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Define the terms deforming force, elasticity and plasticity. What are perfectly elastic and perfectly plastic bodies? Give examples.
Deforming Force: A deforming force is any force applied on the outside to change the shape or size of a material. Such forces can result in either elastic or plastic deformation depending on the intensity of the applied force and material characteristics. Deforming forces can occur from tension, comRead more
Deforming Force: A deforming force is any force applied on the outside to change the shape or size of a material. Such forces can result in either elastic or plastic deformation depending on the intensity of the applied force and material characteristics. Deforming forces can occur from tension, compression, shear, or torsion.
Elasticity:
Elasticity refers to a material’s ability to regain its original shape and size after removal of the applied deforming force. Some materials exhibit this so that they can be deformable in a temporary manner while characteristically, stress and strain are directly proportional within the elastic limit. Restoration to the original state is made possible by interatomic forces.
Plasticity:
Plasticity is the ability of a material to undergo permanent deformation once it has been subjected to a deforming force greater than its elastic limit. Once the force is removed, the material will not return to its original shape and will have altered its structure. Plastic behavior is characterized by a lack of proportionality between stress and strain once the elastic limit has been reached.
Perfectly Elastic Bodies:
Perfectly elastic bodies are materials that can return to their original shape and size after the removal of any applied deforming force, regardless of the magnitude of the force, as long as it does not exceed the material’s elastic limit. They exhibit linear stress-strain behavior and follow Hooke’s Law throughout their entire range of deformation.
Example: An ideal rubber band behaves like a perfectly elastic body, which means it stretches and returns to its original shape once the deforming force is removed.
Perfectly Plastic Bodies:
Perfectly plastic bodies are the ones that fail to regain the shape once they lose the externally applied deforming force. Thus, they go for permanent deformation with no evidence of elastic deformation. After yield point, more stress will create only plastic deformation with no further rise in the level of stress.
Example: Modeling clay is an example of a perfectly plastic body, as it can be easily shaped and will retain the new shape after the applied force is removed.
Understanding these concepts is essential for studying material behavior under various forces and applications in engineering and materials science.
See lessDefine the term compressibility. Give its units and dimensions.
Definition of Compressibility: Compressibility is a measure of the ability of a substance to decrease in volume under pressure. It quantifies how much a material will compress when subjected to an applied external force. The compressibility (β) of a substance is defined as the fractional change in vRead more
Definition of Compressibility:
Compressibility is a measure of the ability of a substance to decrease in volume under pressure. It quantifies how much a material will compress when subjected to an applied external force. The compressibility (β) of a substance is defined as the fractional change in volume per unit increase in pressure.
Mathematical Expression:
Compressibility is mathematically expressed as:
β = – (1/V) * (ΔV/ΔP)
where:
– β is the compressibility,
– V is the initial volume,
– ΔV is the change in volume,
– ΔP is the change in pressure.
Units:
The SI unit of compressibility is the reciprocal of pressure which is usually expressed in terms of:
– Pa⁻¹ (Pascal inverse) or
– N⁻¹ m² (Newton inverse per square meter).
Dimensions:
The dimensions for compressibility can be written as:
[M⁻¹ L³ T²]
Where:
M is mass,
L is length,
T is time.
In various disciplines such as fluid mechanics, material science, and engineering, it is highly relevant to know the compressibility because gases and liquids often react to varying conditions of pressure.
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If the radius of a rotating disc is doubled while keeping its mass constant, how does its moment of inertia about its axis change?
The moment of inertia of a disc is 𝐼 = 1/2𝑀𝑅². If 𝑅 is doubled, 𝐼 ∝ 𝑅², so it increases by a factor of 4. This question related to Chapter 6 physics Class 11th NCERT. From the Chapter 6. System of Particle and Rotational motion. Give answer according to your understanding. For more please visit hereRead more
The moment of inertia of a disc is 𝐼 = 1/2𝑀𝑅². If 𝑅 is doubled, 𝐼 ∝ 𝑅², so it increases by a factor of 4. This question related to Chapter 6 physics Class 11th NCERT. From the Chapter 6. System of Particle and Rotational motion. Give answer according to your understanding.
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Define bulk modulus of elasticity. Give its units and dimensions.
Definition of Bulk Modulus of Elasticity: The bulk modulus of elasticity is the coefficient of a medium's resistance toward uniform compression, defined as a ratio of relative change in volume to the intensity of pressure by which the material volume is decreased or increased. For mathematical expreRead more
Definition of Bulk Modulus of Elasticity:
The bulk modulus of elasticity is the coefficient of a medium’s resistance toward uniform compression, defined as a ratio of relative change in volume to the intensity of pressure by which the material volume is decreased or increased. For mathematical expression the following is employed:
K=-ΔP/(ΔV\V)
where K is the bulk modulus ΔP is the change in pressure ΔV is the change in volume and V is the original volume.
Units:
The SI unit of bulk modulus is Pascal (Pa), which is equal to Newton per square meter (N/m²).
Dimensions:
The dimensions of bulk modulus are expressed as [M L⁻¹ T⁻²], where M is mass L is length and T is time.
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Define modulus of elasticity. Give its units and dimensions. What are different types of moduli of elasticity?
Definition of Modulus of Elasticity: Modulus of elasticity is a measure of the ability of a material to deform elastically under the influence of a force. It is a measure of the ratio of stress (force per unit area) to strain (deformation) in a material. The modulus indicates how much a material wilRead more
Definition of Modulus of Elasticity:
Modulus of elasticity is a measure of the ability of a material to deform elastically under the influence of a force. It is a measure of the ratio of stress (force per unit area) to strain (deformation) in a material. The modulus indicates how much a material will deform under a given load.
Units:
The SI unit of modulus of elasticity is Pascal (Pa), which is equal to Newton per square meter (N/m²).
Dimensions:
The modulus of elasticity is expressed in units of [M L⁻¹ T⁻²], where M stands for mass, L for length, and T for time.
Some Common Moduli of Elasticity:
1. Young’s Modulus (E): It is the tensile or compressive elasticity of a material, that is, the ratio of tensile stress to tensile strain.
2. Bulk Modulus (K): It represents the resistance offered by a material to uniform compression. It is defined as the ratio of the change in pressure to the relative decrease in volume.
3. Shear Modulus (G): Also known as the modulus of rigidity, it measures a material’s response to shear stress. It is defined as the ratio of shear stress to shear strain.
4. Poisson’s Ratio (ν): It is a measure of the ratio of transverse strain to axial strain in a material subjected to axial stress, but not a modulus in the strict sense.
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