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AY BMSc Mechanics > Mechanics Notes > Flashcards

Mechanics Notes Flashcards

1
Q

What are the SI units for length, time, mass and angle?

A 
Length = m 
Time = sec
Mass = kg 
Angle = radian
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2
Q

What is the factor of 10 multiplier for mega (M)?

A

10(6)

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3
Q

What is the factor of 10 multiplier for milli (m)?

A

10(-3)

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4
Q

What is the factor of 10 multiplier for micro (µ)?

A

10(-6)

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5
Q

What is the difference between vectors and scalars?

A 
Scalar = magnitude only 
Vector = magnitude + direction
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6
Q

What are the 2 methods of combining vectors?

A

Graphically

Break down into components

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7
Q

How are rectangular coordinates described?

A

(x,y,z)

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8
Q

How are polar coordinates described?

A

(r, Θ)

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9
Q

How many degrees of freedom are there and what are they?

A

6 degrees of freedom (3 rotational, 3 translational)

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10
Q

Equation for calculating velocity

A

Velocity = distance/time

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11
Q

Units for velocity

A

m/s

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12
Q

Equation for gradient of a line

A

y = mx + c

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13
Q

What does the gradient in a displacement-time graph represent?

A

Velocity

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14
Q

How do you calculate the instantaneous velocity from a displacement-time graph?

A

Gradient of tangent

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15
Q

Equation for acceleration

A

a = ∆v/t

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16
Q

How is displacement calculated from velocity-time graph?

A

Area under graph

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17
Q

What are the SUVAT equations

A 
v = u + at
s = ½(u + v)t
v(2) = u(2) + 2as
s = ut + ½at(2)
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18
Q

What is 1 Newton equivalent to?

A

1 kg metres per second squared

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19
Q

Equation for density

A

p = m/v

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20
Q

What are the units for density?

A

kgm(-3)

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21
Q

Equation for weight

A

W = mg

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22
Q

What is the acceleration due to gravity on earth?

A

9.81

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23
Q

Rate the 3 types of friction from highest to lowest friction

A

Static (highest)
Sliding
Rolling (lowest)

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24
Q

Equation for coefficient of friction

A

µ = F/N

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25
Q

How do you calculate the maximum possible static friction force?

A

F (max) = Wµ

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26
Q

Equation for Pressure

A

P = F/A

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27
Q

Units for Pressure

A

Pascals (Pa)

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28
Q

What is 1 Pascal equivalent to?

A

1 Newton per metre squared

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29
Q

What is Newton’s third law?

A

Every action has an equal and opposite reaction

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30
Q

What is Newton’s second law?

A

F = ma

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31
Q

What is Newton’s 1st law?

A

A body will remain at rest unless acted on by a resultant force

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32
Q

How do you calculate the force of a skier going down a slope?

A

mgsinΘ

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33
Q

How do you calculated the force a skier is exerting on the slope?

A

mgcosΘ

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34
Q

Equation for momentum

A

p = mv

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35
Q

Units for momentum

A

kg m/s

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36
Q

What is a moment (torque)?

A

Tendency of a force to produce a rotation

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37
Q

Equation for moment

A

M = Fd

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38
Q

Units of moment

A

Nm

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39
Q

Equation for mechanical advantage

A

MA = Effort distance/Resistance distance

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40
Q

Describe a first class lever

A

Fulcrum lies between effort and resistance

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41
Q

Describe a second class lever

A

Resistance lies between fulcrum and effort

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42
Q

Describe a third class lever

A

Effort lies between resistance and fulcrum

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43
Q

Does each class of lever work at a mechanical advantage or disadvantage?

A

1st class = Either
2nd class = always advantage
3rd class = always disadvantage

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44
Q

Equation for tangential linear velocity

A

v = rω

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45
Q

Equation for tangential linear acceleration

A

a = rα

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46
Q

Equation for radial linear acceleration

A

a = rω(2)

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47
Q

What does the moment of inertia describe?

A

Measure of a body’s resistance to rotation (depends on distribution of mass and axis of rotation)

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48
Q

Equation for moment of inertia

A

I = mr(2)

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49
Q

What does it mean if a body has a high moment of inertia?

A

It is difficult to rotate

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50
Q

Equation for angular momentum

A

L = Iω

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51
Q

Equation for work

A

w = Fs

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52
Q

Units for work

A

Joules (J)

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53
Q

What is 1 Joule equivalent to?

A

1 kg m(2) s(-2)

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54
Q

Equation for Power

A

Power = work done/time taken

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55
Q

Equation for kinetic energy

A

KE = ½mv(2)

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56
Q

Equation for rotational KE

A

Rotational KE = ½Iω(2)

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57
Q

Equation for potential energy

A

PE = WH

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58
Q

What is the law of conservation of energy

A

Energy cannot be created or destroyed but can be changed from one form to another

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59
Q

Define stress

A

Force per unit area on a body that tends to cause it to change shape

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60
Q

Equation for stress

A

Stres = Force/Area

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61
Q

What units is stress measured in?

A

Pascals (Pa)

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62
Q

Define strain

A

A way of quantifying how something deforms

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63
Q

Equation for strain

A

strain = change in length/original length

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64
Q

What units is strain measured in?

A

Strain has no units as it is a ratio

65
Q

What are the 4 regions of a stress-strain curve?

A

Elastic region
Plastic region
Strain hardening
Necking

66
Q

In which region are stress and strain proportional?

A

Elasic region

67
Q

What does the highest point in a stress-strain graph represent?

A

Ultimate strength

68
Q

What does the area under a stress-strain curve represent?

A

Work done

69
Q

What is Hooke’s law?

A

Up to a certain level of stress, the strain produced is proportional to the applied stress

70
Q

What is Young’s Modulus a measure of?

A

Measure of the stiffness of a material (how difficult it is to deform under loading)

71
Q

Equation for Young’s modulus

A

E = stress/strain

72
Q

Units of Young’s Modulus

A

Pascals (Pa)

73
Q

How can Young’s Modulus be calculated from a stress-strain graph

A

Gradient of the line (up until p limit)

74
Q

What does a high or low Young’s modulus indicate?

A

Low E = flexible

High E = stiff

75
Q

Define rigidity

A

Ability to resist axial deformation

76
Q

Equation for Ridigity

A

G = Young’s Modulus (E) x cross-sec area

77
Q

Definition of stifness

A

Force required to produce a unit deflection

78
Q

Equation for stiffness

A

k = F/∆l

79
Q

Define flexibility

A

Deflection under a unit load (opposite of stiffness)

80
Q

Equation for flexibility

A

f = ∆l/F

81
Q

Describe viscous behaviour of a material

A

“Lazy”
Slow to deform (strain is prolonged)
After load is lifted will not return to previous shape

82
Q

Equation for coefficient of viscocity

A

η = stress/strain rate

83
Q

Example of 2 body materials that exhibit viscoelastic behaviour

A

Articular cartilage

Cortical bone

84
Q

Describe viscoelastic behaviour

A

Responds to rate of loading but returns to original shape eventually

85
Q

Name 2 behaviours that viscoelastic materials exhibit?

A

Creep

Stress relaxation

86
Q

What is creep?

A

The phenomenon of developing strain over time

87
Q

When are materials particularly vulnerable to creep?

A

At high temperatures

88
Q

What is stress relaxation?

A

If a material is kept under constant strain then the stress will gradually diminish over time (change in order of atoms)

89
Q

What are the 5 ways in which a body can be loaded?

A 
Tension 
Compression 
Shear 
Bending 
Torsion
90
Q

What is axial stress?

A

Tensile or compressive forces acting along a geometric axis

91
Q

How is shear stress calculated?

A

shear stress = shearing force/sheared area

92
Q

What is shear strain equivalent to?

A

Angle sheared

93
Q

How is shear strain calculated?

A

tanΦ = distance sheared/distance between 2 shearing forces

94
Q

What is shear strength?

A

Max shear stress a material can withstand before fracturing

95
Q

When does the largest shear stress occur in a material?

A

At 45 degrees to axial loading

96
Q

Equation for modulus of rigidity

A

G = shear stress/shear strain

97
Q

How does the largest shear stress relate to the axial stress?

A

Largest shear stress occurs in the planes at 45 degrees to axial loading and is equal to half the axial stress

98
Q

How does the modulus of rigidity relate to Young’s modulus?

A

G = E/2(1 + v)

v = Poisson’s ratio

99
Q

What are the 2 types of bending?

A

Cantilever

3-point bending

100
Q

Where is bending stress the greatest?

A

The further the layer from the axis the greater the stress

101
Q

What is a bending moment?

A

An internal moment to balance the external applied moments

102
Q

What terms are used to describe positive & negative bending moments?

A 
Sagging = +ve
Hogging = -ve
103
Q

When does the maximum bending moment occur?

A

At max length therefore M = FL

104
Q

An increase in which 2 factors would cause an increase in beam bending strength?

A

Young’s Modulus (E)

Cross-sec area

105
Q

How is the stress at a particular area calculated?

A

strain at particular layer x Young’s Modulus

106
Q

How is the strain at a particular layer of a beam calculated?

A

Displacement from neutral axis/radius

107
Q

Which distribution of mass is mostly likely to resist bending?

A

Mass distributed away from neutral axis

108
Q

How is the maximum bending moment calculated?

A

(max bending stress x second moment of area) / max displacement of extreme layer from neutral axis

109
Q

What is the second moment of area?

A

Measure of how resistant something is to bending

110
Q

What causes a material to have a high second moment of area?

A

Further the material is concentrated away from the neutral axis the higher the SMOA

111
Q

What is the beam equation?

A

M/I = S/Y = E/R

M = Bending Moment
I = second moment of area 
S = stress
Y = distance from enutral axis 
E = Young's Modulus 
R = Radius you bend round
112
Q

Where is the max and min deflection of a beam under torsional stress?

A 
Max = free end 
Min = fixed end
113
Q

What does the modulus of rigidity describe?

A

Indication of how resistant something is to stress (higher = more resistant)

114
Q

How do you calculate shear stress in torsion?

A

(G x angle of twist x radius) / length

115
Q

How do you calculate strain in torsion?

A

(Angle of twist x radius) / Length

116
Q

What is the polar second moment of area?

A

Measure of distribution of material around an axis (and therefore it’s resistance to torsion)

117
Q

Which shape is most effective at resisting torsion?

A

Hollow tube

118
Q

What is the torsion equation?

A

M/J = T/R = GΘ/L

M = Twisting moment 
J = Polar second moment of area
T = sheat stress
R = Radius of cross section 
G = Modulus of rigidity 
Θ = angle of twist 
L = Length
119
Q

How does muscle activity affect stress distribution in bones?

A

Reduces tensile stress as bones are stronger in compression

120
Q

What is a strain gauge and what are it’s advantages and disadvantages of a strain gauge?

A

Measures strain at surface of a structure
Adv - can be applied to actual structure
Disadv - difficult to apply and not intended for complex structures

121
Q

What does photoelasticity do?

A

Enables weak areas of structures to be identified

122
Q

How does the finite element work?

A

Breaks the problem down to millions of small problems that a computer solves

123
Q

Which 3 factors affect failure of a bone under stress?

A

Magnitude of load
Rate of speed load is applied
No. of times load is applied

124
Q

What is the fracture/rupture strength?

A

Stress at which bone fractures

125
Q

What is the difference between a ductile and a brittle fracture?

A 
Ductile = with necking 
Brittle = without necking
126
Q

What characterises a ductile fracture?

A

Necking
Flat granulated central portion
Small shear lip

127
Q

Describe the process of a ductile fracture

A

Begins with the formation of microscopic voids at centre (separation of grain boundaries)
Deformation by shearing also contributes

128
Q

When will a normally ductile material respond like a brittle material?

A

If it has been exposed to fatigue loading

129
Q

Describe the process of a brittle fracture

A

Occurs suddenly without plastic deformation
Fracture surface is flat with granular appearance
Another characteristic appearance is chevron

130
Q

What are stress concentrations?

A

Points at which stress is greater than the average for the material

131
Q

What reduces the risk of stress concentrations?

A

Gentle transitions between cross-sections

Smooth surfaces

132
Q

What test is used to test impact resistance?

A

Charpy impact test

133
Q

What type of material is most impact resistant?

A

Ductile

134
Q

How is impact energy calculated in Charpy’s test?

A

Impact energy = W(ho - hf)

135
Q

At what temperature are materials able to absorb more energy?

A

Higher temps (changes material from brittle to ductile)

136
Q

Is there more energy released from a fatigue fracture or a quickly loaded fracture?

A

If loaded quickly mor eenergy is released if it does fracture

137
Q

Are granular & fibrous layers brittle or ductile fratures?

A

Granular - brittle

Fibrous - ductile

138
Q

What might be seen in the fatigue fracture of a hip prothesis?

A

Clam shell markings

139
Q

Example of fatigue fracture in bone

A

March fracture (in metatarsals)

140
Q

Why is frequency important when considering fatigue fractures?

A

Bone can remodel

141
Q

What can be used to reduce the likelihood of a material corroding?

A 
Passivation layer (already eroded but won't anymore) 
Corrosion resistant material
142
Q

What makes a material particularly vulnerable to corrosion?

A

Crevices

143
Q

What is the most common ferrous allow used?

A

Steel

144
Q

What effect does increasing the carbon content of steel have?

A

Steel becomes harder but more brittle

145
Q

What is the ideal structure of steel?

A

Low carbon inside and high carbon outside

146
Q

What is different about a stainless steel?

A

Contains 12-18% chromium by weight (chromium forms passivation layer)

147
Q

What are the advantages of titanium based alloysl?

A

Lower density
Higher strength-to-weight ratio than aluminium
Excellent corrosion resistance

148
Q

What are the disadvantages of titanium based alloys?

A

High cot
High fabrication cost
Low Young’s modulus (will deform more under load)

149
Q

What are the properties of polymers?

A

Lightweight corrosion resistant electrical insulators
Low tensile strength and melting points
Low density
Easy to manufacture
Exhibit BOTH plastic and elastic behaviour

150
Q

What is the difference between thermoplastics and thermosets?

A

Thermo plastics - display plastic behaviour at high temps can be cooled and reheated
Thermosets - cannot be reformed during formation t hgih temps

151
Q

What are elastomers?

A

Rubbers - can deform by massive amounts without permanent shape change

152
Q

What are the properties of ceramics?

A

Crystalline structure
High hardness but cutable along planes
High melting point
Low electrical and thermal conductivity

153
Q

Where in orthopaedics are ceramics used

A

Heads of hip prostheses

154
Q

How does stiffness relate ro rigidity?

A

Stiffness = rigidity per unit length

155
Q

How do you calculate the maximum shear stress acting in a bar under axial load ?

A

stress/2`

156
Q

What are the units of shear strain?

A

Radians

157
Q

How do you claculate the maximum bending moment?

A

(stress x second moment of srea) / max displacement from neutral axis

158
Q

What is the equation for second moment of area for a rectangular cross section?

A

I - bd(3) / 12

y(max) = ½d

AY BMSc Mechanics (1 decks)

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