Module 3: C6 - Materials

Question 1

What is Hooke’s Law

Answer 1

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

Therefore, 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.

Question 2

What does a Helical Spring undergo when tensile forces and compressive forces are extorted

Answer 2

A helical spring undergoes tensile deformation when tensile forces are exerted and compressive deformation when compressive forces are extorted.

Question 3

What is Hooke’s Law

Answer 3

The extension of a spring is directly proportional to the force applied. This is true as long as the elastic limit of the spring is not exceeded.

For forces less than the elastic limit of the spring, the spring obeys Hooke’s Law

Question 4

What happens when a Spring undergoes Plastic Deformation

Answer 4

When this happens, permanent structural changes to the spring occur and it does not return to its original length when the force is removed.

Question 5

How can you determine the force constant k from a force-extension graph

Answer 5

You can determine the force constant k from the gradient of the linear region of the force-extension graph.

Question 6

Worked Example: Force Constant of a Wire

A shelf of mass 14.00kg is supported by four identical wires. The original length of each wire was 1.800m. When attached to the shelf, the length of each wire is 1.804m. Calculate the force constant of each wire.

Answer 6

Step 1: Select the correct equation to calculate the force F acting on each wire.
The weight W of the shelf can be calculated using W = mg; assume that this weight is shared equally amongst the four wires.

F = weight/4 = 14.00 x 9.81 / 4 = 34.3N

Step 2: Determine the extension x of each wire.
x = new length - original length
= 1.804-1.800 = 0.004m

Step 3: Select the correct equation to calculate k.
F = kx
34.3 = k x 0.004
k = 34.3/0.004 = 9x10^4Nm^1

The force constant of each wire is 9x10^4Nm^-1.

Question 7

How can you Investigate Hooke’s Law

Answer 7

Attach the spring at one end using a clamp, boss, and clamp stand secured to the bench using a G-clamp or a large mass. Set up a meter rule with a resolution of 1mm close to the spring. Suspend slotted masses from the spring and, as you add each one, record the total mass added and the new length of the spring.

Question 8

How can you Improve the Accuracy of the experiment when Investigating Hooke’s Law

Answer 8

You can improve the accuracy of the length measurements using a set square, and by taking reading at eye level to reduce parallax errors. You might also measure the mass of each slotted mass using a digital balance. To obtain reliable results, aim to take at least six different reading and to repeat each one at least once.

Question 9

What does it mean for something to be ‘Elastic’

Answer 9

Up to a certain extension if the force is removed the spring will return to its original length. The spring is said to be behaving elastically.

If this critical extension is exceeded, known as the elastic limit, the spring will be permanently stretched.

Question 10

What does it mean for something to be ‘Plastic’

Answer 10

Plastic behaviour then occurs and Hooke’s law is no longer obeyed by the spring.

Question 11

What is the area underneath a Force-Extension graph

Answer 11

Area Underneath a Force-Extension Graph = Work Done

Question 12

How can you determine the quantity of potential energy stored in the spring

Answer 12

Ee = 1/2 Fx
F = kx

Therefore:
Ee = 1/2kx^2

Question 13

How is extension affected when springs are put in series

Answer 13

Each spring experiences the same pull from the weight of the mass it supports. Therefore, each spring extends the same amount as an individual spring would do.

Question 14

How is the Spring Constant affect when springs are put in series

Answer 14

The combination therefore is more ‘stretchy’ and th effective spring for the combination will be half that of a single spring for two in series, a third for three in series.

Question 15

How is extension affected when springs are put in parallel

Answer 15

The weight is supported by the combination. They share the load and therefore are not stretched as much as they would be if they were on their own supporting the load.

Question 16

How is the Spring Constant affect when springs are put in parallel

Answer 16

The combination therefore is les ‘stretchy’ and the effective spring constant for the combination will be twice that of a single spring for two in parallel, a three times for three in parallel.

Question 17

Worked Example: Firing a Spring

A compressible spring of force constant k = 50Nm^-1 and mass 4.0g is placed around a short horizontal rod. The spring is compressed by 8.0cm and then released.

a) Calculate the elastic potential energy in the spring when compressed

b) Calculate the speed of the spring immediately after it has fully extended. State any assumption made.

Answer 17

a)
Step 1: Write down all the quantities given in this question in SI units
K = 50Nm^-1, m = 4.0x10^-3, x = 0.08m

Step 2: Select the equation for the energy stored in the spring and calculate it.
E = 1/2kx^2 = 1/2 x 50 x 0.08^2 = 0.16J

b)
Step 3: Assume all the elastic potential energy in the spring is transferred to its kinetic energy. Therefore:
Kinetic Energy = 1/2mv^2 = 0.16J

Step 4: Rearrange the equation for v and then substitute the mass of the spring to calculate the speed.

v = √(2 x kinetic energy)/m
v = √(2x0.16)/(4.0x10^-3)
v = 8.9ms^-1

The speed of the spring is 8.9ms^-1

Question 18

Brittle Definition

Answer 18

Does not show plastic deformation and deforms only a little under stress (opposite of plastic)

Question 19

Strong Definition

Answer 19

Large ultimate tensile strength (UTS), holds a lot of force

Question 20

Weak Defintion

Answer 20

Low ultimate tensile strength (UTS) (opposite of strong)

Question 21

Hard Definition

Answer 21

It’s not easily scratched or dented

Question 22

Soft Defintion

Answer 22

Easily scratched or dented (opposite of hard)

Question 23

Ductile Definition

Answer 23

A very plastic material that can be stretched into wires.

Question 24

Tough Definition

Answer 24

Can take lots of kinetic force

Question 25

Malleable Definition

Answer 25

Can easily change shape

Question 26

What is the ‘loop’ formed by the loading and unloading curves

Answer 26

The ‘loop’ formed by the loading and unloading curves is called a hysteresis loop. You will recall that the area under a force-extension graph is equal to work done. More work is done when stretching a rubber band than is done when it’s extension decreases again. Thermal energy is released when the material is loaded then unloaded.

Question 27

Does a Metal Wire follow Hooke’s Law in a loading and unloading graph

Answer 27

The loading graph follows Hooke’s law until the elastic limit of the wire. The unloading graph will be identical for forces less than the elastic limit.

Question 28

Does a Rubber follow Hooke’s Law in a loading and unloading graph

Answer 28

Rubber bands do not obey Hooke’s Law. The rubber band will return to its original length after the force is removed - elastic deformation - but the loading and unloading graphs are both curved and are different.

Question 29

Does a Polythene follow Hooke’s Law in a loading and unloading graph

Answer 29

A polythene strip does not obey Hooke’s Law. Thin strips of polythene are very easy to stretch and they suffer plastic deformation under relatively little force.

Question 30

What is Tensile Stress

Answer 30

Tensile stress is defined as the force applied per unit cross-sectional area of the wire.

Question 31

Equation for Tensile Stress

Answer 31

Tensile Stress = Force / Cross-Sectional Area

σ = F/A

Question 32

What is Tensile Strain

Answer 32

Tensile strain is defined as the fractional change in the original length of the wire.

Question 33

Equation for Tensile Strain

Answer 33

Tensile Strain = Extension / Original Length

ε = x/L

Question 34

How is a Material Dense

Answer 34

Something is dense if it has a large mass per unit volume. Solid materials vary in density mainly because elements have different atomic masses. Lead is much more dense than aluminium, mainly because lead atoms are much heavier than aluminium atoms.

Question 35

How is a Material Tough

Answer 35

A material is tough it is doesn’t break by snapping cleanly. A tough material is resistant to the propagation of cracks. Toughness is the opposite of brittleness. Metals are tough and break by plastic flow. There is no one simple measure of toughness, but a tough material will dissipate a large amount of energy per unit area of new fracture surface.

Question 36

How is a Material Brittle

Answer 36

A material is brittle if it breaks by snapping cleaning. The brittleness of glass is a consequence of defects such as fine surface cracks, which propagate easily through the material.

Question 37

How is a Material Stiff

Answer 37

A material is stiff if it is difficult to stretch or bend the material (e.g, a metal sheet is stiffer than a polythene sheet of the same dimensions). The stiffness is indicated by the Young Modulus.

Question 38

How can Hardness be measured

Answer 38

By using Mohs Hardness Scale

Question 39

What is Stiffness

Answer 39

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 Young Modulus)

Question 40

What is Strength

Answer 40

Strength refers to the ultimate tensile strength (UTS). A greater UTS means a stronger material.

Question 41

What is Toughness

Answer 41

Toughness is a measure of the energy needed to break a material. Toughness is equal to the area under the stress-strain curve.

Question 42

Equation for the Young Modulus

Answer 42

E = σ / ε

Young Modulus = Tensile Strength / Tensile Strain

Question 43

What is P, the Limit of Proportionality on a Stress-Strain Graph

Answer 43

P is the limit of proportionality, where the linear relationship between stress and strain finishes.

Question 44

What is E, the Elastic Limit on a Stress-Strain Graph

Answer 44

E is the elastic limit. Below the elastic limit, the wire will return to its original shape.

Question 45

What is Y, the Yield Point on a Stress-Strain Graph

Answer 45

Y is the yield point, where plastic deformation begins. A large increase in strain is seen for a small increase in stress.

Question 46

What is UTS (Ultimate Tensile Strength) on a Stress-Strain Graph

Answer 46

UTS is the ultimate tensile stress, the maximum stress that is applied to a wire without its snapping.

Question 47

What is S, the Breaking Stress on a Stress-Strain Graph

Answer 47

S is the point where the wire snaps. It is sometimes called the breaking stress.

Question 48

‘5 Stages’ of a Stress-Strain Graph

Answer 48

• Spring follows Hooke’s law; it has elastic behaviour.
• Elastic limit is reached, it is permanently deformed.
• Spring shows plastic behaviour; little force causes big extension.
• Spring has reached its ultimate tensile stress (UTS).
• Spring has reached its breaking point and snaps.

Question 49

What happens in a Stress-Strain graph where the material behave Elastically

Answer 49

Strain is proportional to stress, up to a limit.
This is the initial straight section of the graph. In this part of the graph, the ratio stress / strain is constant and equal to the Young modulus of the material. Here the material behaves elastically.

Question 50

What happens in a Stress-Strain graph where the material reaches the Elastic Limit

Answer 50

The elastic limit is the point beyond which a material does not regain its initial shape when the tension is removed. It is also called the yield point.

Question 51

What happens in a Stress-Strain graph where the material passes beyond the Elastic Limit

Answer 51

When a material is stretched beyond its elastic limit, and is stretched beyond the yield point, it behaves plastically, suffering permanent deformation. The yield stress is the stress at the yield point.

Question 52

What happens in a Stress-Strain graph where the UTS is passed

Answer 52

As the tension is increased beyond the yield point, the
notes
stretched beyond the yield point, it behaves plastically, suffering permanent deformation. The yield stress is the stress at the yield point.
strain increases and a neck forms. Further stretching causes the stress to concentrate at the neck until it breaks. The breaking stress is equal to F / A where F is the force needed to break the material by stretching it and A is the initial area of cross section of the material. The breaking stress is also called the tensile strength of the material.

Question 53

How can you tell if a Material is Stiff or Flexible on a Stress-Strain Graph

Answer 53

Stiff materials will have steep gradients in a stress-strain graph, while flexible materials will have shallow gradients.

Question 54

How is a Material Hard

Answer 54

A material is hard if it is difficult to dent the surface of the material (e.g. a steel knife is much harder than a plastic knife). Hardness is tested by machines that indent the surface. Many ceramics are very hard.

Question 55

How is a Material Malleable

Answer 55

A material is malleable if it is easy it is to hammer or press a sheet of material into a required shape (e.g. a lead sheet is easier to fit on a roof than a steel sheet).

Question 56

How is a Material Ductile

Answer 56

A material is ductile if it is easy to draw a material into a wire (e.g. copper is easier to draw into a wire than tungsten). Metals are ductile because the non-directional metallic bonds allow ions to slide past one another.

Question 57

How is a Material Elastic

Answer 57

A material is elastic if it regains its shape after stretching (e.g. a rubber band regains its original length when released). When a metal or ceramic stretches elastically, the bonds between neighbouring atoms extend very slightly. In a polymer the atoms rotate about their bonds.

Question 58

How is a Material Plastic

Answer 58

A material is plastic if it undergoes large permanent stretching or distortion before it breaks (e.g. a polythene strip stretches permanently if pulled).