Physics Chapter on Stress and Strain

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Questions and Answers

What is shearing strain or shear represented by?

ΔL

εs (correct)

What does the elastic limit refer to?

The strain experienced just before fracture occurs.

The maximum stress within which the body regains its original size after deformation. (correct)

The minimum stress required to start deformation.

The maximum stress at which a body can permanently deform.

According to Hooke's law, stress is proportional to which of the following?

Strain in the elastic limit (correct)

Elastic limit

Shear stress

Volume strain

What happens to a rubber band beyond its elastic limit?

It experiences permanent deformation. Signup and view all the answers

How is the volume strain defined?

Change in volume divided by original volume. Signup and view all the answers

In the stress-strain profile curve, which variable is plotted on the X-axis?

Strain Signup and view all the answers

What is the relationship between force applied and elongation in a wire, according to Hooke's law?

Elongation is directly proportional to the original length of the wire. Signup and view all the answers

What does the slope of the graph in the stress-strain profile indicate?

The elastic modulus or stiffness. Signup and view all the answers

What defines tensile stress in a material?

Internal forces pulling apart the material Signup and view all the answers

What is the relationship between volume stress and pressure?

Volume stress and pressure are considered the same Signup and view all the answers

Which of the following best describes longitudinal strain?

The deformation measured as a change in length Signup and view all the answers

Tensile strain occurs when...

The length of the object increases from its natural state Signup and view all the answers

Which of the following is NOT one of the types of strain mentioned?

Rotational strain Signup and view all the answers

Compressive stress is characterized by...

Shortening of the material Signup and view all the answers

What quantity does strain measure?

The percentage change in length or shape Signup and view all the answers

What type of strain occurs when a rod is compressed?

Compressive strain Signup and view all the answers

What does the bulk modulus measure regarding a material?

The resistance of a solid to change in its volume Signup and view all the answers

What is the relationship between bulk modulus and compressibility?

Bulk modulus is the reciprocal of compressibility Signup and view all the answers

In the context of compressibility, which statement is true?

Compressibility is higher for materials with a small bulk modulus Signup and view all the answers

What happens to the volume of a material when pressure is applied, based on the bulk modulus equation?

The volume decreases due to applied stress Signup and view all the answers

Which of the following units is used for bulk modulus?

Pascal or Newton per square meter Signup and view all the answers

What describes the rigidity modulus or shear modulus?

It is inversely proportional to the angle of shear Signup and view all the answers

If a material has a high bulk modulus, what can be inferred about its compressibility?

It will have low compressibility Signup and view all the answers

When a wire is twisted, how does it relate to the rigidity modulus?

A smaller rigidity modulus means less torque for the same twist Signup and view all the answers

What does the slope of the line OA in the stress-strain curve represent?

Young's modulus Signup and view all the answers

At which point on the stress-strain curve does Hooke's law cease to be valid?

Point A Signup and view all the answers

What happens to the wire when the stress is increased beyond the yield point B?

It undergoes plastic deformation Signup and view all the answers

What is the definition of tensile strength in the context of the stress-strain curve?

The maximum stress the material can withstand before breaking Signup and view all the answers

Which type of modulus is defined as the ratio of tensile stress to tensile strain?

Young's modulus Signup and view all the answers

The point beyond which strain increases even when the load is removed is known as?

Fracture point Signup and view all the answers

What characterizes the plastic behavior of the material in the stress-strain curve?

Permanent deformation after stress is applied Signup and view all the answers

What is the unit of measurement for Young's modulus?

Pascal (Nm-2) Signup and view all the answers

What is the SI unit of shear modulus of elasticity (ηR)?

N m-2 Signup and view all the answers

In the given example, the shear modulus of a metal cube subjected to a shearing force of 4000 N and a displacement of 0.50 cm is calculated using which of the following formulas?

$\frac{F}{A} \cdot \frac{x}{L}$ Signup and view all the answers

Which of the following best describes Young's modulus?

It measures the material's resistance to a change in length. Signup and view all the answers

What can be concluded about wires A, B, and C based on their slopes when stretched?

The slope represents stiffness; greater slope indicates lesser strain. Signup and view all the answers

If the volume of a material changes by 1.5 x 10^-5 m³ under a pressure of 10⁶ Pa, what is the bulk modulus of the material?

6.67 x 1010 N m-2 Signup and view all the answers

When a wire is subjected to a load of 5 kg and has a Young's modulus of 4 x 10¹⁰ N m^-2, which statement is true about its behavior?

It will elongate based on the applied stress. Signup and view all the answers

What relationship does Hooke's Law describe within the elastic limit of a material?

Stress is proportional to strain. Signup and view all the answers

What characteristic indicates that wire A is stiffer compared to wires B and C?

It has a larger slope than others. Signup and view all the answers

Study Notes

Stress

Tensile stress occurs when a material is stretched by equal and opposite forces.
Compressive stress occurs when a material is pushed by equal and opposite forces.
Volume stress occurs when a body is acted upon by forces on its entire surface, with the force at any point perpendicular to the surface and proportional to the area.
Volume stress is the same as pressure.

Strain

Strain describes the deformation of an object when a force is applied.
Strain is the fractional change in the size of an object.
It is a dimensionless quantity with no units.

Types of Strain

Longitudinal strain: defined as the change in length divided by the original length.
- Tensile strain: occurs when the length of a material is increased.
- Compressive strain: occurs when the length of a material is decreased.
Shearing strain (Shear): occurs when a tangential force is applied to a material, causing a deformation that is proportional to the angle of shear.
Volume strain: occurs when a body is subjected to volume stress and the volume changes. Calculated as the change in volume divided by the original volume.

Elastic Limit

The elastic limit is the maximum stress a material can withstand before acquiring permanent deformation.
Beyond the elastic limit, the material will not return to its original size and shape.

Hooke's Law

States that stress is proportional to strain within the elastic limit.
This relationship can be experimentally verified by stretching a wire and measuring the elongation produced.
The graph of force vs. elongation is a straight line passing through the origin.

Stress-Strain Profile Curve

Shows the relationship between stress and strain in a material.
The curve can be divided into different regions:
- Portion OA: Hooke's law is valid, stress is proportional to strain. The slope of this line represents Young's modulus.
- Portion AB: Stress is not proportional to strain, but the material will still return to its original shape. This region ends at the yield point (elastic limit).
- Portion BC: The material will not return to its original shape when the stretching force is removed.
- Portion CD: Strain increases rapidly with an increase in stress.
- Portion DE: The material breaks (ruptures) at the fracture point E. The maximum stress at this point is called the breaking stress or tensile strength.

Moduli of Elasticity

Measure the resistance of a material to deformation.
There are three types:
- Young’s modulus: resistance to change in length. Calculated as tensile stress (or compressive stress) divided by tensile strain (or compressive strain).
- Bulk modulus: resistance to change in volume. Calculated as volume stress (pressure) divided by volume strain.
- Rigidity modulus (Shear modulus): resistance to twisting. Calculated as shear stress divided by shear strain.

Compressibility

The reciprocal of the bulk modulus.
It measures the fractional change in volume per unit increase in pressure.
Gases have high compressibility compared to solids.

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Description

Explore the concepts of stress and strain in materials with this quiz. Understand the different types of stress, such as tensile and compressive, as well as various types of strain. Test your knowledge on how these properties affect material deformation and stability.