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Introduction to materials: density
The study of materials is important to inform decisions about
which materials to use for different things.
density = massvolumer =
m
V
It is important to consider properties of materials such as
density, and how materials react when forces are applied.
The image shows equal
volumes of brass, balsa
wood and polystyrene. Howwould their densities and
masses compare? What
could they be used for?
units: kgm3
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Finding the density
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Calculating the density
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Introduction to springs
The behaviour ofsprings is important since they have many
uses, from car and bike suspension to clock-making.
It is important to know how springs will react when forces
are applied.
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Tensile and compressive forces
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Restoring force
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Hookes law and the force constant
Hookes law states that the extension of a spring,x, is
directly proportional to the force applied to it, F.
Fx or F= kx where k is a constant.
kis called the force constant or the spring constant, orsometimes the stiffness constant. The units ofkare Nm-1.
xoriginal length
F
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Finding the force constant
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Calculating the force constant
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Elastic limit for springs
The elastic limit is a pointbeyond which the spring
will no longer return to its
original shape when the
force is removed.
Elasticity is the ability to
regain shape after deforming
forces are removed.
If a spring is stretched far enough, it reaches the limit of
proportionality and then the elastic limit.
extension
fo
rce
The limit of proportionality is a point beyond which
behaviour no longer conforms to Hookes law.
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What is elastic potential energy?
EPEis the energy stored in a bodydue to a load causing a deformation.
A stretched or compressed material, like
the spring in a jack-in-the-box when the lid
is closed, has elastic potential energy
(EPE) orelastic strain energy stored in it.
According to the principal of conservation of energy, no
energy is created or destroyed when a spring iscompressed. Therefore the work done in compressing the
spring is equal to the EPE stored in it, plus any energy
released as heat and sound.
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Calculating elastic potential energy
Work is done when a
spring is stretched; for
example, in stretching
chest expanders.
EPE = work done
If the conversion of mechanical energy into thermal energy is
ignored, work done is equal to EPE stored in the springs.
= average force extension
For a spring:
= Fd
= average force distance moved
EPE = Fx
EPE = work done
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Work done
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Match up the equations
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Stretching wires the variables
When using wires and
other materials, it is
important to know how
they will stretch if a
force acts on them.
The following propertiesmust be considered:
theYoung modulus (modulus of elasticity) of the material.
the length (L)
the cross-sectional area (a)
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What is the Young modulus?
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Young modulus calculation: example
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Stressstrain graphs
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Finding the Young modulus from graphs
Which material, A or B, has the larger Young modulus and
how can you tell?
tensile strain
ten
silestress
(Nm
2)
A
B
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Stiffness, strength and toughness
Stiffness, strength and toughness are all different properties
of materials.
Toughness is a measure of the energy needed to
break a material. Toughness is equal to the area
under the stressstrain curve.
Strength refers to the ultimate tensile stress (UTS).
A greater UTS means a stronger material.
Stiffness reflects how difficult it is to change the shape
or size of a material.Greater stiffness means a greater
value for the force constant, k, and a steeper gradient of
stressstrain curve (representing the Young modulus).
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More about properties of materials
A strong material may also be brittle, though at first this
seems counterintuitive.
It is also possible for a plastic material to be tough. How
would such a material behave under tensile testing and what
would its stressstrain curve look like?
A strong but brittle material
would have a linear stressstrain
curve, i.e. would break without
any plastic deformation takingplace. However, it would only
break under high stress, so the
end-point of the line would be at
a high y-value on the graph. tensile straintensilestress(Nm2
)high UTS
breaking
point
I i i i h
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Investigating stressstrain graphs
Diff t t f t i l
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Different types of material
M i th Y d l
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Measuring the Young modulus
The Young modulus of a wire can be measured in the
classroom without a tensile testing machine, using the set-up
below.
Young modulus =stress
strain=
FL
Ax
marker on wireruler
length of wire under test
How could the equipment could be used to find theYoung modulus? Remember the equation:
Y d l l l ti
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Young modulus calculations
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Gl
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Glossary
Wh t th k d?
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Whats the keyword?
M lti l h i i
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Multiple-choice quiz