Chapter 6- Materials

Question 1

Within Hooke’s law region

Answer 1

F = kx 
Force = force constant x extension
N = Nm-1 x m

Question 2

Past the elastic limit

Answer 2

Hooke’s law no longer applies (greater extension)

Plastically deformed as it doesn’t return to the same length when you let it go

Question 3

Energy stored in spring

Answer 3

1/2 k x^2

Substitute Hooke’s law into the area under the curve (E = 1/2 Fx)

Question 4

Springs in series

Answer 4

On top of each other

The inverse of the total force constant is the sum of the inverse of each

Question 5

Springs in parallel

Answer 5

Alongside each other
The total force constant is the sum of each individual
The force applied to each is the total force divided by the number of springs

Question 6

Brittle

Answer 6

Fails under load by cracking - little plastic deformation

Question 7

Ductile

Answer 7

Can be drawn into wires and have a very large plastic region

Question 8

Hysteresis Loop

Answer 8

An example is rubber
The area under the loading line is greater than the area under the unloading line
Still follows Hooke’s law
Shows energy is transferred to thermal (difference in areas under)

Question 9

Work from force extension graph

Answer 9

Area under the loading curve

Question 10

Energy stored from force extension graph

Answer 10

Area under unloading curve

Question 11

Stress

Answer 11

The force per cross-section area

Question 12

Stress equation

Answer 12

Stress = Force/Area
σ = F/A

Units Pa or Nm^-2

Question 13

Strain

Answer 13

A measure of the relative change in length, the extension per unit length

Question 14

Strain equation

Answer 14

Strain = extension/original length
ε = x/L

No units

Question 15

Young’s Modulus

Answer 15

Stiffness = Stress/strain
E = σ/ε
E = F/A divided by x/L
E = FL/Ax

Units Pa/Nm^-2

Question 16

Stress-strain vs force-extension graphs

Answer 16

Both have the same shape, stress-strain preferable as they depend on the properties of a material rather than the dimensions

Question 17

Stress-strain graph shape

Answer 17

Increase proportionally until the limit of proportionality, when strain is greater. Then it reaches the elastic limit in this section. It reaches a yield point where a large amount of plastic deformation (strain) happens without extra load. It flattens before increasing slightly to a peak (ultimate tensile strength) before decreasing as it breaks.

Question 18

Metal wire

Answer 18

Follows Hooke’s law until a fairly high elastic limit and then starts to curve
Unloading curve identical to loading before elastic limit
After the elastic limit, the unloading curve is parallel to the the Hooke’s law region all the way up

Question 19

Rubber

Answer 19

Loading curve starts with a high gradient before flattening and then rising again
Unloading curve broadly the same shape but lower
Does not follow Hooke’s law
When strain is the x-axis

Question 20

Polythene

Answer 20

Does not obey Hooke’s law, no elastic region
Loading curve similar to rubber but steeper earlier on
The unloading curve is a steep straight line not passing through the origin to represent plastic deformation

Question 21

Thermal energy wasted from a force extension graph

Answer 21

Area between the loading and unloading curves