Materials

Define density and its unit

• A measure of the ‘compactness’ of a substance. The mass per unit volume

• Unit: $\operatorname{kg}m^{-3}$

State the equation of density

$\rho=\frac{m}{v}$ = mass/volume

Describe the method to find the density of an object.

• Use a mass balance to measure the objects mass

• Use a ruler to measure dimensions of regular object

• Or for irregular objects: Use water displacement method with eureka can and measuring cylinder

State Archimedes principle

The upthrust force is equal to the weight of the fluid displaced. If the upthrust equals the weight of the object, the object will float.

Explain how (heavy cargo) ships float

They are large, so displace large volumes of water, which creates a large upthrust force allowing it to float

State the density of water at atmosphere pressure and room temperature

$$1000\operatorname{kg}m^{-3}$$

State Hooke’s Law

The extension of a wire or a spring is directly proportional to the force applied, up to the limit of proportionality

State the equation relating the force applied and the extension of a wire/string

$F=k\Delta L$, k=spring constant

State what happens to the spring with a greater spring constant

The greater the spring constant the stiffer the spring

Describe A, B, C, D, D-E in relation to Hooke’s law

• A = the linear section where Hooke’s law is being obeyed where the material is behaving elastically

• B = At the end of the linear section: the limit of proportionality

• C = Just beyond the straight section, where it reaches the elastic limit and starts to behave plastically

• D = Point of fracture/break point

• D-E = The unloading data where it has permanently deformed and has not returned to its original length

Describe what a non-linear Force extension graph means

That the material does not obey Hooke’s Law

Describe the graph of a rubber band

The rubber band extends and contracts by different degrees (non-linear=obeys Hooke’s Law) but still behaves elastically as it returns to its original length

Describe how the number of springs in series and parallel affect the spring constant of the system

• Series: $\frac{k}{n}$

• Parallel: $kn$

State 2 equations for elastic potential energy

energy$E_{p}=\frac12F\Delta L=\frac12k\left(\Delta L\right)^2=\frac{F^2}{2k}$

State what must be done to stretch a material

Work must be done

State the other name for elastic potential energy

Elastic Strain energy

State for elastic and plastic deformation the energy before and after being stretched, and how energy is lost

• For elastic deformation, the work done to stretch the material is equal to the amount of energy released when unloaded

• For plastic deformation, the work done to stretch the material is greater than the amount of energy released when unloaded

• Energy is lost through heat

State the energy changes for a mass on a spring

• Top = All GPE

• Equilibrium = Less GPE, More KE and EPE

• Bottom = All EPE

State what happens when a force is applied over a larger area

If a force is applied over a larger area, there is lower pressure and therefore has a smaller effect.

Define stress and strain in words and the units

• Stress = Force per unit cross-sectional area, in Pascals (Pa)

• Strain = Extension per unit length (no units)

In EPE equations what is F

F is the tension (in the string/wire/spring, not the weight)

Describe each point of a stress strain graph

• A = Limit of Proportionality → The point beyond which the extension is not directly proportional to force applied to it

• B = Elastic limit → Maximum force/stress that can be applied to the material before the material is permanently deformed

• C = Yield Point = Where the material continues to deform with no increase/less stress/load

• D = Ultimate tensile stress/strength = The maximum stress a sample can withstand

• E = Breaking Stress = The point at which a material deforms

• m = Young’s Modulus → stress/strain

State 2 equations that can be derived from Young’s Modulus = tensile stress / tensile strain

$$E=\frac{FL}{A\Delta L}=\frac{kL}{A}$$

Define Young’s Modulus

Its a measure of the stiffness of a material

What does it mean when the Young’s Modulus of a material is greater

The greater the Young’s Modulus, the stiffer the material is

Define ductile

The ability to be deformed plastically without breaking/be drawn into wires

Why is a material ductile

The layers of atoms slide over each other, making and breaking bonds, which prevents cracks

Define necking

Where the cross-sectional area of a material decreases significantly and unevenly. It occurs beyond its UTS. It occurs at points of concentrated stress+strain

Define brittle

When a material breaks with very little to no plastic deformation.

Why is a material brittle

Because the atoms are arranged in a giant rigid structure made up of very strong bonds. Applied stress causes tiny cracks which get bigger until fracture (a flat break).

Define a brittle fracture

When a material breaks suddenly with little to no plastic deformation

State some examples of ductile materials

Copper, aluminium, gold

State some examples of brittle materials

Glass, ceramic, cast iron