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Physics Topic 2.2 Strength of Materials

The physical properties of solids

Hookes Law

THE FORCE (F) EXERTED BY A SPRING IS DIRECTLY PROPORTIONAL TO ITSEXTENSION (X)

Formula of Hookes Law

F=-kx

K = constant for the particular spring (constant of proportionality/spring constant)

(- Sign shows that the force exerted by the spring in in opposite direction to theextension)

Elastic limit: when the spring changes shape permanently the load added at this

limit would stretch the string beyond its constant extension rapidly however, beforethe limit, if the load was removed the spring would always go back to its original

shape

Note: the larger the value of k the stiffer the spring

Plastic deformation: when the object has stretched beyond its elastic limit and is

permanently deformed/ cannot return back to its original shape

Elastic Strain Energy (Eel)

The energy stored on a spring = the work done on it as it is stretched = average force

used to stretch it to the extension

Average force used to stretch it:

0+F/2 = F

Note: 0+F because force stretches linearly from zero

Work done = -kx2

Note: area under a force extension graph = work done

Tensile force: a force, which puts the object in tension (tends to pull it apart)

Tensile force per unit area = tensile stress = tensile force/cross sectional area

Units of stress: Nm-2/Pa (theyre the same)

Tensile strength = tensile stress of material when it breaks

Extension per unit length = tensile strain = extension/original length

Units of tensile strain: NO UNITS

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Youngs Modulus = tensile stress/ tensile strain

Units of Youngs Modulus: Nm-2/ Pa (same as tensile stress)Note: the stiffer the material the greater its youngs modulus

Characteristics of Solids

Necking: the narrowing of material when put under stress

Plastic Region: small forces increase extension rapidly, solids that behave like this

are called ductile

Linear Region: the region where stress is directly proportional to strain

Proportionality limit: the limit where the stress stops being directly proportional to

the strain

Elastic limit: when the material stops behaving elastically and behaves plastically,when the stress is removed from the object it wont return to its original shape

Yield Point: small increase in stress causes large increase in strain

Deforming Solids

Stiffness: ability of material to resist tensile force

Tensile strength: tensile force in which materials fail

Compressive force: squashing force, which reduces the volume of the material

Compressive force per unit area = compressive stress = compressive force/area of

cross-section

Units of compressive stress: Nm-2/Pa

Compressive strength = the compressive stress at which material breaks

Extension per unit length = compressive strain = extension/original length

Units of compressive strain: NO UNITS

Strength: the ability to withstand stress

Ductile: materials which show plastic deformation

Brittle: materials that break or snap with little plastic deformation

Hard: materials that resist plastic deformation

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Malleable: materials that show large plastic deformation before cracking or

breaking

Stiff: materials that have the ability to resist tensile force

Tough: materials that are able to withstand impact forces without breaking andrequire a large force to produce a small plastic deformation

Strong: the materials with the ability to withstand stress whether its shear, tensile

or compressive