Boardworks Materials

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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



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



Finding the force constant



Calculating the force constant



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.



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.



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



Work done



Match up the equations



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)



What is the Young modulus?



Young modulus calculation: example



Stressstrain graphs



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



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).



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



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

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