Materials: Solids

Question 1

Explain Hooke’s law

Answer 1

Hooke’s law states that up to a given load, the extension of a spring is directly proportional to the force applied to the spring and is given by F=k∆x

F=k∆x; k - spring constant, ‘represents stiffness’; ∆x - extension

Question 2

Define Stress, Strain and Young Modulus

Answer 2

- Stress = Force/Cross-sectional Area
σ = F/A   [Pa]
- Strain = Extension/Original length 
ε = Δl/l   [no units]
- Young Modulus = Stress/Strain
E = σ/ε   [Pa]

Question 3

Define Strength, Breaking Stress and Stiffness

Answer 3

Strength - an object is strong if it can withstand a large force before it breaks. Defined in terms of breaking stress
Breaking stress/Ultimate Tensile Strength (UTS) - the maximum stress that the material can endure
Stiffness - a stiff material exhibits very small deformations even when subjected to large forces (high Young modulus)

Question 4

Define Elastic and Plastic deformation

Answer 4

Elastic - the material regains its original dimensions when the deforming force is removed
Plastic - the material retains its shape after a deforming force is removed

Question 5

Explain Elastic strain energy:

a) Define
b) Formula
c) Formula with Hooke’s law

Answer 5

a) Potential energy is the ability of an object to do work by virtue of its position or state.
Elastic potential energy or - elastic strain energy - is therefore the ability of a deformed material to do work as it regains its original dimensions.
b) ∆W = Fav∆x; ∆W=Eel=1/2 k∆x^2

Question 6

Define Limit of proportionality, Elastic limit, Yield stress and Energy Density(on a stress/strain graph)

Answer 6

Limit of proportionality - the point at which the wire stops obeying Hooke’s law
Elastic limit - the point beyond which the wire ceases to be elastic. The end of elasticity
Yield stress - for stresses greater than this, the material will become ductile and deform plastically. The beginning of plasticity
Energy Density = Work Done/Volume = Area under the graph

Question 8

Define Brittle

Answer 8

Brittle - a brittle object will shatter or crack when subjected to dynamic shocks or impacts. Brittle materials undergo little or no plastic deformation before breaking (small plastic region) (glass, concrete, biscuits)

Question 9

Define Ductile

Answer 9

Ductile - can be drawn into wires. Most ductile materials are also malleable (copper wires - drawing out cylinders to the desired thickness)

Question 10

Define Hard

Answer 10

Hard - the harder the material, the more difficult it is to indent or scratch the surface. A simple method to compare the hardness of two materials involves finding out which scratches the surface of the other (diamond - can cut stuff)

Question 11

Define Malleable

Answer 11

Malleable - can be hammered into thin sheets (gold - can be hammered into ‘gold leaf’ which can be used for decorations)

Question 12

Define Stiff

Answer 12

Stiff - exhibits very small deformations even when subjected to large forces. A stiff material has a big value of Young Modulus (steel bridge)

Question 13

Define Strong

Answer 13

Strong - how much force can a materialwithstand before breaking (UTS) (glass, in a car window)

Question 14

Define Tough

Answer 14

Tough - a tough material is able to absorb the energy from impacts and shocks without breaking. A lot of plastic deformation in order to absorb energy (car tires get hot as they absorb energy from impacts, made of tough rubber/steel compositions)