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
2
Q
What is the factor of 10 multiplier for mega (M)?
A
10(6)
3
Q
What is the factor of 10 multiplier for milli (m)?
A
10(-3)
4
Q
What is the factor of 10 multiplier for micro (µ)?
A
10(-6)
5
Q
What is the difference between vectors and scalars?
A
Scalar = magnitude only Vector = magnitude + direction
6
Q
What are the 2 methods of combining vectors?
A
Graphically
Break down into components
7
Q
How are rectangular coordinates described?
A
(x,y,z)
8
Q
How are polar coordinates described?
A
(r, Θ)
9
Q
How many degrees of freedom are there and what are they?
A
6 degrees of freedom (3 rotational, 3 translational)
10
Q
Equation for calculating velocity
A
Velocity = distance/time
11
Q
Units for velocity
A
m/s
12
Q
Equation for gradient of a line
A
y = mx + c
13
Q
What does the gradient in a displacement-time graph represent?
A
Velocity
14
Q
How do you calculate the instantaneous velocity from a displacement-time graph?
A
Gradient of tangent
15
Q
Equation for acceleration
A
a = ∆v/t
16
Q
How is displacement calculated from velocity-time graph?
A
Area under graph
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)
18
Q
What is 1 Newton equivalent to?
A
1 kg metres per second squared
19
Q
Equation for density
A
p = m/v
20
Q
What are the units for density?
A
kgm(-3)
21
Q
Equation for weight
A
W = mg
22
Q
What is the acceleration due to gravity on earth?
A
9.81
23
Q
Rate the 3 types of friction from highest to lowest friction
A
Static (highest)
Sliding
Rolling (lowest)
24
Q
Equation for coefficient of friction
A
µ = F/N
25
How do you calculate the maximum possible static friction force?
F (max) = Wµ
26
Equation for Pressure
P = F/A
27
Units for Pressure
Pascals (Pa)
28
What is 1 Pascal equivalent to?
1 Newton per metre squared
29
What is Newton's third law?
Every action has an equal and opposite reaction
30
What is Newton's second law?
F = ma
31
What is Newton's 1st law?
A body will remain at rest unless acted on by a resultant force
32
How do you calculate the force of a skier going down a slope?
mgsinΘ
33
How do you calculated the force a skier is exerting on the slope?
mgcosΘ
34
Equation for momentum
p = mv
35
Units for momentum
kg m/s
36
What is a moment (torque)?
Tendency of a force to produce a rotation
37
Equation for moment
M = Fd
38
Units of moment
Nm
39
Equation for mechanical advantage
MA = Effort distance/Resistance distance
40
Describe a first class lever
Fulcrum lies between effort and resistance
41
Describe a second class lever
Resistance lies between fulcrum and effort
42
Describe a third class lever
Effort lies between resistance and fulcrum
43
Does each class of lever work at a mechanical advantage or disadvantage?
1st class = Either
2nd class = always advantage
3rd class = always disadvantage
44
Equation for tangential linear velocity
v = rω
45
Equation for tangential linear acceleration
a = rα
46
Equation for radial linear acceleration
a = rω(2)
47
What does the moment of inertia describe?
Measure of a body's resistance to rotation (depends on distribution of mass and axis of rotation)
48
Equation for moment of inertia
I = mr(2)
49
What does it mean if a body has a high moment of inertia?
It is difficult to rotate
50
Equation for angular momentum
L = Iω
51
Equation for work
w = Fs
52
Units for work
Joules (J)
53
What is 1 Joule equivalent to?
1 kg m(2) s(-2)
54
Equation for Power
Power = work done/time taken
55
Equation for kinetic energy
KE = ½mv(2)
56
Equation for rotational KE
Rotational KE = ½Iω(2)
57
Equation for potential energy
PE = WH
58
What is the law of conservation of energy
Energy cannot be created or destroyed but can be changed from one form to another
59
Define stress
Force per unit area on a body that tends to cause it to change shape
60
Equation for stress
Stres = Force/Area
61
What units is stress measured in?
Pascals (Pa)
62
Define strain
A way of quantifying how something deforms
63
Equation for strain
strain = change in length/original length
64
What units is strain measured in?
Strain has no units as it is a ratio
65
What are the 4 regions of a stress-strain curve?
Elastic region
Plastic region
Strain hardening
Necking
66
In which region are stress and strain proportional?
Elasic region
67
What does the highest point in a stress-strain graph represent?
Ultimate strength
68
What does the area under a stress-strain curve represent?
Work done
69
What is Hooke's law?
Up to a certain level of stress, the strain produced is proportional to the applied stress
70
What is Young's Modulus a measure of?
Measure of the stiffness of a material (how difficult it is to deform under loading)
71
Equation for Young's modulus
E = stress/strain
72
Units of Young's Modulus
Pascals (Pa)
73
How can Young's Modulus be calculated from a stress-strain graph
Gradient of the line (up until p limit)
74
What does a high or low Young's modulus indicate?
Low E = flexible
| High E = stiff
75
Define rigidity
Ability to resist axial deformation
76
Equation for Ridigity
G = Young's Modulus (E) x cross-sec area
77
Definition of stifness
Force required to produce a unit deflection
78
Equation for stiffness
k = F/∆l
79
Define flexibility
Deflection under a unit load (opposite of stiffness)
80
Equation for flexibility
f = ∆l/F
81
Describe viscous behaviour of a material
"Lazy"
Slow to deform (strain is prolonged)
After load is lifted will not return to previous shape
82
Equation for coefficient of viscocity
η = stress/strain rate
83
Example of 2 body materials that exhibit viscoelastic behaviour
Articular cartilage
| Cortical bone
84
Describe viscoelastic behaviour
Responds to rate of loading but returns to original shape eventually
85
Name 2 behaviours that viscoelastic materials exhibit?
Creep
| Stress relaxation
86
What is creep?
The phenomenon of developing strain over time
87
When are materials particularly vulnerable to creep?
At high temperatures
88
What is stress relaxation?
If a material is kept under constant strain then the stress will gradually diminish over time (change in order of atoms)
89
What are the 5 ways in which a body can be loaded?
```
Tension
Compression
Shear
Bending
Torsion
```
90
What is axial stress?
Tensile or compressive forces acting along a geometric axis
91
How is shear stress calculated?
shear stress = shearing force/sheared area
92
What is shear strain equivalent to?
Angle sheared
93
How is shear strain calculated?
tanΦ = distance sheared/distance between 2 shearing forces
94
What is shear strength?
Max shear stress a material can withstand before fracturing
95
When does the largest shear stress occur in a material?
At 45 degrees to axial loading
96
Equation for modulus of rigidity
G = shear stress/shear strain
97
How does the largest shear stress relate to the axial stress?
Largest shear stress occurs in the planes at 45 degrees to axial loading and is equal to half the axial stress
98
How does the modulus of rigidity relate to Young's modulus?
G = E/2(1 + v)
| v = Poisson's ratio
99
What are the 2 types of bending?
Cantilever
| 3-point bending
100
Where is bending stress the greatest?
The further the layer from the axis the greater the stress
101
What is a bending moment?
An internal moment to balance the external applied moments
102
What terms are used to describe positive & negative bending moments?
```
Sagging = +ve
Hogging = -ve
```
103
When does the maximum bending moment occur?
At max length therefore M = FL
104
An increase in which 2 factors would cause an increase in beam bending strength?
Young's Modulus (E)
| Cross-sec area
105
How is the stress at a particular area calculated?
strain at particular layer x Young's Modulus
106
How is the strain at a particular layer of a beam calculated?
Displacement from neutral axis/radius
107
Which distribution of mass is mostly likely to resist bending?
Mass distributed away from neutral axis
108
How is the maximum bending moment calculated?
(max bending stress x second moment of area) / max displacement of extreme layer from neutral axis
109
What is the second moment of area?
Measure of how resistant something is to bending
110
What causes a material to have a high second moment of area?
Further the material is concentrated away from the neutral axis the higher the SMOA
111
What is the beam equation?
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
Where is the max and min deflection of a beam under torsional stress?
```
Max = free end
Min = fixed end
```
113
What does the modulus of rigidity describe?
Indication of how resistant something is to stress (higher = more resistant)
114
How do you calculate shear stress in torsion?
(G x angle of twist x radius) / length
115
How do you calculate strain in torsion?
(Angle of twist x radius) / Length
116
What is the polar second moment of area?
Measure of distribution of material around an axis (and therefore it's resistance to torsion)
117
Which shape is most effective at resisting torsion?
Hollow tube
118
What is the torsion equation?
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
How does muscle activity affect stress distribution in bones?
Reduces tensile stress as bones are stronger in compression
120
What is a strain gauge and what are it's advantages and disadvantages of a strain gauge?
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
What does photoelasticity do?
Enables weak areas of structures to be identified
122
How does the finite element work?
Breaks the problem down to millions of small problems that a computer solves
123
Which 3 factors affect failure of a bone under stress?
Magnitude of load
Rate of speed load is applied
No. of times load is applied
124
What is the fracture/rupture strength?
Stress at which bone fractures
125
What is the difference between a ductile and a brittle fracture?
```
Ductile = with necking
Brittle = without necking
```
126
What characterises a ductile fracture?
Necking
Flat granulated central portion
Small shear lip
127
Describe the process of a ductile fracture
Begins with the formation of microscopic voids at centre (separation of grain boundaries)
Deformation by shearing also contributes
128
When will a normally ductile material respond like a brittle material?
If it has been exposed to fatigue loading
129
Describe the process of a brittle fracture
Occurs suddenly without plastic deformation
Fracture surface is flat with granular appearance
Another characteristic appearance is chevron
130
What are stress concentrations?
Points at which stress is greater than the average for the material
131
What reduces the risk of stress concentrations?
Gentle transitions between cross-sections
| Smooth surfaces
132
What test is used to test impact resistance?
Charpy impact test
133
What type of material is most impact resistant?
Ductile
134
How is impact energy calculated in Charpy's test?
Impact energy = W(ho - hf)
135
At what temperature are materials able to absorb more energy?
Higher temps (changes material from brittle to ductile)
136
Is there more energy released from a fatigue fracture or a quickly loaded fracture?
If loaded quickly mor eenergy is released if it does fracture
137
Are granular & fibrous layers brittle or ductile fratures?
Granular - brittle
| Fibrous - ductile
138
What might be seen in the fatigue fracture of a hip prothesis?
Clam shell markings
139
Example of fatigue fracture in bone
March fracture (in metatarsals)
140
Why is frequency important when considering fatigue fractures?
Bone can remodel
141
What can be used to reduce the likelihood of a material corroding?
```
Passivation layer (already eroded but won't anymore)
Corrosion resistant material
```
142
What makes a material particularly vulnerable to corrosion?
Crevices
143
What is the most common ferrous allow used?
Steel
144
What effect does increasing the carbon content of steel have?
Steel becomes harder but more brittle
145
What is the ideal structure of steel?
Low carbon inside and high carbon outside
146
What is different about a stainless steel?
Contains 12-18% chromium by weight (chromium forms passivation layer)
147
What are the advantages of titanium based alloysl?
Lower density
Higher strength-to-weight ratio than aluminium
Excellent corrosion resistance
148
What are the disadvantages of titanium based alloys?
High cot
High fabrication cost
Low Young's modulus (will deform more under load)
149
What are the properties of polymers?
Lightweight corrosion resistant electrical insulators
Low tensile strength and melting points
Low density
Easy to manufacture
Exhibit BOTH plastic and elastic behaviour
150
What is the difference between thermoplastics and thermosets?
Thermo plastics - display plastic behaviour at high temps can be cooled and reheated
Thermosets - cannot be reformed during formation t hgih temps
151
What are elastomers?
Rubbers - can deform by massive amounts without permanent shape change
152
What are the properties of ceramics?
Crystalline structure
High hardness but cutable along planes
High melting point
Low electrical and thermal conductivity
153
Where in orthopaedics are ceramics used
Heads of hip prostheses
154
How does stiffness relate ro rigidity?
Stiffness = rigidity per unit length
155
How do you calculate the maximum shear stress acting in a bar under axial load ?
stress/2`
156
What are the units of shear strain?
Radians
157
How do you claculate the maximum bending moment?
(stress x second moment of srea) / max displacement from neutral axis
158
What is the equation for second moment of area for a rectangular cross section?
I - bd(3) / 12
| y(max) = ½d
