3.4 | materials

what are tensile forces?

forces that act away from the center and stretch a material.

what are compressive forces?

forces that act towards the center and compress a material.

what is hooke's law?

for a material within its elastic limit, the force applied is directly proportional to its extension, expressed as f = kx.

what is the force constant in hooke’s law?

the force constant k measures stiffness; a larger k means a stiffer material. it is measured in newtons per meter

what happens at the elastic limit of a material?

beyond it, the material will not return to its original shape and hooke’s law no longer applies.

what does a force-extension graph show for a spring?

it shows linear behavior up to the elastic limit (elastic deformation), followed by nonlinear behavior (plastic deformation).

how does a metal wire behave in a force-extension test?

it obeys hooke’s law up to its elastic limit, then shows plastic deformation. unloading reveals permanent extension.

how does rubber behave under force?

rubber does not obey hooke’s law and does not plastically deform. it forms a hysteresis loop, indicating energy lost as heat.

how does polythene behave under force?

it does not obey hooke’s law and plastically deforms even under small forces, making it easy to reshape.

how can force-extension characteristics be investigated?

use a clamp setup, ruler, fiducial marker, and standard masses. record extension for each force and graph results to find k.

how do you reduce error in a force-extension experiment?

read measurements at eye-level, use a set square, and analyse only the linear section of the force-extension graph.

how do you calculate spring constants in series?

1/k₁ + 1/k₂ + … = 1/ktotal.

how do you calculate spring constants in parallel?

ktotal = k₁ + k₂ + …

what is elastic potential energy?

the energy stored when a material is elastically deformed, given by e = ½fx or e = ½kx².

what happens to work done during plastic deformation?

it is not stored as elastic potential energy but used to permanently rearrange atoms in the material.

what is tensile stress?

the force per unit cross-sectional area, measured in pascals (pa): stress = f/a.

what is tensile strain?

the extension per unit original length: strain = x/l. it has no unit.

what is the young modulus?

the ratio of stress to strain: young modulus = stress/strain. it measures stiffness independent of shape and size.

how is the young modulus determined experimentally?

measure the diameter of a wire with a micrometer, apply known forces, measure extensions, and plot stress vs strain to find the gradient.

what is ultimate tensile strength (uts)?

the maximum stress a material can withstand before breaking. it appears as the peak on a stress-strain graph.

how does a brittle material behave in a stress-strain graph?

it shows elastic behavior until it snaps without plastic deformation; the loading and unloading curves are identical.

how does an elastic material behave in a stress-strain graph?

it stretches under stress without permanent deformation, but the unloading curve differs due to energy loss.

how does a ductile material behave under stress?

it shows elastic deformation followed by plastic deformation and can be drawn into wires or hammered into sheets.