Materials (Unit 2) Flashcards
Density
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
Nm^-1
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.
or
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=Fs, 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
None
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
