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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 = mass volume

=mV

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. How would their densities and masses compare? What could they be used for?

units: kg m–3


Finding the density


Calculating the density



Introduction to springs

The behaviour of springs 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.


Tensile and compressive forces


Restoring force


Hooke’s law and the force constant

Hooke’s law states that the extension of a spring, x, is directly proportional to the force applied to it, F.

F x or F = kx where k is a constant.

k is called the force constant or the spring constant, or sometimes the stiffness constant. The units of k are Nm-1.

xoriginal length

F


Finding the force constant


Calculating the force constant


Elastic limit for springs

The elastic limit is a point beyond 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

forc

e

The limit of proportionality is a point beyond which behaviour no longer conforms to Hooke’s law.



What is elastic potential energy?

EPE is the energy stored in a body due 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) or elastic strain energy stored in it.

According to the principal of conservation of energy, no energy is created or destroyed when a spring is compressed. 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 × extensionFor 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 properties must be considered:

the Young modulus (modulus of elasticity) of the material.

the length (L)

the cross-sectional area (a)


What is the Young modulus?


Young modulus calculation: example


Stress–strain 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

sile

str

ess

(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 stress–strain 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 stress–strain 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 stress–strain curve look like?

A strong but brittle material would have a linear stress–strain curve, i.e. would break without any plastic deformation taking place. 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 strain

ten

sile

str

ess

(Nm

–2)

high UTS

breakingpoint


Investigating stress–strain graphs


Different types of material


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 =stressstrain

=FLAx

marker on wireruler

length of wire under test

How could the equipment could be used to find the Young modulus? Remember the equation:


Young modulus calculations



Glossary


What’s the keyword?


Multiple-choice quiz

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1 of 36© Boardworks Ltd 2009. 2 of 34© Boardworks Ltd 2009