Materials - Hooke’s Law, Energy Stored

forces that produce extension

tensile forces

forces that produce compression

compressive forces

tensile force

equal and opposite forces acting on a material to stretch it

compressive force

two or more forces together that reduce the length or volume of an object

tensile deformation

a change in the shape of an object due to tensile forces

compressive deformation

a change in the shape of an object due to compressive forces

elastic deformation

a reversible change in the shape of an object due to a compressive or tensile force - removal of stress or force will return the object to its original shape and size (no permanent strain)

plastic deformation

an irreversible change in the shape of an object due to a tensile or compressive force - removal of the stress or force produces permanent deformation

Hooke’s Law

the force applied is directly proportional to the extension of the spring unless the limit of proportionality is exceeded

F = kx

force constant

a quantity determined by divided force by extension (or compression) for an object obeying Hooke’s Law - called constant of proportionality “k” in Hooke’s Law, measured in Nm⁻¹

stiffness

the ability of an object to resist deformation

elastic limit

the value of stress or force beyond which elastic deformation becomes plastic deformation and the material or object will no longer return to its original shape and size when the stress or force is removed

limit of proportionality

the value of stress or force beyond which stress is no longer directly proportional to extension

Improving Hooke’s Law experiment (4)

Length:

• use a set square

• take reading at eye level to reduce parallax errors

Mass:

• use a digital balance

Take 6 different reading and repeat each one

How to find work done from a graph

Area under a force-extension graph

elastic potential energy

the energy stored in an object because of its deformation

steps to relate work done and Hooke’s Law (4)

• W = area under graph - W = ½ Fx

• F = kx - W = ½ (kx)x

• ∴ W = ½ kx²

• where W is directly proportional to x²

F-x graph of a metal wire

unloading curve is identical to loading curve if forces are under elastic limit, otherwise unloading is parallel but not equal

F-x graph of rubber

gap in between shows thermal energy produced

hysteresis loop

a loop-shaped plot obtained when loading and unloading a material produce different deformations - more work is done in stretching a band than releasing it

F-x graph of polythene

suffer plastic deformation under relatively little force