4. Mechanics & Materials Flashcards
1
Q
What is a vector?
A
A physical quantity that has a direction as well as a magnitude
2
Q
Examples of vectors?
A
- field strength
- force
- momentum
- weight
- velocity
- acceleration
- displacement
3
Q
What is a scalar?
A
A physical quantity that is not directional
4
Q
Examples of scalars?
A
- density
- charge
- resistance
- work done
- energy
5
Q
How can a vector be represented?
A
By an arrow
6
Q
What does the length of an arrow representing a vector determine?
A
The magnitude of the vector quantity
7
Q
How to resolve vectors into their horizontal and vertical components?
A
- use angle of vector (Θ)
- for sinΘ
- then for cosΘ
8
Q
If two forces act on an object, when is equilibrium achieved?
A
When the two forces are equal and opposite
9
Q
If three forces act on an object, when is equilibrium achieved?
A
When the resultant of any two of the forces is equal and opposite to the third force
10
Q
What are the ways to work out forces on an object when it is in equilibrium?
A
- vector triangle
* resolve the components
11
Q
What is the centre of gravity of an object?
A
The point through which the entire weight of the object may be considered to act
12
Q
Word equation to calculate the moment of a force?
A
Force x Perpendicular distance from the line of action of the force to the pivot
13
Q
What is the principle of moments?
A
For any object that is in equilibrium, the sum of the clockwise moments about a point is equal to the sum of the anticlockwise moments about that same point
14
Q
What is a couple?
A
A pair of equal and opposite forces, not acting in the same straight line
15
Q
What is the turning effect that couples create called?
A
A torque
16
Q
How to calculate the torque of a couple?
A
torque = one of the forces x perpendicular distance between them
17
Q
What are the two conditions for equilibrium?
A
- there is no net (resultant force)
2. there is no turning effect (moment) about any point
18
Q
What is the centre of mass of a body?
A
The point on an object where the mass may thought to be concentrated
19
Q
How to find COM of symmetrical objects?
A
Along the line of symmetry, or where multiple lines of symmetry intersect
20
Q
How to find COM of non-symmetrical objects?
A
If an object swings freely, when it stops the COM is on a vertical line passing through the pivot
21
Q
When an object is in equilibrium, what is true of the vertical forces?
A
They are equal in magnitude and opposite in direction
22
Q
When an object is in equilibrium, what is true of the horizontal forces?
A
They are equal in magnitude and opposite in direction
23
Q
When an object in equilibrium is supported at one point, what is the support force equal to?
A
It is equal and opposite to the total downward force acting on the object
24
Q
How to calculate average speed?
A
distance / time
25
How to calculate acceleration?
change in velocity / time
26
How to calculate average velocity?
displacement / time
27
What does velocity measure?
The rate of change of displacement
28
What does acceleration measure?
The rate of change of velocity
29
What is the gradient in a distance-time graph?
Speed
30
What is the gradient in a displacement-time graph?
Velocity
31
What is the gradient in a velocity-time graph?
Acceleration
32
What is the gradient in an acceleration-time graph?
Rate of change of acceleration
33
What is the area underneath a velocity-time graph?
Displacement
34
What is the area underneath an acceleration-time graph?
Velocity
35
What do negative values of displacement or velocity on a graph indicate?
Motion in the opposite direction
36
On a velocity-time graph, what does a straight upwards line represent?
Constant acceleration
37
On a velocity-time graph, what does a straight horizontal line represent?
Constant velocity
38
On a velocity-time graph, what does a straight downwards line represent?
Constant deceleration
39
On an acceleration-time graph, what does a horizontal line represent?
An object travelling at constant acceleration - or no acceleration so constant velocity
40
On an acceleration-time graph, what does a straight line downards represent?
Acceleration is speeding up, but at a slowing rate
41
On an acceleration-time graph, what does a straight downwards line, below the zero line, represent?
Negative acceleration - the deceleration is slowing down, and area below zero line so negative change in velocity
42
What is the equation for an object's speed, moving at constant speed on a circle?
v = 2πr / T
where T = time to move round once
43
What are suvat equations?
Equations describing motion
44
When can suvat equations be used?
When acceleration is constant
45
What do the letters in suvat stand for?
* s - displacement
* u - initial velocity
* v - final velocity
* a - acceleration
* t - time
46
How is the equation a=(v-u)/t derived using a graph?
* velocity-time graph
* gradient = acceleration
* increase in y = v-u
* over increase in x = t
47
How is the equation s=(u+v)t÷2 derived using a graph?
* velocity-time graph
* area underneath = displacement
* area of trapezium = 1/2(a+b)h
* s = 1/2(u+v)t = (u+v)t÷2
48
What is the suvat equation that doesn't include s?
v=u+at
49
What is the suvat equation that doesn't include u?
s=vt-1/2at²
50
What is the suvat equation that doesn't include v?
s=ut+1/2at²
51
What is the suvat equation that doesn't include a?
s=[(u+v)/2]t
52
What is the suvat equation that doesn't include t?
v²=u²+2as
53
What experiment can be used to measure g?
* drop an object from a height - measure using meter rule
* use light gates to measure time taken for object to fall
* s=1/2at² ∴ s=1/2gt²
54
What is a projectile?
An object that is projected or thrown through the air at an angle
55
What can be done with a projectile's initial velocity?
Can be separated into components
56
When calculating projectiles, what force is ignored?
Air resistance
57
Ignoring air resistance, what is the only force acting on a projectile?
Gravity
58
What does gravity acting objects mean for the components of projectiles?
* gives a downward acceleration - so affects vertical component of velocity
* horizontal component of velocity remains constant
59
Which component of acceleration of a projectile is affected by gravity?
The vertical component
60
Which value is the same for both components when calculating projectiles?
Time
61
What is a resultant force?
A single force that has the same effect as all the forces combined
62
What is Newton's 1st law?
An object will remain at rest or continue to move with a constant velocity as long as the forces acting on it are balanced
63
When is an object's momentum not constant?
When there is a resultant unbalanced force acting on it
64
What is inertia?
The resistance to change velocity
65
What does the inertia of an object depend on?
Its mass
66
How does a bigger mass affect inertia?
Bigger mass = bigger force to overcome its inertia and change its motion
67
When travelling in a car and decelerating, what keeps you moving?
Your inertia - until something stops you, hopefully your seatbelt
68
Word equation for momentum?
Mass x velocity
69
Symbol equation for momentum?
ρ = mv
70
What is the unit for momentum?
kgms⁻¹ or Ns
71
What do objects have when stationary, in terms of momentum and inertia?
They have no momentum, but still have inertia
72
Is inertia a scalar or a vector?
Scalar
73
Is momentum a scalar or a vector?
Vector
74
What is Newton's 2nd law?
The rate of change of momentum of an object ∝ to resultant force acting on it. Change in momentum takes place in the direction of the force
75
If mass is constant, how can change in momentum be calculated?
Δρ = mv - mu
76
What can F ∝ Δρ/Δt be simplfied to? And under what condition?
F = m [(v-u)/Δt]
| if the mass of the object doesn't change
77
What is tension equal to (in terms of mass and force)?
T = ma + mg
78
What is force equal to (in terms of tension and weight)?
F = T - mg
79
What happens in terms of forces when two objects interact?
They exert equal and opposite forces on eachother
80
What is true about pairs of forces acting on different objects?
They are always the same type of force
81
What is Newton's 3rd law?
If object A exerts a force on object B, then object B exerts an equal and opposite force of A
82
Do forces act in isolation?
No - they act in pairs
83
Why do pairs of forces not cancel each other out?
They act on different objects
84
How can Newton's laws show conservation of momentum?
* 3rd says F₁=-F₂
* 2nd says F=ma so ΔPB/ΔTB = ΔPA/ΔTA
* ΔTB=ΔTA ∴ ΔPB=-ΔPA
* ∴ ΔPB+ΔPA = 0
85
What is the principle of conservation of momentum?
When bodies in a system interact, the total momentum remains constant - provided no external force acts on the system
86
What is the principle of conservation of momentum - in simple terms?
Total momentum before = total momentum after
| provided no external forces act
87
What happens to momentum when objects collide?
Momentum is conserved
88
What is assumed when two objects collide and momentum is conserved?
There are no external forces acting
89
During a collision, will energy and momentum be conserved if there are no external forces acting?
* momentum will be conserved
| * energy might be conserved
90
How is the kinetic energy before and after an elastic collision?
Ek before = Ek after
91
What are the types of collision?
* elastic
| * inelastic
92
Are collisions between snooker balls elastic or inelastic?
Very nearly elastic
93
What is the difference between elastic and inelastic collisions?
* elastic - Ek before = Ek after
| * inelastic - Ek before > Ek after
94
Are collisions between molecules in a gas elastic or inelastic?
Elastic
95
What would it mean if collisions between molecules in a gas were inelastic instead of elastic?
Repeated collisions would slow gas molecules down, and would eventually settle at the bottom of a container
96
Are most collisions elastic or inelastic?
Inelastic
97
What happens to the kinetic energy that is 'lost' during an inelastic collision?
It is transferred to other forms
98
What is the 'lost' energy usually converted to during inelastic collisions?
Internal (heat) energy
99
What type of collision is undergone in crash barriers and crumple zones of cars?
Inelastic
100
Why are crash barriers and crumple zones designed to collide inelastically?
To absorb the kinetic energy in a crash
101
Which principle can be applied to explosions?
The principle of conservation of momentum
102
What can the principle of conservation of momentum be used for?
* collisions
| * explosions
103
In exam questions, what is the movement of all objects involved in explosions?
Initially, they are all stationary
104
What is the initial momentum of explosions when the objects are both stationary?
Total initial momentum is zero
105
What is impulse equal to?
The change in momentum
106
What is the equation to show impulse?
Δp = FΔt
107
What is the advantage of 'following through' in sports?
* keeps force acting on ball for longer
| * refer to F = Δp/Δt
108
What is the advantage of drawing your hands back when catching a ball?
* reduces sting
* as Δp happens over a longer time
* reducing force on hands
109
What happens to Δp when there is a greater force on an object, acting for longer?
Greater change in the object's momentum
110
What is the area underneath a force-time graph?
Impulse
111
What is the area underneath a force-time graph NOT referred to as?
Change in momentum
112
What is the area underneath a force-time graph?
Impulse (kgms⁻¹)
113
What is the equation for work done that includes displacement?
W = Fx
114
What does the x stand for in the equation W=Fx?
Displacement
115
For equation W=Fx, what must be done if force and displacement are not in the same direction?
The force needs to be resolved to find the component acting in the direction of the displacement
116
What can work done also be referred to as?
Energy transferred
117
What is the definition of 1J
The work done when a force of 1N moves through a distance of 1m (in the direction of the positive force)
118
What is power?
The rate at which work is done
119
What is the symbol equation for power that involves work done?
P = ΔW / Δt
120
What is 1W in derived units?
1 Js-1
121
What equation can be used to calculate power that involves velocity?
P = Fv
122
What equation for power might not be on the data sheet?
P = Fv
123
What is true for the velocity in P=Fv?
It is constant
124
What are the types of energy?
* heat
* light
* chemical
* sound
* electrical
* nuclear
* elastic potential
* kinetic
* gravitational potential
125
How is the equation for gravitational potential energy derived?
* W = Fx
* = Weight x Δh
* Work done = Ep gained
* so Ep = weight x change in height
* Ep = mgh
126
How is the equation for elastic potential energy derived?
* F = kx
* when a spring is stretched, work is done
* (area under f-x graph) = 1/2kx
* W = Fx
* W = 1/2 kx x x
* W = 1/2ke²
127
How is the equation for kinetic energy derived?
* an object gains Ek if a force does work on it
* W = Fx
* & F=ma → so W=mas
* suvat to find F → s=[(u+v)/2]/t & a=(v-u)/t
* subs a and s into W=mas to get W=1/2m(v²-u²)
* so Ek = 1/2mv²-1/2mu²
128
What is the principle of conservation of energy?
Energy can be transferred from one form to another, but it cannot be created or destroyed
129
What is true of the total energy when using the law of conservation of energy?
The total amount of energy always stays the same
130
Equation for efficiency?
Efficiency = useful energy output / total energy output
131
What is the unit for efficiency?
No unit
132
What does it mean when energy is 'wasted'?
It is transferred to internal (heat) energy
133
What is density defined as?
A substance's mass per unit volume
134
Equation for density?
ρ = m/v
135
Method for finding density of a regular solid?
* ruler - measure width, length and height
* top-pan balance - measure mass
* use ρ = m/v
136
Method for finding density of an irregular solid?
* top-pan balance - measure mass
* use a eureka can to measure water displaced by object
* volume of water = volume of object
* use ρ = m/v
137
What type of force is acting when a spring is squashed?
Compressive
138
What type of force is acting when a spring is lengthened?
Tensile
139
What is Hooke's law?
The force needed to stretch a string is proportional to the extension of the spring from its natural length, provided the elastic limit isn't exceeded
140
What is the equation for Hooke's law?
F = kΔL
141
What does it mean for the stiffness of the spring when spring constant is larger?
It is a stiffer spring
142
What happens to a spring when it is stretched beyond its elastic limit?
It doesn't regain its initial length when the force applied is removed
143
How can the spring constant of springs 'in parallel' be calculated?
Multiply the spring constants together of the original springs
144
How can the spring constant of two springs 'in series' be calculated?
1/kₜₒₜₐₗ = 1/kₑₐ𝒸ₕ x number of springs
145
What is the area underneath a force-extension graph equal to?
Strain energy (as work done = force x distance)
146
Equation for strain energy?
Eₑ = 1/2kΔL²
147
When does the equation Eₑ = 1/2kΔL² apply?
Only if the spring obeys Hooke's law
148
In materials, what does the stiffness depend on?
Material, length and cross-sectional area
149
What is the equation for Young Modulus?
k = EA / l
150
What does the 'E' mean in k = EA / l?
Young Modulus
151
What is the definition of stress on a material?
The force acting per unit cross sectional area
152
Equation for stress?
Force / cross sectional area (σ = F/A)
153
What is stress measured in?
pascals (Pa)
154
What is the breaking stress of a material?
The maximum stress it can withstand without fracture
155
What can breaking stress also be referred to as?
Ultimate tensile stress
156
What happens when materials get a thinner section when they are stretched?
They break here as stress is increased here
157
What is strain defined as?
The extension produced per unit length
158
Equation for strain?
Extension / length (ε = x / l)
159
What is strain measured in?
Has no units
160
Equation for Young Modulus, E?
Tensile stress, σ / Tensile strain, ε
161
How can the two separate equations for stress and strain be simplified?
* σ=F/A divided by ε=x/l
* F/A x L/ΔL = FL/AΔL
* F/ΔL is spring constant
* so E = kL/A
162
On a stress-strain graph showing a stiff and a flexible material, which material has the line with the steepest gradient?
The stiff material
163
What are materials that permanently deform described as?
Plastic
164
What are materials that return to their original shape after the stretching force is removed called?
Elastic
165
What can plastic materials also be described as?
* ductile - can be drawn into wires
| * malleable - they can be hammered into sheets
166
Describe the force-extension graph of a metal wire.
* loading - the line starts straight, and curves as it surpasses the limit of elasticity
* unloading - the line doesn't come back along the same line as when loading
* difference between loading and unloading lines = permanent extension of wire
167
Describe the force-extension graph of a rubber band.
* loading - the line is curved
* unloading - the line is curved, but doesn't follow the same curve as the loading line
* unloading line finishes at the origin - rubber returns to its original shape
168
What is the opposite of a tough material?
A brittle material
169
What happens when you try to deform a malleable material e.g. lead?
It deforms plastically - gives way gradually, absorbing a lot of energy before it snaps
170
Do brittle materials deform plastically?
No
171
Do brittle materials absorb much energy before they break?
No, unlike plastic materials
172
What are force-extension graphs used for, vs stress-strain graphs?
* force-extension → usually for objects e.g. particular spring
* stress-strain → usually for materials (of any size)
173
What does the gradient represent on force-extension and stress-strain graphs?
* force-extension → spring constant (Nm⁻¹)
| * stress-strain → Young Modulus, E (Nm⁻² or Pa)
174
What is the Young Modulus measured in?
Nm⁻² or Pa
175
What does the area represent on force-extension and stress-strain graphs?
* force-extension → work done (1/2kΔL²) in J
| * stress-strain → work done per unit length (W/V) in Jm⁻³
176
What is work done per unit length measured in?
Jm⁻³
177
On a force-extension graph, what does it mean if the area of the unloading graph is smaller than that of the loading graph?
Some energy has been transferred
178
What is the reason for energy transference on a force-extension graph?
Some energy stored in the object (e.g. rubber band) becomes the internal energy of the molecules when the rubber band unstretches
179
On a force-extension graph, what does the area between the loading and unloading curve represent?
Difference between energy stored in the object when it is stretched and the useful energy recovered from it when it is unstretched
180
Brief explanation of experiment to find the Young Modulus of a wire?
* stress → wire with mass attached - measure mass using top-pan balance and use W=mg. measure diameter of wire using micrometer, then calculate area
* then stress = F/A
* strain → measure extension by measuring distance marker moves from original position, and length of wire. calculate strain
* vary mass for range of values - plot stress-strain graph
181
How to improve accuracy in the experiment to calculate the Young Modulus of a wire?
* use long thin wire and heavier weights → greater Δl so smaller % uncertainty
* measure diameter accurately using micrometer
* measure wire by holding ruler as close to the wire as possible
182
In an experiment to calculate the Young Modulus of a wire, how can kinks in the wire be avoided?
Weights are added at the beginning, before length measured
183
In an experiment to calculate the Young Modulus of a wire, how can we make sure there is no thermal expansion?
By comparing the test wire to a control wire
184
What is the elastic limit?
The point beyond which a wire will not return to its original length after weight has been added and then remove
