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Questions and Answers
What does Hooke's Law primarily describe?
What does Hooke's Law primarily describe?
Which of the following best defines Young's Modulus?
Which of the following best defines Young's Modulus?
How is the Bulk Modulus calculated?
How is the Bulk Modulus calculated?
What is the primary cause of elasticity in rubber and polymers?
What is the primary cause of elasticity in rubber and polymers?
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In the context of elasticity, what does the term 'strain' refer to?
In the context of elasticity, what does the term 'strain' refer to?
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What is the relationship between stress and strain within elastic limits according to Hooke's Law?
What is the relationship between stress and strain within elastic limits according to Hooke's Law?
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What does the Coefficient of Elasticity relate to?
What does the Coefficient of Elasticity relate to?
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What does the Modulus of Rigidity express?
What does the Modulus of Rigidity express?
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What is the equation for work done during shearing strain?
What is the equation for work done during shearing strain?
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How is Poisson's ratio defined?
How is Poisson's ratio defined?
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What does the moment of inertia (I) refer to in the context of Young's modulus under non-uniform bending?
What does the moment of inertia (I) refer to in the context of Young's modulus under non-uniform bending?
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What is the relationship defined by the equation K = Pv/v?
What is the relationship defined by the equation K = Pv/v?
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Which factor does NOT affect the work done during tensile stress?
Which factor does NOT affect the work done during tensile stress?
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What is the first torsion pendulum known for?
What is the first torsion pendulum known for?
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In the equation W = ʃˇ˳ P dv, what does the variable P represent?
In the equation W = ʃˇ˳ P dv, what does the variable P represent?
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What is the correct expression for the work done during volume strain?
What is the correct expression for the work done during volume strain?
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Study Notes
Chapter 3: Elasticity
- Elasticity is a body's ability to resist deformation and return to its original shape after the deforming force is removed.
- Solid objects deform when significant forces are applied.
- If the material is elastic, the object returns to its original shape upon force removal.
- The reason for elastic behavior varies between materials.
- In metals, atomic lattice changes size and shape when force is applied, returning to the original lower energy state when force is removed.
- In rubbers and polymers, stretching of polymer chains causes elasticity.
Stress and Strain
- Stress is the internal resistive force per unit area of a body.
- Stress = Force/Cross-Sectional Area
- Strain is the ratio of the change in length to the original length of a wire.
- Strain = Elongation/Original Length
Hooke's Law and Coefficient of Elasticity
- Hooke's Law states that within elastic limits, stress is proportional to strain.
- Within elastic limits, tension is proportional to extension.
- Stress ∝ Strain
- A ∝ I/L (proportional relation between area and length)
Young's Modulus
- Young's modulus (Y) is the ratio of normal stress to longitudinal strain.
- Y = (Normal Stress)/(Longitudinal Strain) = (F/A)/(ΔL/L)
- Y = (MgxL)/(πr²×L)
Bulk Modulus
- Bulk modulus (K) is the ratio of volume stress to volume strain.
- K = (Volume Stress)/(Volume Strain) = (PV)/(ΔV)
Modulus of Rigidity
- Modulus of Rigidity (η) is the ratio of tangential stress to shearing strain.
- η = (Tangential Stress)/(Shear Strain) = (F/A)/θ = T/θ
Work Done During Longitudinal Strain
- The longitudinal strain equation demonstrates the material's extension when a load or stress is applied.
- Y = Stress/Strain
- F = AY/L × (x)
- dw = Fdx
- W = Integral(AY/L x dx)
- W = 1/2 (F/A) × (ΔL/L) = 1/2 × stress × strain
Work Done During Volume Strain
- K = Pv/v
- P = Kv/V
- dw = Fdx = PA dx, dw = Pdv
- W = Integral P dv
- W = 1/2 k/v v² = 1/2 (k/v v) x (v)
- W = 1/2 Pv = 1/2 × (stress) × (volume strain)
Work Done During Shearing Strain
- Shearing strain = θ
- Modulus of rigidity = η (F/A)/ θ
- F = η ΑΘ
- F= ηL²Θ,
- W = ∫on L Idl
- W = 1/2 η LI²
- W = F/LI
- W = 1/2 Fl
- W = 1/2 × (tangential force)× (Displacement)
- W = (F/A) × (Θ)
- W = 1/2 × Shearing stress × Shearing strain
Poisson's Ratio
- Poisson's Ratio (σ) is the ratio of lateral strain to longitudinal strain.
- σ = Lateral Strain/Longitudinal Strain.
- Lateral strain = Change in diameter/Original diameter = δD/D
- Longitudinal strain = Change in length/Original length = δL/L
- σ = (δD/D)/(δL/L)
Experimental Determination of Y by Loading a Rectangular Thin Bar at The Center
- The Young's modulus (Y) of a material in a non-uniform bending bar (central loading) is given by:
- Y = (mgl³)/(48le)
- m = Mass loaded
- g = Acceleration due to gravity
- l = Length between knife edges
- b = Breadth of bar
- d = Thickness of bar
- e = Depression of bar
Torsional Oscillations
- A torsion pendulum involves a body suspended by a thread or wire which twists in one direction, then the opposite.
- The period of oscillation (T) for a torsion pendulum is given by:
- T = 2π√(I/C)
- I = Moment of inertia of suspended body
- C = Couple/unit twist
- C = (1/2)πηγ⁴/l (expression for couple per unit twist)
- γ = rigidity modulus
- r = radius of suspension wire
- l = length of suspension wire
- Substituting relation for C in T, a formula for rigidity modulus is derived.
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Description
Explore the concepts of elasticity, stress, and strain in this quiz. Understand how materials deform under force and return to their original shape. Learn about Hooke's Law and the coefficient of elasticity, essential topics in the study of physics.
