Module 3.4 - Hooke's law ✓

Question 1

State Hooke’s law?

Answer 1

The force applied to a spring is directly proportional to the extension of the spring provided the elastic limit is not exceeded

Question 2

What is the Hooke’s law equation?

Answer 2

F = Kx

Question 3

What is the limit of proportionality (P)?

Answer 3

The limit of proportionality is the point at which a material stops obeying Hooke’s law, but will still return to its original shape if the stress is removed

Question 4

What is the elastic limit (E)?

Answer 4

The elastic limit is the point at which, if exceeded, a material starts to behave plastically (will be permanently stretched).

Question 5

How do you combine force constants of springs in series?

Answer 5

1/Kt = 1/K1 + 1/K2

Question 6

How do you combine the force constants of springs in parallel?

Answer 6

Kt = K1 + K2

Question 7

Explain elastic deformation (in terms of the atoms in the material)?

Answer 7

1) When the material is under tension, its atoms are pulled apart from one another
2) Atoms can move slightly relative to their equilibrium positions, without changing position in the material
3) Once load is removed, the atoms return to their equilibrium distance apart

Question 8

Explain plastic deformation (in terms of atoms in the material)?

Answer 8

Some atoms in the material move relative to one another, so when the load is removed the atoms don’t return to their original positions

Question 9

What is Tensile stress?

Answer 9

Tensile stress - the force applied per unit cross-sectional area

Question 10

What is the equation for tensile stress?

Answer 10

σ = F/A
stress = force / cross-sectional area

Question 11

What is stress measured in?

Answer 11

Pascals (Pa). or newtons per square metre (Nm^-2)

Question 12

What is tensile strain?

Answer 12

Tensile strain - The extension per unit length of a material`

Question 13

What is the equation for tensile strain?

Answer 13

ɛ = x/l
strain = extension/original length

Question 14

What are the units for tensile strain?

Answer 14

No units :)

Question 15

What is breaking stress (B)?

Answer 15

Breaking stress is the stress at which a material breaks.

Question 16

What happens at the breaking stress point B?

Answer 16

Eventually the atoms in the material are pulled so far apart that they separate completely and the material breaks.

Question 17

What is the Ultimate Tensile Stress (UTS) of as material?

Answer 17

Ultimate Tensile Stress - The maximum stress that a stretched material can withstand before breaking

Question 18

How do you find work done to deform a stretched/compressed material?

Answer 18

Work done to deform a material is the area under the force/extension graph.
NOT the same as F*x. It’s actually W = ½Fx

Question 19

How is energy transferred when work is done to stretch a material?

Answer 19

Before the elastic limit, work done is stored as elastic potential energy in the material (except for rubber)
Therefore area under force-extension graph = EPE

Question 20

What is the equation for elastic potential energy for an extended/compressed material?

Answer 20

E = ½Kx^2
E = ½Fx

Question 21

Derive the equation E=½kx^2

Answer 21

1) W = Fx, however the force on a material being stretched isn’t constant so you need to use the average force applied between 0 and F (i.e. ½F). So W = ½Fx
2) Therefore EPE, E = ½Fx
3) Because Hooke’s law is being obeyed (before limit of proportionality) then F = kx. So E=½kx^2

Question 22

What is the Young’s modulus of a material?

Answer 22

Young’s modulus - A measure of the stiffness of a material. The ability of a material to withstand changes in length under tension/compression

Question 23

What is the equation for the Young’s modulus?

Answer 23

Young’s modulus = stress/strain

E = σ/ɛ

Question 24

What are the units for Young’s modulus?

Answer 24

Pascals or Newtons per square metre (Pa/Nm^-2)

Question 25

How do you calculate the elastic potential energy per unit volume from a stress/strain graph?

Answer 25

The elastic potential energy per unit volume for a material is the area under the material's stress strain graph

Question 26

What is the equation for elastic potential energy per unit volume?

Answer 26

Energy per unit volume = ½σɛ | PROVIDED HOOKE'S LAW IS OBEYED

Question 27

What is the Yield point Y of a material?

Answer 27

Yield Point - The stress at which a large amount of plastic deformation will take place without any extra load

Question 28

What does the graph for a ductile material look like?

Answer 28

E.g. a metal wire. It has ALL ZE POINTS | P, E, Y1 (yield point), Y2(lowest point after yield point), UTS, B

Question 29

What happens after the yield point?

Answer 29

Beyond the yield point, at y2, a small increase in stress causes a large increase in strain. The wire undergoes 'plastic flow'

Question 30

What does the stress-strain graph for a brittle material look like?

Answer 30

It has a limit of proportionality then a breaking point soon after. It DOES NOT undergo plastic deformation.

Question 31

Why do brittle materials have no elastic limit?

Answer 31

When stress is applied to a brittle material, tiny cracks at the material's surface get bigger and bigger until the material breaks completely. < Called brittle fracture!

Question 32

What is the difference between a stiff and strong material?

Answer 32

Stronger materials have higher breaking stresses, however stiffer material will have lower strain. A strong and stiff material will have high breaking stress but low strain, whereas a weak and less stiff will have a low breaking stress but a large strain.

Question 33

Why do different polymeric materials have different stress-strain graphs?

Answer 33

The molecules making up polymeric materials are arranged in long chains which have a range of properties so different polymers have different stress-strain graphs.

Question 34

What is the stress-strain graph for polythene?

Answer 34

Look in book because hard to describe

Question 35

What type of material is polyethene?

Answer 35

Polyethene is a ductile material despite behaving plastically when stretched

Question 36

How does rubber behaved when stretched?

Answer 36

Rubber behaves elastically, returning to its original length when the load is removed

Question 37

Explain why the loading and unloading curves for rubber are different?

Answer 37

Some of the elastic potential energy stored in stretched rubber is converted to heat, meaning the energy released when the rubber is unloaded is less than the work done to load/stretch it.

Question 38

What does the area between the loading and unloading stress-strain curves for rubber give you?

Answer 38

The amount of energy converted to heat per unit volume is given by the area between the loading and unloading curves