Materials

Question 1

What is meant by density?

Answer 1

The mass per unit volume of an object

Question 2

What do objects made from low-density materials typically attain in terms of mass?

Answer 2

They usually have a lower mass

Question 3

What is the density equation?

Answer 3

ρ = m/V

Where:
* ρ = density (kgm^-3)
* m = mass (kg)
* V = volume (m³)

Question 4

How is the volume of a sphere calculated?

Answer 4

V = 4/3 πr³

Where:
* V = volume (m³)
* r = radius of sphere (m)

Question 5

How is the volume of an equal sided cube calculated?

Answer 5

V = d³

Where:
* d = length of the equal cube faces (m)

Question 6

How is the volume of a cuboid calculated?

Answer 6

V = l x w x h

Where:
* l = length (m)
* w = width (m)
* h = height (m)

Question 7

How is the volume of a cylinder calculated?

Answer 7

V = πr² x l

Where:
* πr² = area of a circle (m²)
* l = length of the cylinder (m)

Question 8

What does Archimedes’ principle state?

Answer 8

An object submerged in a fluid at rest has an upward buoyancy force (upthrust) equal to the weight of the fluid displaced by the object

Question 9

What is meant by buoyancy?

Answer 9

The ability of an object to float or rise up when placed in a fluid (water or air)

Question 10

When a buoyant object is submerged in a fluid, why does it stop sinking?

Answer 10

The object sinks until the weight of the fluid displaced is equal to its own weight. Therefore the object floats when the magnitude of the upthrust equals the weight of the object.

Question 11

How can the magnitude of upthrust acting on a submerged object be calculated?

Answer 11

• Find the volume V of the submerged object (which is also the volume of the displaced fluid)
• Find the weight of the displaced fluid
• Since m = ρV (density x volume), upthrust is equal to F = mg (which is the weight of the fluid displaced by the object)

Question 12

How does Archimedes’ principle explain how boats float?

Answer 12

• The boat has a weight that acts down into the water
• When this happens, water is displaced, and the boat sinks into the water
• When the amount of water displaced is an equal weight to that of the boat, an upthrust (buoyancy force) of an equal magnitude to the boats weigth is applied, meaning that the boat floats
• mass of displaced water = mass of boat submerged

Question 13

How can the density equation (ρ = m/V) and the weight equation (W = mg) be combined to create an equation to find the force of upthrust on a submerged object?

Answer 13

• Re-arrange the density equation for mass: m = ρV
• Substitute in for m in the weight equation: W = ρVg
• W = ρVg

Question 14

What is the definition of viscous drag?

Answer 14

The frictional force between an object and a fluid which opposes the motion between the object and the fluid

Question 15

How is viscous drag calculated?

Answer 15

Using Stokes’ Law:

F = 6πηrv

Where:
* F = viscous drag (N)
* η = coefficient of viscosity of the fluid (Ns m^-2 or Pa s)
* r = radius of the object (m)
* v = velocity of the object (ms^-1)

Question 16

What is meant by a coefficient?

Answer 16

A number that multiplies a variable, showing how much influence that variable has in an equation.

(e.g. in the term 6𝑥, the number 6 is the coefficient of 𝑥)

Question 17

What is Stokes’ Law?

Answer 17

F = 6πηrv

Where:
* F = viscous drag (N)
* η = coefficient of viscosity of the fluid (Ns m^-2 or Pa s)
* r = radius of the object (m)
* v = velocity of the object (ms^-1)

Question 18

Wnat is meant by the viscosity of a fluid?

Answer 18

How much a fluid resists flowing (or how thick it is)

Question 19

What is meant by the coefficient of a fluids viscosity (can just be called viscosity)?

Answer 19

An indication of how much the fluid will resist flow

Question 20

What is the relationship between the rate of flow of a fluid and its (coefficient of) viscosity?

Answer 20

They are inversely proportional

(If the rate of flow of the fluid is slow, a.k.a the fluid moves slowly, then its viscosity is high)

Question 21

At an objects terminal velocity, what can be said about the forces acting on it?

Answer 21

They are balanced, and the object is in equilibrium

(The object is moving at a constant velocity as it cannot accelerate further)

Question 22

How can terminal velocity be useful when working with Stokes’ Law?

Answer 22

At terminal velocity, the forces acting on an object are balanced meaning:

W = F_d + U

Where:
* W = weight of the sphere (N)
* F_d = the drag force (N)
* U = upthrust (N)

Question 23

How can the weight of a spherical object falling at terminal velocity be found using volume, density, and gravitational force?

Answer 23

W = v_sρ_sg

WHICH EQUALS

W = 4/3 πr³ρ_sg

Where:
* v_s = volume of the sphere (m³)
* ρ_s = density of the sphere (kg m^-3)
* g = gravitational force (N kg^-1)

Question 24

In terms of an object being submerged, what value is the weight of the fluid being displaced equal to?

Answer 24

The force of upthrust acting on the object

Question 25

How can the terminal velocity of a spherical object falling through a viscous liquid be calculated?

Answer 25

v_term = (2πr²g(ρ_s - ρ_f))/9πη Where: * v_term = terminal velocity (ms^-1) * g = gravitational force (N kg^-1) * ρ_s = density of the sphere (kg m^-3) * ρ_f = density of the fluid (kg m^-3) * η = viscosity of the fluid (Ns m^-2 or Pa s)

Question 26

What relationships does the equation below show involving the terminal velocity of a spherical object moving through a viscous fluid? v_term = (2πr²g(ρ_s - ρ_f))/9πη

Answer 26

Terminal velocity is: * directly proportional to the square of the radius of the sphere * inversely proportional to the viscosity of the fluid

Question 27

What are the conditions that must be met for the Stokes' law equation to be used?

Answer 27

* The flow must be **laminar** * The object must be small * The object must be spherical * The motion between the sphere and the fluid must be at a slow speed

Question 28

What is meant by **laminar** flow?

Answer 28

When an object moves through a fluid (or vice versa) the layers in a fluid: * all move in the same direction * do not mix This tends to happen for slow-moving objects or slow-flowing liquids

Question 29

What is meant by **turbulent** flow?

Answer 29

When an object moves through a fluid (or vice versa) the layers in a fluid: * all move in different directions * mix with each other

Question 30

How can the viscosity of a fluid be changed?

Answer 30

With a change in temperature

Question 31

What is the relationship between temperature and the viscosity of a **liquid**?

Answer 31

Since a liquids viscosity depends on intermolecular forces, its **viscosity tends to decrease** (becomes less viscous) **as temperature increases** (η ∝ 1/T)

Question 32

What is the relationship between temperature and the viscosity of a **gas**?

Answer 32

Since a gases viscosity depends on intermolecular collisions, its **viscosity tends to increases** (become more viscous) **as temperature increases** (η ∝ T)

Question 33

How can the viscosity of a fluid be calculated when an object is falling at terminal velocity through it?

Answer 33

η = (2r²g(ρ_s - ρ_f))/9v_term Where: * η = viscosity (Ns m^-2 OR Pa s) * r = radius of the sphere (m) * g = gravitational force (N kg^-1) * ρ_s = density of the sphere (kg m^-3) * ρ_f = density of the fluid (kg m^-3) * v_term = terminal velocity (ms^-1)

Question 34

If a material obeys Hooke's law, what relationship would be seen?

Answer 34

The extension of the material is directly proportional to the applied force (load) up to the limit of proportionality

Question 35

What would happen to a vertically positioned wire if a force is added to the bottom of it?

Answer 35

The wire would stretch

Question 36

What is Hooke's law equation?

Answer 36

∆F = k∆x Where: * F = applied force (N) * k = spring constant (N m^-1) * ∆x = extension (m)

Question 37

What is meant by the spring constant?

Answer 37

A property of a material that is stretched which measures its stiffness

Question 38

If an object has a large spring constant, what does that say about its stiffness?

Answer 38

It has a high stiffness

Question 39

What types of deformation of a material does Hooke's law apply to?

Answer 39

* Extension (stretching) * Compression (squeezing)

Question 40

What is meant by the extension of an object?

Answer 40

How much it has increased in length

Question 41

What is meant by the compression of an object?

Answer 41

How much it has decreased in length

Question 42

What are the features of a force-extension graph in regards to Hooke's law?

Answer 42

The key features of the graph are: * **The limit of proportionality** - the point beyond which Hooke's law is no longer true when stretching a material (i.e. the extension is no longer proportional to the applied force), which is shown on the graph where the line starts to curve (flatten out) * **Elastic limit** - the maximum amount a material can be stretched and still return to its original length (above which the material will no longer be **elastic**). This point is always **after** the limit of proportionality. * **The spring constant** - given by the gradient of this graph

Question 43

What does it mean if a material is **elastic**?

Answer 43

The material returns to its original shape and size once a force is removed

Question 44

What is meant by **stress** in terms of materials?

Answer 44

The applied force per unit cross sectional area of a material

Question 45

What are the two types of forces that can act on a material?

Answer 45

* Tensile forces (which pull on an object and extend it) * Compressive forces (which push onto an object and compress/squash it)

Question 46

What is the equation for **stress**?

Answer 46

σ = F/A Where: * σ = stress (Pa or Nm^-2) * F = force (N) * A = cross-sectional area (m²)

Question 47

What are the units of **stress**?

Answer 47

Newtons per squared metre (Nm^-2) **OR** Pascals (Pa)

Question 48

What is meant by the **ultimate tensile stress** of a wire?

Answer 48

The maximum force per original cross-sectional area that a wire is able to support until it breaks

Question 49

What is meant by **strain** in terms of materials?

Answer 49

The extension per unit length of a material (a.k.a. the ratio between the extension/compression and the original length)

Question 50

What property of a material can be defined as the deformation of a solid due to stress in the form of elongation or contraction?

Answer 50

Strain

Question 51

What is the equation for **strain**?

Answer 51

ε = ∆x/x Where: * ε = strain * ∆x = extension (m) * x = length (m)

Question 52

What are the units of **strain**?

Answer 52

No units (it is a ratio)

Question 53

What is the definition of the Young modulus?

Answer 53

The measure of the ability of a material to withstand changes in length with an added force (i.e. how stiff a material is)

Question 54

What is the Young Modulus equation?

Answer 54

E = σ/ε Where: * E = Young modulus (Pa) * σ = stress (Pa) * ε = strain

Question 55

What is the relationship between **stress** and **strain**?

Answer 55

They are directly proportional (σ ∝ ε)

Question 56

What is the gradient given by a stress-strain graph when it is linear?

Answer 56

The Young Modulus

Question 57

What type of graph can show the way that a material responds to a tensile force?

Answer 57

A force-extension graph

Question 58

What does it mean if a material is **brittle**?

Answer 58

The material fractures after its elastic limit is exceeded (e.g. glass)

Question 59

What does it mean if a material is **ductile**?

Answer 59

The material has the capacity to **deform plastically**, such as being drawn into a wire (e.g. steel and copper)

Question 60

What is the main difference between **elastic** and **plastic** deformation?

Answer 60

* Elastic deformation means the object will return to its original shape or length when the force acting on it is removed. * Plastic deformation means that the object will permanently deform and therefore doesn't return to its original shape or length. This happens after the elastic limit of a material has been exceeded.

Question 61

What can be inferred about Hooke's Law if a force-extension graph shows a straight line through the origin?

Answer 61

This suggests that the material obeys Hooke's law up until a point (the limit of proportionality)

Question 62

On an applied force-extension graph, what type of deformation is shown **before** the elastic limit?

Answer 62

Elastic deformation

Question 63

On an applied force-extension graph, what type of deformation is shown **after** the elastic limit?

Answer 63

Plastic deformation

Question 64

What is the **yield point** on an applied force-extension graph?

Answer 64

Where the material continues to stretch even though no extra force is being applied to it

Question 65

What indication of the properties of materials do stress-strain curves give?

Answer 65

* The maximum stress and strain that a material can withstand and still obey Hooke's law * Whether it exhibits elastic and/or plastic behaviour * The value of their Young Modulus * The value of their **breaking stress**

Question 66

What is meant by the **breaking stress** of a material?

Answer 66

The stress at the point where the material breaks

Question 67

What key features of a material do both force-extension and stress-strain graphs show?

Answer 67

* The limit of proportionality * The elastic limit * The yield point * Elastic deformation * Plastic deformation

Question 68

What two features of a material can't be found on a force-extension graph, but can be found on a stress-strain graph?

Answer 68

* The Young Modulus (from the gradient) * The breaking stress

Question 69

What is meant by the point of the **limit of proportionality** on force-extension and stress-strain graphs?

Answer 69

The point beyond which, Hooke's law is no longer true when stretching a material (i.e. the extension is no longer proportional to the applied force). This is shown on the graphs where the line starts to curve (flatten out)

Question 70

What is meant by the **elastic limit** point on force-extension or stress-strain graphs?

Answer 70

The maximum amount a material can be stretched and still return to its original length (above which the material will no longer be **elastic**). This point is always **after** the limit of proportionality.

Question 71

How can the **elastic strain energy** be determined on a force-extension graph for a material which obeys Hooke's law?

Answer 71

By finding the area under the graph

Question 72

What is meant by the **elastic strain energy** of a material?

Answer 72

A store of all the work done (J) to stretch a material before it reaches its elastic limit (whilst it obeys Hooke's Law)

Question 73

What is the equation for calculating the elastic strain energy of a material?

Answer 73

∆E_el = 1/2 F∆x Where: * E_el = elastic energy (or work done) (J) * F = average force (N) * ∆x = extension (m)

Question 74

How can the elastic strain energy of a material be calculated when combining Hooke's law?

Answer 74

∆E_el = 1/2 k(∆x)² Where: * E_el = elastic strain energy (J) * k = spring constant (Nm^-1) * ∆x = extension (m)