3.4 Materials Flashcards

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1
Q

what is the definition of Hooke’s law?

A

Hooke’s law states that the extension of an object is proportional to the force that causes it, provided that the elastic limit is not exceeded

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2
Q

what is the formula for Hooke’s law?

A

F = kx
where F is equal to the force
x is equal to the extension
k is equal to the force or spring constant

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3
Q

what does the force constant k dependent on?

A

the material being stretched

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4
Q

what can the force constant be used, or in other words when is F = kx valid?

A

when the material is undergoing ELASTIC deformation, as soon as the deformation becomes plastic, the force constant is no longer constant because the force per unit extension is not constant

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5
Q

what does the force constant k tell you?

A

the force per unit extension

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6
Q

what does Hooke’s law apply to?

A

wires being stretched and springs and most other materials

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7
Q

what is elasticity?

A

elasticity is the property of a body to resume to its original shape or size once the deforming force or stress has been removed

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8
Q

what are tensile forces?

A

stretching or pulling force on either end in opposite directions but equal size which increases the objects length (positive extension)

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9
Q

what are compressive forces?

A

compressive or squashing force

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10
Q

what is the gradient of a force-extension graph equal to?

A

k, the force or spring constant

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11
Q

what is the definition of deformation?

A

deformation is the change in shape or size of an object

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12
Q

what does elastic deformation mean?

A

the material returns back to its original shape when the deforming force is removed

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13
Q

what does plastic deformation mean?

A

the material does not return back to its original shape when the deforming force is removed, the deformation is plastic

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14
Q

outline an investigation to see force-extension characteristics for materials (not a wire)

A
  • clamp the object being tested at the top and measure its original length using a ruler (could be a spring, rubber band, polythene strip etc.)
  • ruler can either be held parallel or can be directly clamped
  • add weights one at a time to the bottom of the object and record the new length
  • calculate extension using = new length - original length
  • plot a graph of force (weight) against extension, F = kx therefore gradient = k (before the object exceeds its limit of proportionality)
  • make sure you carry it out safely, wear safety goggles and ensure there is a box underneath the weights to catch them
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15
Q

what does a line of constant gradient (linear relationship) on a force-extension graph tell you?

A

the material is obeying Hooke’s law

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16
Q

outline an investigation to see force-extension characteristics for a wire

A
  • clamp a long, thin copper wire using a g clamp firmly at one end of the wire
  • attach a pulley at the other with a weight hanger to keep the wire taught
  • then attach a marker or mark on a position on the wire with a ruler in a fixed position lined up with the marker
  • begin to add masses to the end of the wire at the pulley to stretch the wire
  • record the mass of weights used to find the force
  • record the extensions after each added mass
  • plot a graph of force against extension
  • make sure you carry it out safely, wear safety goggles and ensure there is a box underneath the weights to catch them
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17
Q

what is the area under a force-extension graph equal to?

A

the work done to extend that material by that amount (energy stored)

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18
Q

does Hooke’s law apply to compressive forces?

A

yes - k has the same value for both tensile and compressive forces, the only difference is that the extension is negative (as the material is being squashed) but don’t worry about that in questions

19
Q

what is the formula for elastic potential energy stored in a wire (for a material obeying Hooke’s law and where the elastic limit has not been reached)?

A

EPE = 0.5Fx

area under the line, there is a half because the force is changing from zero up to max, so we take average force

20
Q

how can 0.5Fx be rewritten as?

A

since F = kx

EPE = 0.5Fx can be rewritten as EPE = 0.5kx^2

21
Q

when the load is removed (before the elastic limit has been reached) what happens to the elastic potential energy stored?

A

it is released as it returns to its original shape

22
Q

what are the rules for the force constant k when combining springs in both parallel and series?

A

in SERIES 1/k = 1/k1 + 1/2 + 1/k3
in PARALLEL, k = k1 + k2 + k3
(same as capacitors, opposite to resistors)

23
Q

what is the point called on a force-extension graph where the line starts to curve and what is happening? (for a ductile material like a wire)

A

the limit of proportionality- when the force is great enough, the graph will begin to curve as the extension is no longer proportional to the force (the material will still behave elastically after this point, but not for much more load)

24
Q

what is the point after the limit of proportionality called and what is happening? (for a ductile material like a wire)

A

this point is called the elastic limit and beyond this point the material will not show elastic behaviour, any further load will permanently deform the material and it will not return to its original shape

25
Q

what is the region past the elastic limit referred to as and what does it look like on a the force-extension graph? (for a ductile material like a wire)

A

curved line with decreasing gradient which is a region of PLASTIC BEHAVIOUR, the material is deforming plastically and will not return to its original shape

26
Q

where the line stops is known as what on a force-extension graph? (for a ductile material like a wire)

A

fracture, this is the point at which the material breaks, snaps or shatters

27
Q

what is tensile stress and what is the formula, symbol and units?

A

stress is defined as the force per unit cross-sectional area and therefore has units Nm^-2 (also known as pascals like pressure)

stress (σ) = force / area

28
Q

what is tensile strain and what is the formula, symbol and units?

A

strain is defined as the extension per unit length it has no units and is dimensionless

strain (ε) = extension / original length

29
Q

what is the formula for the Young Modulus? and what are the units?

A

Young’s modulus = tensile stress / tensile strain or σ / ε
which can be rewritten as (F/A) / (X/L) =
FL / XA
-the units are the same as stress, pascals or Nm^-2

30
Q

what is the Young Modulus a measure of?

A

the stiffness of a material
a HIGH young’s modulus means a very stiff material, will not alter its shape easily, can undergo high stress
a LOW young’s modulus means a less stiff material, will alter its shape easily, cannot undergo high stress

31
Q

the young modulus can only be calculated when stress and strain are proportional to one another and when does this occur?

A

up to the limit of proportionality (where the graph starts to curve)

32
Q

outline an investigation to determine the young modulus of a metal

A
  • set up the investigation by using a clamp to fix one end of a long, thin wire to the bench and have a pulley attached to a set of weights at the other end (edge of table)
  • first work out cross-sectional area of wire using a micrometer to find diameter
  • start with the smallest weight to straighten the wire (do not include this in final calculations)
  • then draw a marker on wire and measure the distance between fixed end and marker, this is the unstretched length
  • then increase the weight and recording the new distance from the marker each time
  • to work out the extension find the difference between these values and the unstreched length
  • plot a graph of stress against strain to calculate the young modulus (in Pa), remember stress = force/area and strain = extension/original length
33
Q

what does the gradient of a stress-strain graph tell you?

A

the materials Young’s Modulus (where the line is straight and hence where Hooke’s law is being obeyed)

34
Q

what does a larger spring/force constant mean?

A

the material is STIFFER, more force is required to extend the material by 1 metre

35
Q

what does a stress-strain graph look like for a brittle material like glass or concrete?

A

-straight line through the origin until the line stops abruptly where the material breaks or fractures
(small area under curve because very little EPE has been stored)
-brittle materials distort very little and a high amount of stress is required to break brittle materials
-linear relationship (no plastic deformation only elastic deformation)

36
Q

what is the definition for ultimate tensile strength?

A

the maximum stress a material can withstand before breaking (while being pulled or stretched) before it fails or breaks

37
Q

what is a brittle material?

A

a brittle material will break with little or no plastic deformation

38
Q

what is a ductile material?

A

a ductile material can be drawn into wires and will show plastic deformation under tensile stress before breaking

39
Q

what is a malleable material?

A

a malleable material can be hammered or beaten into flat sheets and will show extensive plastic deformation when subjected to compressive forces

40
Q

what is a hard material?

A

a hard material will resist plastic deformation by surface indentation or scratching

41
Q

what is stiffness?

A

stiffness is the ability of a material to resist a tensile force

42
Q

what is a polymeric material?

A

a polymeric material is made of long chains of molecules called polymers (also known as plastics)

43
Q

what does a stress-strain graph look like for a polymeric material and what does this tell you?

A
  • curved s shape line - the degree of strain can be extremely high, however it is difficult to stretch further without snapping
  • it can withstand high stress due to the nature of the molecules