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Physics > Y2: Option C - Engineering Physics > Flashcards

Y2: Option C - Engineering Physics Flashcards

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1
Q

What is Inertia

A

A measure of how much an object resists a change in velocity

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2
Q

What is the moment of inertia

A

A measure of how difficult it is to rotate, or change the rotational speed of an object

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3
Q

What is the equation for the moment of inertia for a point mass

A

I = mr^2

I: Moment of inertia (kgm^2)
m: Mass (kg)
r: Distance from the axis of rotation (m)

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4
Q

What is the equation for the moment of inertia for an extended object

A

The moment of inertia is calculated as the sum of all the individual moments of inertia, of each point mass that makes up the object.

∴ I = Σmr^2

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5
Q

How does the distribution of an object’s mass alter it’s moment of inertia

A

For a point mass, I = mr^2
∴ I ∝ r^2
∴ The moment of inertia for a point mass is greater, if it is further form the axis of rotation
A spinning object can be modelled as a collection of point masses
∴ If the same mass is distributed further from the axis, the overall moment of inertia will increase

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6
Q

What is the equation for the moment of inertia for a hollow ring (hoop)

A

I = mr^2

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7
Q

What is the equation for the moment of inertia for a solid wheel

A

I = 1/2(mr^2)

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8
Q

What is the equation for the moment of inertia for a hollow sphere

A

I = 2/3(mr^2)

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9
Q

What is the equation for the moment of inertia for a solid sphere

A

I = 2/5(mr^2)

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10
Q

What is the equation for rotational kinetic energy

A

Ek = 1/2(Iω^2)

For linear motion, Ek = 1/2(mV^2)
For a rotating object, ω = V/r
∴ V = ωr
∴ Ek = 1/2(m(ωr)^2)
∴ Ek = 1/2(mr^2(ω^2))
I = mr^2
∴ Ek = 1/2(Iω^2)

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11
Q

What is angular displacement (θ rad)

A

The angle through which a point has been rotated

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12
Q

What is angular velocity (ω rads^-1)

A

The vector quantity describing the angle an object rotates through each second

∴ ω = Δθ/Δt

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13
Q

What is angular speed (ω)

A

The scalar magnitude of the angular velocity

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14
Q

What is the angular acceleration (α rads^-2)

A

The rate of change of the angular velocity

∴ α = Δω/Δt

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15
Q

What is the equation that relates linear (a) and angular (α) acceleration

A

a = αr

α = Δω/Δt
ω = V/r
∴ α = (1/r)(ΔV/Δt)
a = ΔV/Δt
∴ α = (1/r)a
∴ a = αr

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16
Q

What are the quantities for rotational motion that correspond with linear motion

A

S ⇒ θ
U ⇒ ω1
V ⇒ ω2
A ⇒ α
T = T

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17
Q

What are the equations for rotational motion (SUVAT equivalent)

A

ω2 = ω1 + αt
θ = 1/2(ω2+ω1)t
θ = (ω1)t - 1/2(αt^2)
θ = (ω2)t + 1/2(αt^2)
(ω1)^2 = (ω2)^2 + 2αθ

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18
Q

What is given by the gradient of an ‘Angular displacement-time’ graph

A

Gradient = ω

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19
Q

What is shown by a straight line on an ‘Angular displacement-time’

A

ω is constant (α = 0)

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20
Q

What is shown by a convex ‘Angular displacement-time’

A

+α (acceleration)

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21
Q

What is shown by a concave ‘Angular displacement-time’

A

-α (deceleration)

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22
Q

What is given by the gradient of an ‘Angular velocity-time’ graph

A

Gradient = α
∴ + grad = acceleration
∴ - grad = deceleration

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23
Q

What is given by the area under the curve of an ‘Angular velocity-time’ graph

A

Area = θ

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24
Q

What is shown by a convex ‘Angular velocity-time’

A

Increasing α

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25
Q

What is shown by a concave ‘Angular velocity-time’

A

Decreasing α

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26
Q

What is a couple

A

A pair of forces that cause no resultant linear motion, but which cause an object to turn

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27
Q

What is torque

A

The turning effect of a force (or couple) on an object

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28
Q

What is the equation relating torque and perpendicular force

A

T = Fr

F: force
r: perpendicular distance to the axis of rotation
∴ T = Fr cosθ

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29
Q

What is the equation relating torque, and the moment of inertia of the rotating object

A

T = Iα

T = Fr, and F=ma
∴ T = mar
a = αr
∴ T = α(mr^2)
I = mr^2
∴ T = Iα

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30
Q

What is the equation for the work done to rotate an object

A

W = Tθ

For a linear system, W = Fs
For a rotation, s = θr
∴ W = Frθ
T = Fr
∴ W = Tθ

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31
Q

What is the equation for rotational power

A

P = Tω

Power = rate of change of energy (Work done)
∴ P = ΔW/Δt
W = Tθ
∴ P = Δ(Tθ)/Δt
ω = Δθ/Δt
∴ P = Tω

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32
Q

What is frictional torque

A

The opposing torque experienced by a rotating system due to the friction of it’s components

T(net) = T(applied) - T(friction)

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33
Q

What is a flywheel

A

A heavy wheel with a high moment of inertia, to resist changes in rotational motion

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34
Q

How is energy stored in a flywheel

A

Flywheels are charged as they as spun, with the input torque stored as rotational kinetic energy.
(just enough power is constantly supplied to keep the flywheel fully changed until the energy is required)

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35
Q

What factors effect the energy storage capacity of a flywheel

A
  • Mass:
    (Ek ∝ I), and (I ∝ m)
    ∴ Ek ∝ m
  • Mass distribution:
    (Ek ∝ I), and (I ∝ r^2)
    ∴ Ek ∝ r^2
  • Angular speed:
    Ek ∝ ω^2
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36
Q

What are the practical limits of increasing the energy storage capacity of a flywheel

A
  • May be impractical
    eg. large, heavy wheel may not fit into the machine
  • May damage the machine
    eg. Increasing ω will increase the centrifugal force, potentially damaging the mechanism
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37
Q

How is the energy storage capacity of modern flywheels improved

A
  • Usually carbon fibre
    (although they have a lower mass, can reach much higher speeds without causing damage)
  • Friction is reduced
    (eg. lubrication, levitating wheel with superconductors, work in a vacuum, etc)
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38
Q

How may a flywheel be used in a system

A
  • Smoothing torque:
    If input power varies, flywheels uses spurts of energy to change up, and supply constant torque to the system as they decelerate
  • Smoothing angular velocity:
    A charged flywheel will maintain the angular velocity of rotating components when the power supply stops
  • Supplying additional energy:
    If the system is required to exert varying forces, a constant power input can charge a flywheel which will decelerate to release spurts of energy
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39
Q

What are some examples of flywheel applications:

A
  • Potter’s wheel
  • Regenerative braking
  • Power grids
  • Wind turbines
  • Riveting machine
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40
Q

What are flywheel batteries

A

Machines designed to store as much energy as possible
(as much Ek as the ω, r and m of the wheel allows)

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41
Q

What are the advantages of flywheels

A
  • They are very efficient
  • They last a long time without degrading
  • Recharge time is short
  • React and discharge quickly
  • Environmentally friendly
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42
Q

What are the disadvantages of fly wheels

A
  • Much larger and heavier than other storage methods
  • Pose a safety risk as the wheel could break apart at high speeds (protective casing increases weight)
  • Energy lost through friction
  • Can oppose direction changes in moving objects
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43
Q

What is the angular momentum of a rotating object

A

The product of the moment of inertia and angular velocity of a rotating object

∴ Angular momentum = Iω
(Angular version of mv)

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44
Q

What is the law of the conservation of angular momentum

A

When no external force is applied (torque, friction, etc), the total angular momentum of a system remains constant

∴ I1ω1 = I2ω2

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45
Q

What is angular impulse

A

The change in angular momentum
= Δ(Iω)

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46
Q

What is the equation that links torque and angular impulse

A

TΔt = Δ(Iω)

T = Iα
α = = Δω/Δt
∴ T = Δ(Iω)/Δt
(⇒ ∴ T = rate of change of angular momentum)
∴ TΔt = Δ(Iω)

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47
Q

What is translational motion

A

The movement of the centre of mass of an object

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48
Q

What is rotational motion

A

The rotation of an object about it’s centre of mass

49
Q

What is rolling

A

A combination of rotational and translational motion

50
Q

What is the equation relating GPE and Ek for a rolling object

A

Ep = Ek(trans) + Ek(rot)
∴ Ep = 1/2(mV^2) + 1/2(Iω^2)

51
Q

What is the equation for the linear velocity of a rolling object

A

V = √((2Ep)/(m+(I/r^2)))

Ep = Ek(trans) + Ek(rot)
∴ Ep = 1/2(mV^2) + 1/2(Iω^2)
ω = V/r
∴ Ep = 1/2(mV^2) + 1/2(I(V/r)^2)
∴ V = √((2Ep)/(m+(I/r^2)))

52
Q

What is a system in thermodynamics

A

A volume of space filled with a gas

53
Q

What is the difference between an open and closed system

A
  • Open system: Gas can flow in/out
  • Closed system: Gas can’t enter or escape
54
Q

What is the first law of theromdynamics

A

Heat supplied to a system either increases the internal energy of the system or enables it to do work

∴ Q = ΔU + W

Q: Energy transferred to the system by heating
ΔU: Change in internal energy
W: The work done by the system

55
Q

What does the +/- sign indicate about Q, for the first law of thermodynamics.

A
  • If energy is transferred to the system (system is heated), Q is POSITIVE
  • If energy is transferred away from the system (system is cooled), Q is NEGATIVE
56
Q

What does the +/- sign indicate about ΔU, for the first law of thermodynamics.

A
  • If the internal energy of the system increases, ΔU is POSITIVE
  • If the internal energy of the system decreases, ΔU is NEGATIVE
57
Q

What is a non-flow process

A

Changes to a gas in a closed system, as air can’t flow in or out

58
Q

What is the relationship between temperature, pressure and volume, during all non-flow processes for an ideal gas

A

(p1V1)/(T1) = (p2V2)/(T2)

For an ideal gas, pV = nRT
R is constant (Molar gas constant = 8.31 JK^-1mol^-1)
n is fixed as change occurs in closed system
∴ pV/T = Constant
∴ p1V1/T1 = p2V2/T2

59
Q

What is an isothermal change

A

A change that occurs at a constant temperature
(Assumed for slow changes)

60
Q

What is the equation for the first law of thermodynamics, during an isothermal change to an ideal gas

A

Q = W

For an ideal gas, U ∝ T
T = constant
∴ ΔU = 0
∴ Q = 0 + W
∴ Q = W
If energy is applied to a system, it will result in an equivalent amount of work done (and vice versa)

61
Q

What is the relationship between pressure and volume, during an isothermal change for an ideal gas

A

p1V1 = p2V2
(Boyle’s Law)

62
Q

What is an adiabatic change

A

A change that occurs with no heat transfer in our out of the system
(Usually assumed for Fast changes, as there isn’t enough time for heat to be transferred)

63
Q

What is the equation for the first law of thermodynamics, during an adiabatic change to an ideal gas

A

ΔU = -W

No heat is transferred
∴ Q = 0
∴ 0 = ΔU + W
∴ ΔU = -W
Any work done will result in an opposite change to the internal energy (and vice versa)

64
Q

What is the relationship between pressure and volume, during an isothermal change for an ideal gas

A

p1(V1)^𝛾 = p2(V2)^𝛾

𝛾: adiabatic constant

65
Q

What is the equation for work done during changes at a constant pressue

A

W = pΔV

Work done = Force x distance ⇒ W=FΔx
Pressure = Force / Area ⇒ F=pA
∴ W = pAΔx
AΔx = ΔV
∴ W = pΔV

66
Q

What is the relationship between temperature and volume, during a change at a constant pressure for an ideal gas

A

V1/T1 = V2/T2
(Charles’ Law)

67
Q

What is the equation for the first law of thermodynamics, during a change at a constant volume

A

Q = ΔU

If volume is constant, no work is done (W=0)
∴ Q = ΔU + 0
∴ Q = ΔU
Any heat transferred to or from the system directly changes the internal energy of the gas

68
Q

What is the relationship between temperature and pressure, during a change at a constant volume for an ideal gas

A

P1/T1 = P2/T2
(Pressure Law)

69
Q

What is a pV diagram and what does it show for a non-flow process

A
  • Graph showing the relationship between pressure and volume during the change
  • Arrow can be drawn on the curve to indicate the direction of the change
70
Q

What does the area under a pV graph show for a non-flow process

A

Work done

71
Q

What is an isotherm and what does it show

A

Isotherm = Curve on pV diagram for isothermal change

  • Shows p ∝ 1/V, as PV=constant
  • T is constant, but curve approaches closer to origin if T is lower (as work done is less)
72
Q

What is the difference between a pV graph for an isothermal and adiabatic change

A

The curve for an adiabatic change has a steeper gradient than for an isothermal change

73
Q

What is the difference between the work done for an isothermal and adiabatic change

A
  • More work is required for adiabatic compression than for isothermal compression
  • More work is required for isothermal compression than for adiabatic compression

(larger area under pV curve = More work done)

74
Q

What is the difference between the gradient of a pV graph for an isothermal and adiabatic process

A

Isothermal:
pV = constant
∴ let pV = k
∴ p = kV^-1
∴ dp/dV = -kV^-2
k = pV
∴ dp/dV = -(pV)V^-2
∴ dp/dV = -p/V

Adiabatic
pV^𝛾 = constant
∴ let pV^𝛾 = k
∴ p = kV^-𝛾
∴ dp/dV = -𝛾kV^-𝛾-1
k = pV^𝛾
∴ dp/dV = -𝛾(pV^𝛾)V^-(𝛾+1)
∴ dp/dV = -𝛾p/V

Therefore, the gradient of an adiabatic curve is steeper than an isothermal curve, by a factor of 𝛾

75
Q

What does a pV graph look like for a change at a constant volume

A

Vertical line
∴ W = 0 (no area under graph)

76
Q

What does a pV graph look like for a change at a constant volume

A

Horizontal line
(Work done as volume changes)

77
Q

What is a cyclic process and how is it shown on a pV graph

A

If a system undergoes different processes one after another, and returns to the original temperature and pressure before begining the processes again.
This is shown by a closed loop on a pV graph

78
Q

What is the net work done during a cyclic process and how can it be determined from a pV graph

A

The difference between the work done by the system and the work done on the system
∴ Shown by the area inside the loop on a pV graph

79
Q

What is a 4 stroke engine

A

An internal combustion engine where fuel is burned once every 4 strokes (1 stroke = up or down)

80
Q

What is the 4-stroke cycle of a petrol engine

A

1) Induction
- Piston starts at the top and moved down, drawing in an air-fuel mix through the inlet valve
- Constant pressure (just below atmospheric)

2) Compression
- Inlet value closes and piston moves up, compressing the air (Increased p, decreased V)
- Just before the end of the stroke, the spark plug ignites the fuel causing a sudden temp and pressure increase, at almost constant volume

3) Expansion
- The hot gas expands, and does work on the piston pushing it down (decreased p, increased V)
- Work done by gas to expand is greater than work done on gas to compress it, as temp is higher
(∴ Net output work drives engine)
- Just before the end of the stroke, the exhaust valve opens and the pressure decreases

4) Exhaust
- The piston moves up and the burned gas leaves through the exhaust valve
- Constant pressure (just above atmospheric)

81
Q

How is the 4-stroke cycle of a diesel engine different to a petrol engine

A

Undergo the same 4-stroke cycle with several slight differences for diesel:
- Only air drawn in during induction
- No spark plug: Air compressed until temp high enough for ignition, then diesel sprayed in by fuel injectors
- No sharp peak before expansion, as injected fuel heats up, increasing the volume at an almost constant pressure, before expansion occurs

82
Q

What is an indicator diagram

A

A pV graph showing the changes experienced by the system during a 4-stroke engine cycle

83
Q

What is a theoretical indicator diagram

A

pV graph for the cycle of a 4-stroke engine, if it were to occur under perfect conditions

84
Q

What is an Otto cycle

A

The theoretical cycle for a 4-stroke petrol engine

85
Q

What is a Diesel cycle

A

The theoretical cycle for a 4-stroke diesel engine

86
Q

What assumptions are made about the system for a theoretical indicator diagram

A
  • The same gas is taken continuously around the cycle
  • Pressure and temperature changes are instantaneous
  • Heat source is external
  • Engine is frictionless
87
Q

What are the 4 stages of an Otto cycle

A

1) Gas is compressed adiabatically
2) Heat is supplied whilst volume is constant (increase p)
3) Gas is allowed to cool adiabatically
4) system is cooled at constant volume

88
Q

What are the 4 stages of a Diesel cycle

A

1) Gas is compressed adiabatically
2) Heat is supplied whilst pressure is constant (increase V)
3) Gas is allowed to cool adiabatically
4) system is cooled at constant volume

89
Q

What are the differences between real and theoretical engines

A
  • Corners of theoretical indicator diagram are not rounded, as it is assumed that the same air is cycled continuously
  • In real engine, volume is not constant during heating, as this could only occur is p and T changes were instantaneous
  • Theoretical loop doesn’t include negative work between exhaust and induction, as it assumes same air is cycled again
  • Real temperature rise is less than theoretical, as engines have an internal heat source, and the fuel is not completely burned (∴ <max energy released)
  • Net work done is greater for theoretical engines, as real engines require energy to overcome friction (∴ inside real loop is smaller)
90
Q

What is the indicated power of an engine

A

The net work done by the engine cylinders in 1 second
(∴ = Max theoretical power generated by gases in engine cylinder)

91
Q

What is the equation for the indicated power of an engine

A

Indicated power = (Area of loop)x(No. of cycles per second)x(No. of cylinders)

92
Q

What is the input power of an engine

A

The amount of heat energy per unit time that could potentially be released from burning fuel

93
Q

What is the equation for the input power of an engine

A

Input power = Calorific value x Fuel flow rate

(⇒ Calorific value = How much energy the fuel has stored per unit volume)

94
Q

What is the output (brake) power of an engine

A

The useful power output at the crankshaft

95
Q

What is the equation for the output power of an engine

A

P = Tω
(rotational power)

96
Q

What is the friction power of an engine

A

The power needed to overcome the friction of an engine

97
Q

What is the equation for the friction power of an engine

A

Friction power = Indicated power - Output power

98
Q

What is the thermal efficiency of an engine

A

Ratio of the energy available from the fuel, to the energy generated by the engine
(Affected by how well energy is transferred into work)

99
Q

What is the equation for the thermal efficiency of an engine

A

Thermal efficiency = Indicated power / Input power

100
Q

What is the mechanical efficiency of an engine

A

Ratio of the power generated by the cylinders to the power output at the crankshaft
(Affected by the amount of energy lost due to friction between moving parts)

101
Q

What is the equation for the mechanical efficiency of an engine

A

Mechanical efficiency = Output power / Indicated power

102
Q

What is the overall efficiency of an engine

A

Ratio of the energy available from the fuel, to the power output at the crankshaft
(Accounts for both mechanical and thermal efficiency)

103
Q

What is the equation for the overall efficiency of an engine

A

Overall efficiency = Output power / Input power
(∴ = Mechanical efficiency x Thermal efficiency)

104
Q

What are heat engines

A

Engines that convert heat energy into work

105
Q

What is the second law of thermodynamics

A

It is impossible for heat from a high temperature source to produce an equal amount of work
∴ All heat engines must must operate between a heat source and a heat sink, as some heat must increase the temp of the engine and then be disspursed
(otherwise engine temp would reach source temp and work would stop)

∴ Q(H) = W + Q(C)

Q(H): Heat transfer from the heat source
W: Work done by the engine
Q(C): Heat loss to surroundings (transfer to heat sink)

106
Q

What is the efficiency of a heat engine

A

The ratio of the heat transferred from the source, to the useful output work
(Affected by the difference between the source and sink temperature)

107
Q

What is the equation for the efficiency of a heat engine, relating to the 2nd law of thermodynamics

A

Efficiency = Q(H)-Q(C) / Q(H)

Efficiency = W/Q(H)
W = Q(H)-Q(C)
∴ Efficiency = Q(H)-Q(C) / Q(H)

108
Q

What is the maximum theoretical efficiency of a heat engine

A

T(H)-T(C) / T(H)

Ratio of Q(H):Q(C) = Ratio of T(H):T(C)
Efficiency = Q(H)-Q(C) / Q(H)
∴ Max theoretical Efficiency = T(H)-T(C) / T(H)
as T = max energy transfer

109
Q

What is the efficiency for real life heat engines less than the maximum theoretical efficiency

A
  • Energy lost to overcome friction
  • Fuel doesn’t burn entirely
    etc.
110
Q

How is efficiency maximised in heat engines

A

To maximise the efficiency of a heat engine, as much input energy as possible must be transferred usefully (∴ Q(C) low as possible)
However, some heat is always lost to the surroundings (Q(C) must be >0), so to avoid wasting energy, some ‘combined heat and power (CHP)’ plants use released heat for other purposes, such as heating local houses, generating electricity, etc.

111
Q

What is a reversed heat engine

A

An engine that transfers heat energy from a cold space to a hot space
- Heat naturally flows from hot to cold, ∴ work is required to transfer
- There will always be some energy in the cold space to be transferred, as the temp as above absolute 0

112
Q

Why are 100% efficient heat engines and reversed heat engines impossible

A

According to the second law of thermodynamics (Q(H) = W + Q(C)), there must always be a transfer of energy between a hot and cold space.
If 100% of the energy from the hot space was converted into work (or vice versa for reverse engines), the engine temp would eventually be the same as source temp, so no work would be done

T(C) > 0
Max theoretical Efficiency = T(H)-T(C) / T(H)
∴ Efficiency < 1

113
Q

How do refrigerators work as reversed heat engines
(process of refrigeration)

A

A refrigerant moves through coils, travelling inside and outside of the fridge:
- The liquid refrigerant outside the fridge is decompressed, decreasing the pressure and therefore decreasing it’s temperature as it flows into the fridge.
- It then begins to absorb energy from it’s surroundings as it travels through the evaporator coils inside the fridge, decreasing the temperature of the surroundings as the refrigerant heats up to become a gas.
- As it leaves the fridge, the gaseous refrigerant is compressed, increasing the pressure, and therefore the temperature.
- It then begins to travel through the condenser coils outside the fridge, where it releases it’s energy to the surroundings, cooling as it returns to a liquid
- The cycle then repeats as energy is absorbed from in the fridge and released to the surroundings, due to the work done during the compression and decompression stages

114
Q

How do heat pumps work as reversed heat engines

A

Work similar to refrigerators, as the refrigerant is sequentially compressed and decompressed to transfer energy from the cold space (outside the house), to the hot space (inside the house)

However, for a heat pump:
- Heat given out by compressed refrigerant usually heats a water tank
- A fan will usually amplify the absorption of heat in the cold space

115
Q

What is the coefficient of performance (COP)

A

A measure of how well work is transferred into heat energy by a reverse heat engine:
- Ratio of Q:W
- ∴ = 1/efficiency, so shows how well work causes energy transferer, (whereas shows how well energy transfer causes work, in regular heat engines)
- Can be greater than 1

116
Q

What is the equation for the COP for a refrigerator

A

COP(ref) = Q(C) / (Q(H) - Q(C))

For a refrigerator, the heat removed from the cold space determines how well it works
∴ COP(ref) = Q(C)/W
W = Q(H) - Q(C)
∴ COP(ref) = Q(C) / (Q(H) - Q(C))

117
Q

What is the maximum theoretical COP for a refrigerator

A

At max theoretical efficiency:
COP(ref) = T(C) / (T(H) - T(C))

118
Q

What is the equation for the COP for a heat pump

A

COP(hp) = Q(H) / (Q(H) - Q(C))

For a heat pump, the heat transferred to the hot space determines how well it works
∴ COP(hp) = Q(H)/W
W = Q(H) - Q(C)
∴ COP(hp) = Q(H) / (Q(H) - Q(C))

119
Q

What is the maximum theoretical COP for a heat pump

A

At max theoretical efficiency:
COP(hp) = T(C) / (T(H) - T(C))

Physics (14 decks)

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