Material Stress and Elasticity Quiz

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Questions and Answers

What does the Elasticity Modulus measure in materials?

The temperature stability of a material

The density of a material under pressure

The ability of a material to return to its original shape after deformation (correct)

The thermal conductivity of a material

Which formula is commonly used to calculate the Elasticity Modulus?

E = rac{ ext{strain}}{ ext{change in length}}

E = rac{ ext{stress}}{ ext{strain}} (correct)

E = ext{mass} imes ext{acceleration}

E = ext{pressure} imes ext{volume}

If a material has a high Elasticity Modulus, what can be inferred about its properties?

It is lightweight and low in density

It is rigid and does not easily deform (correct)

It is ductile and can easily deform

It has high thermal expansion

In solving problems involving Elasticity Modulus, which parameter is NOT typically considered?

The final temperature of the material Signup and view all the answers

When calculating the Elasticity Modulus, which of the following is true?

Strain can be defined as the change in length divided by the original length Signup and view all the answers

What characteristic do materials with large plastic deformation exhibit before fracture?

They can absorb significant energy. Signup and view all the answers

Which property is essential for a cable designed to absorb energy or shock?

Ability to exhibit large plastic deformation Signup and view all the answers

Why is the ability to absorb shock important in certain materials?

To reduce the risk of fracture. Signup and view all the answers

When a material exhibits large plastic deformation, what occurs just before it breaks?

It expands without returning to original shape. Signup and view all the answers

What is a primary focus of the study of stress as described?

The internal resistance of the body Signup and view all the answers

Which statement best describes the nature of forces involved in stress?

Stress involves balancing internal and external forces. Signup and view all the answers

What is a common application of materials that exhibit large plastic deformation?

Safety gear in sports Signup and view all the answers

What does the study of stress investigate?

The equilibrium established within a body Signup and view all the answers

What role do externally applied forces play in the concept of stress?

They are countered by internal forces to achieve balance. Signup and view all the answers

Why is understanding stress important in mechanics?

It allows for the analysis of material behavior under combined forces. Signup and view all the answers

What is the pressure at which the sphere is submerged?

2 x 10^7 N/m² Signup and view all the answers

What is the initial volume of the sphere in air?

0.5 m³ Signup and view all the answers

At what depth is the sphere submerged if the pressure is 2 x 10^7 N/m²?

Approximately 2000 meters Signup and view all the answers

Which factor is most likely to influence the change in volume of the sphere once submerged?

Material of the sphere Signup and view all the answers

What will likely happen to the volume of the sphere when submerged in the ocean?

It will decrease slightly. Signup and view all the answers

What is the cross-sectional area of the wire calculated in the solution?

3.8 x 10^-6 m^2 Signup and view all the answers

What stress value is derived from the given force and cross-sectional area?

100 MPa Signup and view all the answers

How is strain defined in the example provided?

The ratio of change in length to original length Signup and view all the answers

What value of Young's modulus (E) is given in the solution?

120 x 10^9 Pa Signup and view all the answers

In the given example, what is the displacement of the cube of gelatin due to a tangential force?

0.64 cm Signup and view all the answers

Study Notes

Stress

Stress is defined as the internal resistance of a material to the external forces applied to it.
Stress is measured in units of pascals (Pa) or newtons per square meter (N/m²).
The formula for stress is: Stress = Force / Area

Elasticity Modulus

The Elasticity Modulus (also known as Young's Modulus) is a material property that represents its stiffness.
It describes the relationship between stress and strain.
It is defined as the ratio of stress to strain in the elastic region of a material's behavior.
The formula for Elasticity Modulus: E = Stress / Strain
The units of Elasticity Modulus are the same as the units of stress: pascals (Pa) or newtons per square meter (N/m²).
A higher Elasticity Modulus indicates a stiffer material.
A lower Elasticity Modulus indicates a more flexible material.

Example Problem

A wire with a diameter of 2.2 mm is subjected to a force of 380 N. The wire stretches by 0.1 mm.
The cross-sectional area of the wire is calculated using the formula for the area of a circle: A = πD²/4
The stress is calculated by dividing the force by the cross-sectional area.
The strain is calculated by dividing the change in length by the original length.
The Elasticity Modulus is calculated by dividing the stress by the strain.
In the example, the Elasticity Modulus is found to be 120 x 10⁹ Pa.

Gelatin Cube

A gelatin cube with sides of 5.0 cm undergoes a displacement of 0.64 cm on its upper surface due to a tangential force.
This displacement represents a strain, which can be calculated as the change in length divided by the original length.

Sphere in Ocean

A sphere with a volume of 0.5 m³ is submerged in the ocean to a depth where the pressure is 2 x 10⁷ N/m².
The pressure on the sphere causes a change in volume.
The change in volume can be determined by applying the appropriate formula for volumetric changes due to pressure.

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Description

Test your understanding of material stress and elasticity modulus in this quiz. Explore the concepts of stress, the elasticity modulus, and practical application through example problems. Perfect for students studying material science or mechanics.