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Could you show the derivation of elastic strain energy per unit volume?
Wiki User
∙ 12y ago
U= vol metric integral1/2(stress* strain)dxdydz
Wiki User
∙ 12y ago
The elastic strain energy per unit volume, also known as the strain energy density, can be derived by integrating the stress-strain curve over the strain range. The area under the stress-strain curve represents the work done on the material, which is equivalent to the strain energy stored. By dividing this strain energy by the volume of the material, the strain energy density per unit volume can be obtained.
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Why gas molecules are elastic?
Gas molecules are elastic because they possess kinetic energy, allowing them to move and collide with other molecules. When gas molecules collide with each other or with the walls of their container, they transfer energy back and forth, resulting in elastic collisions that maintain constant pressure and volume within the gas.
Why gas molecules are perfectly elastic?
Gas molecules are perfectly elastic because they do not lose any kinetic energy when they collide with each other or the walls of their container. This means that their total energy remains constant, leading to elastic collisions. Additionally, gas molecules are considered point masses with negligible volume, contributing to their elastic behavior.
Cohensive energy derivation?
Cohesive energy is the energy required to completely separate a solid into its individual atoms or molecules. It is a measure of the strength of the intermolecular forces holding the solid together and is related to the bond strength between the atoms or molecules in the solid. Cohesive energy is typically expressed in units of energy per mole or energy per unit volume.
What causes rocks to undergo stress?
Stress is the force per area, which has the same units as pressure. An elastic material's response to stress is called the strain which is the change in its dimensions divided by its original dimension, such as a change in length divided by length, or change in volume divided by volume. It is a fundamental law that the stress is proportional to the strain, with the proportionality constant being the elastic modulus of the material, Young's modulus for change in length or the the compressibility for change in volume. For shear forces, the modulus is called the shear modulus and the strain is the deformation in the direction of the force divided by the distance from the fixed base that the forces is exerted.
Assumption of kinetic theory of gas?
The volume occupied by gas molecules is negligible when compared to volume occupied by the gas.The collisions between gas molecules-gas molecules and gas molecules-walls of the container are perfectly elastic.
What is strain energy due to torsion?
Strain energy due to torsion is the energy stored in a material when it is twisted under a torque load. It is calculated as the integral of shear stress and strain over the volume of the material. This energy represents the ability of the material to deform plastically under torsional loading.
What are the derivation of volume of solid figures?
area
Is defined as ratio of uniform stress to volume strain?
is defined as ratio of uniform stress to volume strain
Show the derivation of the formula of the volume of a cube?
Volume=lbh in a cube,l=b=h therefore,volume=a^3
What is the derivation of the formulae of the volume of the cube?
The volume of a cube is V = x3. The derivative of this is (d/dV)x = 3x2.
What is the derivation of the formula of the volume of a cube?
The volume of a cube is V = x3. The derivative of this is (d/dV)x = 3x2.
How do you find modulus of resilience?
Resilience is the ability of a material to absorb energy when it is deformed elastically, and release that energy upon unloading. The modulus of resilience is defined as the maximum energy that can be absorbed per unit volume without creating a permanent distortion.It can be calculated by integrating the stress-strain curve from zero to the elastic limit. In uniaxial tension,whereUr is the modulus of resilience,σy is the yield strength,andE is the Young's modulus.
Why gas molecules are elastic?
Gas molecules are elastic because they possess kinetic energy, allowing them to move and collide with other molecules. When gas molecules collide with each other or with the walls of their container, they transfer energy back and forth, resulting in elastic collisions that maintain constant pressure and volume within the gas.
Why gas molecules are perfectly elastic?
Gas molecules are perfectly elastic because they do not lose any kinetic energy when they collide with each other or the walls of their container. This means that their total energy remains constant, leading to elastic collisions. Additionally, gas molecules are considered point masses with negligible volume, contributing to their elastic behavior.
What is the derivation of the formula for volume and total surface area of a cylinder?
Volume = Пr2h Area = 2Пr2+2Пrh (where r=radius of base, h=height of cylinder)
Does the volume of beaker depend on the vapor pressure?
No. The volume remains the same unless the material from which it is made is flexible and elastic
What is proof Stress for Steel?
proof stress can be found by referring to the stress/strain curve at the point where strain is = 0.2% original volume (the material has grown 0.2% in volume) proof stress will be given as a measurement of energy (MPa,KPa etc.) as it specifically refers to the amount of energy required to stress the material to 0.2% its original volume.
