DEVIL PHYSICSTHE BADDEST CLASS ON

CAMPUSPRE-IB PHYSICS

GIANCOLI LESSON 9-6ELASTICITY: STRESS AND STRAIN

Objectives

Understand how elasticity is related to Hooke’s Law for springs.

Know that the change in length of an object is proportional to the force placed on the object, but only to the proportional limit.

Understand the meaning of the terms elastic region, proportional limit, elastic limit, plastic region, and breaking point.

Objectives

Know that the elastic modulus, or Young’s modulus, is a ratio of the stress on an object to the strain of the object.

Differentiate between tensile stress, compressive stress, and shear stress.

Solve problems using elastic modulus, shear modulus, and bulk modulus.

Introductory Video:Stress and Strain

Reading Activity Questions?

Hooke’s Law

The change in length of an object is directly proportional to the amount of force placed on it

Normally thought of in terms of springs where k is the spring constant

The same is true for any material – but only to a certain point

LkF kxF

Elasticity Hooke’s Law holds true for all materials

up to the material’s proportional limit

Beyond the proportional limit, the change in length per force applied increases

Elasticity The material will return to its original

shape when the force is removed, provided the elastic limit is not exceeded

Once the elastic limit is exceeded, permanent deformation, or permanent set, occurs

Elasticity Deformation continues until the

breaking point Breaking, or fracture, is the subject of

Lesson 9-7 The maximum force that can be

applied to a material without breaking is its ultimate strength

Elasticity When force is applied to a material, it is

said to undergo stress Stress is defined as force per unit cross-

sectional area

The ratio of the change in length to the original length is called strain

AF

areaforcestress

0___

LL

lengthoriginallengthinchangestrain

Elasticity Cross-Sectional Area

Cylindrical rod – πr2 Rectangular rod – l x w Triangular prism – ½ bh

Elasticity Experimentation has found that

the change in length of an object is directly proportional to the force placed on in, but inversely proportional to the object’s cross-sectional area

This value is specific to the material the object is made of

Elasticity The elastic modulus, E, replaces the

spring constant in Hooke’s Law The elastic modulus, or Young’s

modulus, is the ratio of stress to strain

Elasticity

LL

AF

LLAFE

LL

lengthoriginallengthinchangestrain

AF

areaforcestress

strainstressE

0

0

0___

Elasticity Rearranging, we find a formula for the

change in length, ΔL, of a material with an elastic modulus E, cross-sectional area A, original length L0, subjected to a force F

0

0

1 LAF

EL

LL

AFE

Elasticity This formula applies

equally to tensile stress and compressive stress 0

0

1 LAF

EL

LL

AFE

Values for elastic moduli are found in Table 9-1 on page 254 in your textbook and in the data guide

Notice the applied force is perpendicular to the cross-sectional area

Shear Modulus A similar formula applies

to shear stress using the shear modulus, G

0

0

0

1 LAF

GL

LL

AFG

LL

AFE

In tensile or compressive stress, the applied force is perpendicular to the cross-sectional area

In shear stress, the applied force is parallel to the cross-sectional area

Bulk Modulus A third situation arises

when an object is subjected to forces from all sides

Like a submarine at the bottom of the ocean or a balloon when the air inside is expanding

This creates a change in volume instead of just length

LL

AFG

LL

AFE

0

0

Bulk Modulus The proportionality constant

for this situation is called bulk modulus, B

ΔP is the change in pressure Pressure is defined as force

per area and is thus the equivalent of stress

ΔV is the change in volume and V0 is the original volume

The minus sign indicates volume decreases with applied force

0

0

0

VVPB

LL

AFG

LL

AFE

Sample Problems?

Σary Review

Do you understand how elasticity is related to Hooke’s Law for springs?

Do you know that the change in length of an object is proportional to the force placed on the object, but only to the proportional limit?

Do you understand the meaning of the terms elastic region, proportional limit, elastic limit, plastic region, and breaking point?

Σary Review

Do you know that the elastic modulus, or Young’s modulus, is a ratio of the stress on an object to the strain of the object?

Can you differentiate between tensile stress, compressive stress, and shear stress?

Can you solve problems using elastic modulus, shear modulus, and bulk modulus?

QUESTIONS?

#44-52Homework