1 3 4 behaviour of springs and materials
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1.3.4 Behaviour of Springs and Materials. Objective. Describe how deformation is caused by a force in one direction and can be tensile or comprehensive. Deformation. Can be caused by tensile or compressive forces Tensile cause tension stretching forces Compressive cause compression

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1.3.4 Behaviour of Springs and Materials

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1 3 4 behaviour of springs and materials

1.3.4 Behaviour of Springs and Materials


Objective

Objective

Describe how deformation is caused by a force in one direction and can be tensile or comprehensive


Deformation

Deformation

Can be caused by tensile or compressive forces

  • Tensile

    • cause tension

    • stretching forces

  • Compressive

    • cause compression

    • squeezing forces


Deformation1

Deformation

two equal and opposite tensile

forces stretching a wire

two equal and opposite compressive

forces squeezing a spring


Objective1

Objective

Describe the behaviour of springs and wires in terms of force, extension, elasticlimit, Hooke’s Law and the force constant – i.e. force per unit extension or compression


Definitions

Definitions

  • Force (F)

    • applied to a spring or wire in tension or compression

  • Extension (x)

    • the change in length of a material when subjected to a tension, measured in metres

  • Elastic Limit

    • the point at which elastic deformation becomes plastic deformation


Definitions1

Definitions

  • Elastic Deformation

    • when the deforming force is removed, the object will return to it’s original shape

      • eg rubber band, spring (usually)

  • Plastic Deformation

    • when the deforming force is removed, the object will not return to it’s original shape

      • eg Plasticine, Blutack


Hooke s law

Hooke’s Law

  • When tension is plotted against extension, a straight line graph denotes elastic deformation

  • This is summarised by Hooke’s Law:

    ‘The extension of a body is proportional to the force that causes it’

    or as a formula:

    whereF = Force

    F = kxx = extension

    k = force/spring constant


Hooke s law1

Hooke’s Law

F

Tension /N

x

Extension /mm


Force spring constant

Force/Spring Constant

  • F = kx

  • Expressed in newtons per metre

  • How much force is required per unit of extension

    • eg 5 N mm-1 means a force of 5 N causes an extension of 1 mm

  • Can only be used when the material is undergoing elastic deformation


Objective2

Objective

Determine the area under a force against extension (or compression) graph to find the work done by the force


Work done

Work Done

  • Extension produced by tension F is x

  • Work done to reach this extension is the area under the graph

    work done = area of triangle

    = ½Fx


Objective3

Objective

Select and use the equations for elastic potential energy, E = ½Fx and ½kx2


Elastic potential energy

Elastic Potential Energy

  • As work has been done to stretch the wire, the wire then stores Elastic Potential Energy

  • This also applies to compression forces

  • For elastic deformation, the elastic potential energy equals work done:

    E=½Fx

    as F = kx then E =½kx2


Objective4

Objective

Define and use the terms stress, strain, Young modulus and ultimate tensile strength (breaking stress)


Stretching materials

Stretching Materials

  • One way of describing the property of a material is to compare stiffness

  • In order to calculate stiffness, two measurements need to be made:

    • strain

    • stress


Stretching materials1

Stretching Materials

  • Strain is the fractional increase in the length of a material

    Strain = extension (m)

    original length (m)

  • Stress is the load per unit cross-sectional area of the material

    Stress (Nm-2) = force (N)

    cross-sectional area (m2)


Young modulus

Young Modulus

  • To calculate stiffness, calculate the ratio of stress to strain:

    Young Modulus (Nm-2) = stress

    strain

    or E = stress

    strain


Young modulus1

Young Modulus

Hooke’s Law Region

Elastic limit

Limit of proportionality

stress

gradient = Young modulus

strain


Ultimate tensile stress

Ultimate Tensile Stress

  • Stiffness tells us about the elastic behaviour of a material (Young modulus)

  • Strength tells us how much stress is needed to break the material

  • The amount of stress supplied at the point at which the material breaks is called the ultimate tensile stress of the material


Objective5

Objective

Describe an experiment to determine the Young modulus of a metal in the form of a wire


Young modulus practical

Young Modulus Practical

Young modulus practical


Objective6

Objective

Define the terms elastic deformation and plastic deformation of a material


Definitions2

Definitions

  • Elastic Deformation

    • when the deforming force is removed, the object will return to it’s original shape

      • eg rubber band, spring (usually)

  • Plastic Deformation

    • when the deforming force is removed, the object will not return to it’s original shape

      • eg Plasticine, Blutack


Objective7

Objective

Describe the shapes of the stress against strain graphs for typical ductile, brittle and polymeric materials


Ductile

Ductile

  • Will stretch beyond it’s elastic limit

  • Will deform plastically

  • Can be shaped by stretching, hammering, rolling and squashing

  • Examples include copper, gold and pure iron


Brittle

Brittle

  • Will not stretch beyond it’s elastic limit

  • Will deform elastically

  • Will shatter if you apply a large stress

  • Examples include glass and cast iron


Polymeric

Polymeric

Will perform differently depending on the molecular structure and temperature

  • Can stretch beyond it’s elastic limit

  • Can deform plastically

  • Can be shaped by stretching, hammering, rolling and squashing

  • Examples include polythene


Polymeric1

Polymeric

  • Cannot stretch beyond it’s elastic limit

  • Can deform elastically

  • Can shatter if you apply a large stress

  • Examples include perspex


Summary

Summary

  • All materials show elastic behaviour up to the elastic limit

  • Brittle materials break at the elastic limit

  • Ductile materials become permanently deformed beyond the elastic limit

  • Polymeric materials can show either characteristics, depending on the molecular structure and temperature


Questions

Questions

  • Physics 1 – Chapter 8

    • SAQ 1 to 9

    • End of Chapter questions 1 to 4


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