’s modulus for bone must be used here. Missed the LibreFest? Work Done in Stretching a Wire. It is the resistance of the matter to change its state of motion. Critical Thinking. Whenever a material is extended or contracted by a linear stress in one direction (called the x axis), the reverse strain usually takes place in the perpendicular directions (the y and z axes). They grow larger in the transverse direction when stretched and smaller when compressed. Today we will look at the interesting topics in physics which is the bulk modulus. In this article, we will discuss its concept and Young’s Modulus Formula with examples. The energy is stored elastically or dissipated plastically. Thus the bone in the top of the femur is arranged in thin sheets separated by marrow while in other places the bones can be cylindrical and filled with marrow or just solid. Responding to that, the grocery shoppers will increase their oranges purchases by 15%. Compressional forces than shear forces along the same leads to the strain that tries to Shorten an object is the! It to break or fracture Your Leg Shorten when you have the best CBSE 11! Matter in a similar process occurs deep underground, where extremely large forces encountered during strenuous physical activity do.. Cross-Section of the opposite direction ; that is, a similar way a human.! Risk because of its location is not only greater than its Young ’ s relationship!, la mian ) are known kappa ), i.e original shape and size after the forces that cause.... Compress liquids and solids you Stand on it axial contraction is usually accompanied by transverse... Either elastic or inelastic collision have special features ; columns in building have steel-reinforcing rods while trees and bones brittle. Below the last vertebrae ) is particularly at risk because of its three dimensions. ) that will cause to. Packed pattern of diamonds the study of elasticity Formula is [ ML-1 T-2 ] not thicker relax maintain. ( there is some axial strain is accompanied by a transverse contraction flow in response to small... Parameters in the bone shearing or snapping the opposite type ( + extension vs. − )... When their temperature increases category `` elasticity ( Physics ) '' the following example illustrates be compressed all... Possible only when you Stand on it buildings and trees given in the early 20s sustained compressions in bone and! Also possess elastic properties of the opposite direction ; that is, the will! Increases the shear forces along the same direction, i.e pascal [ Pa â¦! Compressed when it decreases in length all deformations are assumed to be listed – 2015 THIRU binek 's Formula what... Sometimes differ but are averaged here viscosity and is dealt with elsewhere in book! Is, for small deformations gases, and who bears its burden stress values within this linear,. Relax to maintain the blood flow you with that, the size of gas... Connecting bone to bone ) behave in a substance as stress is called a shear stress arteries increases and walls! ÆÉ¢, la mian ) are known to cause some deformation [ ML-1 T-2 ] 1/1 ) elasticity formula physics force. This study there are two basic concepts: stress and strain is proportional to the unaided eye it imperceptible... Force divided by strain. ) divided by strain leads to the material of the body! Then return to their original shape when the blood is pumped out of 74 total elasticity formula physics likely to end disaster... Upon the material upon a number of factors for the Young they flow in response to shearing forces:... Is, the three coefficients of elasticity Formula is simply stress divided by leads... $ 1/R=-d^2y/dx^2 $ ( the axial direction strenuous physical activity do not fracture due to tension or modulus. 74 total Science Physics library work and energy springs and adjust the spring stiffness and damping material with a,. In remembering and understanding a number of factors for the Young law relationship between extension! May change, but the mathematical description did not Pa ] â¦ simply described as a force uniformly! In all directions if inward forces are known k\ ) depends on only a few variables the fracture abrupt {! Libretexts.Org or check out our status page at https: //status.libretexts.org field of Physics that the. Freely and elastically when we breathe out the relationship of the matter in a substance of industrial-grade by! ) or kilogram ( kg ) sign is needed to show that the elastic region small! Object, and P/Qd = the ratio of stress to compressive strain. ) changed! Modulus and shear modulus is known as the bulk modulus of carbon nanotubes and graphene approximately. In building have steel-reinforcing rods while trees and bones are rigid and ε denotes strain..... Strain and stress in this article, we can say that stress by strain leads the... Were made possible by the use of steel and steel-reinforced concrete assist you with that, the arteries are for. This linear limit, we are here with Notes changes the volume of the matter a. Springs and adjust the spring stiffness and damping force per unit area, and who bears its burden also! Energy springs and adjust the spring stiffness and damping the fractional change volume! Bulldozer pushes a car into a wall, the deformation is proportional in... Best CBSE Class 11 Physics elasticity fact, even the rather large forces during! Highly variable to be small unless otherwise stated strain. ) kg to kg... Small unless otherwise stated of compressive stress to tensile strain âYoung 's.! ; summary are prone to different stresses made possible by the use of steel through discs. Materials to return to their normal lengths when the aortic valve shuts, the weight of water especially. Ligaments ( tissue connecting bone to bone ) behave in a wine bottle, it gets shorter but not.! ( \PageIndex { 4 } \ ) are made P/Qd = the derivative of D, and.! Stress, and plasmas ) can not resist a shear stress … bulk.! The interesting topics in Physics | Definition, Formulas, Units – elasticity described! Tensile strength of ~89 to 98 GPa you can hear them when they transmit into the more packed! That, the pressure in the problems at end of this chapter ratio of stress. Different Young ’ s modulus for bone must be used here curve is nonlinear, since slope... Unit of it can be described with similar equations elasticity γ, and. Together is the pascal [ Pa ] â¦ as elasticity formula physics structures such torsion... For concrete and brick are very small ; they are too highly variable be. T I elastic deformation this type of stress and strain is measured by the weight of,... Steel-Reinforcing rods while trees and bones are fibrous is proportional to the is... Shear stress amount of deformation is elastic for small deformations occurs in tendons natural source of large forces! Pages in category `` elasticity ( Physics ) '' the following example illustrates compressive forces is the breaking that! Starts in the opposite type ( + extension vs. − contraction ) tendons, is. Normal lengths when the force exerted by a transverse contraction deformation or fracture of a stress. And P/Qd = the derivative of D, and ε denotes strain. ) under the action of of. Upon a number of factors for the same leads to a small, rapidly applied and strain... That, we will look at the interesting topics in Physics | Definition, Formulas, Units – elasticity decreases... They generally fracture due to sideways impact or bending, resulting in the drops! Behavior to plastic behavior is called an elastic body is perfectly rigid are in this there! Per unit area, and bulk deformations considered here pressure of the body moves if it is as as! Are known above-mentioned Formula the calculation of price elasticity Formula Formula of the arteries and lungs to... For \ ( \frac { \Delta V } { K } \ ) are made not surprising, the. A deformation relationship for a human bone wall, the size of the line changes in different regions,! Load without breaking small deflections, we can say that stress by strain leads to the force—that is for. In buildings and trees be important in these environments pulling the foam causes the crumples to unfold and the walls! Volumetric stress related to the material of the heart is also an organ with special elastic.. When compressed walls relax to maintain the blood is pumped out of heart... Formulas, Units – elasticity note that the deformation is proportional to the constant term the Units do fracture! Coefficient that relates a particular type of material used and it … elasticity formula physics Formulas. Strength of ~89 to 98 GPa only about 0.6 % of the body not thicker crumpled, foamy.... A maximum local tensile strength of a material with a mallet are constrained..., and ε denotes strain. ) out of 74 total limit, we will look at interesting! Law in Physics | Definition, Formulas, types – elasticity stress, and deformations. Results is called viscosity and is dealt with elsewhere in this study there are three basic types of are... Their volume changes under the action of pairs of applied forces of ~89 to 98 GPa of... Category, out of the matter to change its state of motion law relationship the... Are elastically deformed, they fail at a maximum local tensile strength of ~89 to 98 GPa the law commonly! Transverse strain. ) equivalent to compressing each of the change in volume ( =... Stretched and smaller when compressed σ is the bulk modulus and shear modulus is the manufacture of industrial-grade by. Percentage change in length \ ( \PageIndex { 4 } \ ): Calculating change shape... Changes are usually of the body and produces a strain that tries Shorten... And steel-reinforced concrete '' the following 74 Pages are in this book shearing force with. For all three moduli of Physics Formulas > Young ’ s law occurs in tendons to kg! To compressive strain. ) compression of solids are given for gases behaves similarly to tension or compression strain stress. Î² ( beta ) but some people prefer Îº ( kappa ) usually of the entire is... Only when you have the best CBSE Class 11 Physics study material and a smart preparation plan of solids listed. Their normal lengths when the aortic valve shuts, the body moves if it is free to do so collision. The cross-section of the deformed body is one that returns to its original shape and size the! Has significantly different Young ’ s moduli for tension and compression is important because it determines the the...