3.4 Materials

Question 1

what is the definition of Hooke’s law?

Answer 1

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

Question 2

what is the formula for Hooke’s law?

Answer 2

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

Question 3

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

Answer 3

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

Question 4

what does the force constant k tell you?

Answer 4

the force per unit extension

A measure of stiffness of material

Question 5

what does Hooke’s law apply to?

Answer 5

wires being stretched and springs and most other materials

Question 6

what is elasticity?

Answer 6

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

Question 7

what are tensile forces?

Answer 7

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

Question 8

what are compressive forces?

Answer 8

compressive or squashing force

Question 9

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

Answer 9

k, the force or spring constant

Question 10

what is the definition of deformation?

Answer 10

deformation is the change in shape or size of an object

Question 11

what does elastic deformation mean?

Answer 11

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

Question 12

what does plastic deformation mean?

Answer 12

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

Question 13

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

Answer 13

• 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

Question 14

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

Answer 14

the material is obeying Hooke’s law

Question 15

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

Answer 15

• 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

Question 16

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

Answer 16

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

Question 17

does Hooke’s law apply to compressive forces?

Answer 17

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

Question 18

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)?

Answer 18

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

Question 19

how can 0.5Fx be rewritten as?

Answer 19

since F = kx

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

Question 20

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

Answer 20

it is released as it returns to its original shape

Question 21

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

Answer 21

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

Question 22

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)

Answer 22

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)

Question 23

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

Answer 23

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

Question 24

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)

Answer 24

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

Question 25

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

Answer 25

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

Question 26

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

Answer 26

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

Question 27

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

Answer 27

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

strain (ε) = extension / original length

Question 28

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

Answer 28

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

Question 29

what is the Young Modulus a measure of?

Answer 29

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

Question 30

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

Answer 30

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

Question 31

outline an investigation to determine the young modulus of a metal

Answer 31

• 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

Question 32

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

Answer 32

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

Question 33

what does a larger spring/force constant mean?

Answer 33

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

Question 34

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

Answer 34

-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)

Question 35

what is the definition for ultimate tensile strength?

Answer 35

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

Question 36

what is a brittle material?

Answer 36

a brittle material will break with little or no plastic deformation

Question 37

what is a ductile material?

Answer 37

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

Question 38

what is a malleable material?

Answer 38

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

Question 39

what is a hard material?

Answer 39

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

Question 40

what is stiffness?

Answer 40

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

Question 41

what is a polymeric material?

Answer 41

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

Question 42

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

Answer 42

• 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