Mechanical Properties of Solids Quiz
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Questions and Answers

What is the elongation of the thighbone under the extra load?

  • 1.59 mm (correct)
  • 2.2 mm
  • 3.18 mm
  • 0.70 mm

The stress on the rod is calculated with the formula Stress = F/A.

True (A)

What is the strain regarding the elongation of the thighbone?

1.59 x 10^-3

The effective radius of the performer's thighbone is ____ cm.

<p>2.0</p> Signup and view all the answers

Which unit is used to express stress?

<p>N/m² (A)</p> Signup and view all the answers

Match the following terms with their definitions:

<p>Stress = Force per unit area Strain = Deformation per unit length Elongation = Increase in length Load = Weight applied to a structure</p> Signup and view all the answers

The total mass supported by the performer's legs in the human pyramid is 280 kg.

<p>True (A)</p> Signup and view all the answers

Calculate the stress on the rod if the applied force is $100 × 10^3 N$ and the area is $3.14 × 10^{-2} m^2$.

<p>3.18 × 10^8 N/m²</p> Signup and view all the answers

What is the term for the tendency of a material to return to its original shape after deforming forces are removed?

<p>Elasticity (B)</p> Signup and view all the answers

Plastic materials tend to regain their original shape after deformation.

<p>False (B)</p> Signup and view all the answers

What is the primary difference between elastic and plastic deformation?

<p>Elastic deformation is temporary and allows the material to return to its original shape, while plastic deformation is permanent and does not return to the original shape.</p> Signup and view all the answers

Materials that do not return to their original shape after deformation are known as ______.

<p>plastic materials</p> Signup and view all the answers

Match the following types of deformation with their characteristics:

<p>Elastic deformation = Temporary change that can revert Plastic deformation = Permanent change that does not revert Stress = Force applied over a certain area Strain = Measure of deformation</p> Signup and view all the answers

Which material is an example of an ideal plastic?

<p>Putty (B)</p> Signup and view all the answers

The elastic behavior of materials is irrelevant in engineering design.

<p>False (B)</p> Signup and view all the answers

What role does the elastic behavior of materials play in engineering design?

<p>It helps determine how materials will respond to forces and stresses, ensuring the safety and integrity of structures.</p> Signup and view all the answers

What is the term for the change in length in the perpendicular direction of a body under stress?

<p>Longitudinal strain (A)</p> Signup and view all the answers

Volumetric strain is defined as the ratio of change in volume to the original volume.

<p>True (A)</p> Signup and view all the answers

What does Hooke's law state regarding stress and strain?

<p>Stress and strain are proportional to each other for small deformations.</p> Signup and view all the answers

The internal restoring force per unit area when a body is subjected to hydraulic compression is known as __________.

<p>hydraulic stress</p> Signup and view all the answers

Match the following terms with their definitions:

<p>Longitudinal strain = Change in length to original length Volume strain = Change in volume to original volume Hydraulic stress = Internal restoring force per unit area Hooke's law = Proportionality between stress and strain</p> Signup and view all the answers

In which region of a stress-strain curve does Hooke's law hold true?

<p>From O to A (D)</p> Signup and view all the answers

A body subjected to hydraulic pressure loses its shape permanently.

<p>False (B)</p> Signup and view all the answers

What happens to the stress-strain curve in the region where Hooke's law is obeyed?

<p>The curve is linear.</p> Signup and view all the answers

Which of the following is the correct formula for tensile stress according to Hooke's law?

<p>F/A = Y∆L/L (B)</p> Signup and view all the answers

Shear stress is defined in the same way as tensile stress and can apply to liquids.

<p>False (B)</p> Signup and view all the answers

What does the symbol 'G' represent in the context of shear stress?

<p>Shear modulus</p> Signup and view all the answers

In terms of stress, the equation for hydraulic compression is expressed as p = B (∆V/V), where p represents the ______.

<p>hydraulic stress</p> Signup and view all the answers

Match the following variables related to Hooke’s law with their respective meanings:

<p>Y = Young's modulus A = Cross-sectional area p = Hydraulic pressure B = Bulk modulus</p> Signup and view all the answers

Which type of deformation involves horizontal displacement of one face of a solid?

<p>Shear deformation (A)</p> Signup and view all the answers

The Young’s modulus is applicable for liquids and gases.

<p>False (B)</p> Signup and view all the answers

What does ∆L/L represent in Hooke's law?

<p>Tensile or compressive strain</p> Signup and view all the answers

Which material has a larger value of Young's modulus?

<p>Metals (B)</p> Signup and view all the answers

A material that stretches more is considered more elastic.

<p>False (B)</p> Signup and view all the answers

What is the name of the elastic constant that describes the change in lateral dimensions when a wire is under longitudinal strain?

<p>Poisson ratio</p> Signup and view all the answers

Stress is not a ______ quantity since it cannot be assigned a specific direction.

<p>vector</p> Signup and view all the answers

Match the following materials with their properties related to elasticity:

<p>Steel = Higher Young's modulus Rubber = Lower Young's modulus Copper = Moderate elasticity Elastomers = High stretchability</p> Signup and view all the answers

What does a large value of Young's modulus indicate about a material?

<p>It requires a large force for small length changes (B)</p> Signup and view all the answers

Stress can be assigned a specific direction like force can.

<p>False (B)</p> Signup and view all the answers

What is the relationship between stress and strain described by Young’s modulus?

<p>Proportional</p> Signup and view all the answers

What is the diameter of the wires mentioned in the context?

<p>0.25 cm (D)</p> Signup and view all the answers

The shear modulus of aluminium is 25 Pa.

<p>False (B)</p> Signup and view all the answers

What is the mass supported by the four identical cylindrical columns?

<p>50,000 kg</p> Signup and view all the answers

The rectangular cross-section dimensions of the copper piece are 15.2 mm and ______.

<p>19.1 mm</p> Signup and view all the answers

Match the material to its property:

<p>Steel = Good tensile strength Aluminium = Lightweight and resistant to corrosion Copper = Excellent electrical conductivity Brass = Corrosion-resistant alloy</p> Signup and view all the answers

What is the vertical deflection of the face of the cube made of aluminium when a 100 kg mass is attached?

<p>0.5 mm (B)</p> Signup and view all the answers

The bulk modulus of water is less than that of air at constant temperature.

<p>False (B)</p> Signup and view all the answers

How many wires support the rigid bar of mass 15 kg?

<p>Three wires</p> Signup and view all the answers

Flashcards

Stress calculation

Stress is calculated by dividing force by area.

Stress Unit

The unit for stress is N/m^2 (Pascals).

Elongation formula

Elongation (∆L) is calculated by multiplying stress by length and dividing by Young's modulus(Y).

Young's Modulus

Material constant related to the stiffness of a material

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Strain calculation

Strain is the ratio of elongation (∆L) to the original length(L)

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Strain unit

Strain is unitless

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Human pyramid stress

The combined weight of performers and equipment is supported by the legs of a performer in the human pyramid.

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Combined load in a composite system

If components are connected in series (end to end), the elongation is calculated by summing the elongations of individual components for each component and the total load will be the same for each component.

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Elasticity

The property of a material to return to its original shape and size after an applied force is removed.

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Elastic Deformation

The change in shape or size of an object due to an applied force, which is completely recovered when the force is removed.

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Plasticity

The property of a material to undergo permanent changes in shape or size when an external force is applied.

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Rigid Body

A solid that has a definite shape and size, not easily deformable.

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Deformation

Change in shape or size of an object caused by an applied force.

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Stress

The internal force acting per unit area within a material resisting deformation.

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Strain

The amount of deformation in a material, expressed as a ratio of change in length to original length.

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Hooke's Law

The law stating that the stress is directly proportional to the strain within the elastic limit of a material.

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Longitudinal Strain

Change in length perpendicular to the original length of a body, divided by the original length.

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Hydraulic Compression

A decrease in volume without a change in shape, under a pressure on all surfaces.

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Hydraulic Stress

Internal restoring force per unit area during hydraulic compression, same as applied hydraulic pressure.

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Volume Strain

Change in volume divided by original volume. It is the strain from hydraulic compression or pressure.

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Hooke's Law

For small deformations, stress and strain are directly proportional.

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Stress-Strain Curves

Graphs showing how a material deforms with increasing load. Varied between materials.

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Elastic Behavior

Material's ability to regain its original dimensions/shape after the applied force is removed within the linear region of the stress-strain curve.

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Linear Region (Stress-Strain)

Portion of the stress-strain curve where the material obeys Hooke's law, stress and strain are proportional.

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Hooke's Law (Tensile/Compressive)

For a solid under tension or compression, stress (force per area) is proportional to strain (change in length divided by original length).

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Young's Modulus

A material property that describes its stiffness under tension or compression.

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Shear Stress

Stress arising from forces applied parallel to a surface, causing deformation.

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Shear Modulus

Material property describing resistance to shear deformation.

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Bulk Modulus

Material property indicating resistance to volume change under pressure.

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Tensile Stress

Force per unit area applied in a direction pulling an object.

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Strain (Tensile/Compressive)

Change in length/original length.

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Stress

Force per unit area.

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Young's Modulus

A material property representing a material's stiffness, showing the ratio of stress to strain in elastic deformation.

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Elasticity (material)

Material's tendency to recover its original shape after deformation. A material that stretches less for a given load is more elastic.

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Stress-Strain Graph

Graphical representation of stress versus strain, used to determine material properties.

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Yield Strength

The stress at which a material begins to deform plastically, meaning it doesn't return to its original shape.

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Poisson's Ratio

A material constant describing the lateral strain in materials under axial stress.

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Strain

Measure of deformation of a material, expressed as the ratio of change in length to original length.

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Stress

Force applied per unit area of a material.

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Young's Modulus Comparison

Different materials have different Young's moduli, indicating different stiffness.

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Wire Elongation (Steel/Brass)

The change in length of a steel or brass wire under a load, calculated using material properties and applied force.

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Aluminium Cube Deflection

Vertical shift of an aluminum cube's face when a mass is added, related to shear modulus, applied force, and cube dimensions.

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Column Compressional Strain

Change in length of a steel column supporting a load, calculated with material properties and load distribution.

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Copper Strain Calculation

Calculating the deformation (strain) of copper under a given tensile force (applied load), using cross-section dimensions

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Maximum Cable Load

The maximum weight a steel cable can carry without exceeding its maximum allowable stress.

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Wire Diameter Ratios

Determining the relative diameters of copper and iron wires to achieve the same tension, given lengths and a rigid support.

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Wire Elongation (Vertical Circle)

Change in length of a steel wire under a rotating mass, considering rotational speed and material properties.

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Water Bulk Modulus

Measure of water's resistance to compression under pressure, calculated using initial/final volumes and pressure.

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Study Notes

Mechanical Properties of Solids

  • Solids have definite shape and size
  • Forces are required to change (deform) the shape or size of a body
  • Elasticity is the tendency of a body to regain its original shape and size when the applied force is removed
  • Elastic deformation is the deformation caused by elasticity
  • Plasticity is the property by which a substance does not regain its original shape and size
  • Stress is the restoring force per unit area
  • Strain is the ratio of change in dimension to the original dimension
  • Hooke's Law states that stress and strain are proportional for small deformations
  • Stress = k × strain
  • k is the modulus of elasticity
  • Stress-strain curves show the relationship between stress and strain for a given material
  • Understanding stress-strain curves helps in structural and manufacturing design
  • Young's Modulus (Y) is the ratio of tensile (or compressive) stress to longitudinal strain
  • Y =(F/A)/(∆L/L) = (F × L) / (A × ∆L)
  • Young's modulus has units of N/m² (or Pa)
  • Shear Modulus (G) is the ratio of shearing stress to shearing strain
  • G = (F/A)/(∆x/L) = (F × L) / (A × ∆x)
  • Bulk Modulus (B) is the ratio of hydraulic stress to volume strain
  • B = - p/(∆V/V)
  • Compressibility is the reciprocal of bulk modulus
  • Various materials have different elastic moduli, which affect their behavior under stress
  • Solids are less compressible than liquids, which are less compressible than gases
  • Elastomers exhibit large strains before failure, unlike other materials
  • Elasticity is important for structural design, materials selection, and understanding how materials deform under load
  • Applications of elastic behavior are in cranes, bridges, automobiles, and artificial limbs

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Mechanical Properties of Solids PDF

Description

Test your knowledge on the mechanical properties of solids with this quiz. Explore concepts such as elasticity, stress, strain, and Hooke's Law. Dive deep into the principles that govern how solids behave under various forces and their implications in structural design.

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