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Flashcards in Materials (Unit 2) Deck (32):


Mass per unit volume


Units of density

kg m^-3


Hooke's Law

Extension is proportional to the force applied, up to the limit of proportionality.


Features of graph of force against extension confirming Hooke's Law

Straight line, through the origin.


Units of spring constant



Springs in series

Both springs experience the same force, F.
The total extension (of both springs together) is the sum of the extension of each spring individually.


(Identical) Springs in parallel

The force, F, applied to the spring combination is shared across each of the springs individually (if there are two identical springs, each spring experiences a force of 1/2F.
All springs have the same extension (and equals the extension for the spring combination).


Elastic Limit

The maximum amount a material can be stretched by a force and still return to its original length when the force is removed


Limit of Proportionality

Point beyond which force is no longer proportional to extension.


Elastic behaviour

material will return to its original length (when force removed) with no permanent extension.


Plastic behaviour

material will be permanently extended (when force is removed).


Area under a force/extension graph

area under a graph of force against extension is work done on spring and hence the energy stored, as it is loaded.
area under a graph of force against extension is the work done by the spring, and hence energy released, as it is unloaded.


Area between the loading and unloading curves of an elastic band

internal energy retained, eg as heat, within the elastic band


Derivation of
energy stored = ½ F(delta)l

• Energy stored in a stretched spring = work done stretching the spring.
• Work done = Force x distance (moved in the direction of the force)
• As spring is stretched the force gets bigger (and so isn’t constant).
• Force is proportional to Extension, so,
average force = ((F+0)/2 ), which = ½ F.
• The work done = average force x distance moved
• Energy stored = work done = ½ F delta L
• This is the area under the graph of Force against Extension (½ base x height).


Derivation of
energy stored = ½ F(delta)L
from a graph of force against extension

• W=Fs, so area beneath line from origin to L represents the work done to compress/extend spring.
• work done (on spring) equals the energy it stores.
• area under graph = area of triangle = ½ base x height, therefore energy stored = ½ F x L.


Tensile stresstensile (stretching) force divided by its cross-sectional area

tensile (stretching) force divided by its cross-sectional area


Units of stress

Pa or Nm-2


Tensile strain

extension of material divided by its original length


Units of strain



Breaking stress (ultimate tensile stress)

(tensile) stress needed to break a solid material


Description of stiffness

requires a large force (or stress) for a small deformation (or extension)


Description of fracture

Non-brittle fracture
Material necks (becomes narrower at its weakest point) which reduces the cross-sectional area so increases stress at that point until the wire breaks (at that point)
Brittle fracture
No plastic deformation, usually snaps suddenly without any noticeable yield (through crack propagation).


Description of brittle

a material that fractures without any plastic deformation


Description of ductile

material can be drawn into a wire (exhibits a lot of plastic deformation)


Description of strength (or weakness)

Material with a higher (or lower) breaking stress.


Young Modulus

ratio of tensile stress to tensile strain


Units of Young Modulus

Pa or Nm-2


Use of stress/strain curves to find Young Modulus

from a graph of stress against strain, Young Modulus is the gradient of the linear section of the graph (the region where stress and strain are directly proportional)


Area under a graph of stress against strain

energy stored per unit volume


One simple method of measuring Young Modulus

Measurements to make
• Original length of wire, L, with a ruler
• Diameter of wire with a micrometer
• Mass attached to end of wire
• Length of stretched wire with a ruler.
Reducing Uncertainty in each measurement
• Repeat measurements of length
• Repeat measurements of diameter of wire at different points
• Check for zero error on electronic scales
• Check for zero error on micrometer
How measurements are used to determine Young Modulus
• F=weight=mg
• Extension L = stretched length – original length
• Cross-sectional area of wire A = (pi)d2 / 4.
• Stress = F/A; Strain = L/L
• Plot a graph of stress (y-axis) against strain (x-axis)
• Young Modulus is gradient of linear section of graph


Interpretation of force against extension curves

See sheet


Interpreting stress/strain graphs

See sheet