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AQA A Level Physics > 6. Further Mechanics and Thermal Physics > Flashcards

6. Further Mechanics and Thermal Physics Flashcards

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1
Q

What are Newton’s three laws of motion?

A
  1. An object stays at rest or in uniform motion unless acted upon by a force
  2. The rate of change of momentum of an object is proportional to the resultant force acting upon it
  3. When two objects interact, they exert equal and opposite forces on each other
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2
Q

Symbol for momentum?

A

p

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3
Q

Unit for momentum?

A

kg ms-1

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4
Q

How is F=ma derived from Newton’s second law?

A
  • F ∝ Δp / Δt
  • F ∝ mΔv/Δt
  • F=ma or F=kma
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5
Q

When is F=ma true?

A

When mass is constant

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6
Q

How would you generally give NII?

A

F = Δ(mv)/Δt

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7
Q

How would you give NII if mass remains constant?

A

F = mΔv/Δt or F=ma

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8
Q

How would you give NII if mass is changing?

A

F = vΔm/Δt

where Δm/Δt is mass change per second

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9
Q

What is the symbol for angular displacement?

A

θ

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10
Q

What is the unit for angular displacement?

A

rad

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11
Q

What is the symbol of angular velocity?

A

ω

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12
Q

What is the unit for angular velocity?

A

rad s-1

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13
Q

If a wheel takes T seconds to rotate once, what angle will it turn through each second?

A

2π/T radians

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14
Q

What will the frequency of a rotation of a wheel that takes T seconds to rotate once be?

A

f=1/T

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15
Q

What is angular displacement given by?

A

θ = 2πt / T or θ = 2πft

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16
Q

How do we get the equation ω = 2πf?

A
  • circumference = 2πr
  • time for one rotation = distance travelled / velocity = 2πr / v or 2π / ω
  • so 2πr / v = 2π / ω therefore v = r ω
  • also θ = 2πft and ω = θ / t
  • ∴ ω = 2πf
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17
Q

What is centripetal acceleration given by?

A

a = v2 / r

= ω2 r

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18
Q

How do we know there must be a centripetal force when a bike wheel is rotating?

A

It is accelerating as it is changing direction, so there must be a force

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19
Q

Why does kinetic energy stay constant when a bike wheel rotates?

A
  • W=Fd in direction of force

* because F is at 90 degrees to v, no work is done

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20
Q

What is the equation for centripetal force?

A

F = mv2 / r

= mrω2

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21
Q

Is centripetal force a type of force?

A

No, it is a description of a force - it is a force that causes the acceleration to be towards the centre

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22
Q

When is the centripetal force required increased?

A
  • mass increased
  • speed increased
  • or radius decreased
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23
Q

For questions about cars going over bumps/hills, what will the fastest speed that the car can travel over the hill be given by?

A

mg = mvmax2 / r or vmax = √gr

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24
Q

For questions about cars going round bends, what will the maximum friction be given by?

A

Frictionmax = m vmax2 / r

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25
Q

For questions about cars on banked tracks, what can tanθ be given by?

A

tanθ = v2 / gr

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26
Q

What are oscillations?

A

Wobbling about a centre point

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27
Q

What is equilibrium?

A

The centre point

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28
Q

What is amplitude (A)?

A

The maximum displacement form centre point

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29
Q

What happens in TSM if there is no friction?

A

The amplitude is constant (free oscillation)

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30
Q

How does free oscillation occur?

A

There is no friction, so the amplitude is constant

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31
Q

What is the period (T)?

A

Time for one complete oscillation

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32
Q

What is the frequency (f)?

A

The number of oscillations per second (Hz)

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33
Q

How is simple harmonic motion defined?

A

As oscillating motion where the acceleration is proportional to the displacement in the opposite direction to the displacement

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34
Q

What is acceleration proportional to in SHM?

A

Directly proportional to displacement from the equilibrium point (a ∝ x)

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35
Q

What are the conditions for SHM?

A
  • acceleration ∝ displacement from the equilibrium point (a∝x)
  • displacement and acceleration are in opposite directions (a∝ -x) OR acceleration is always towards equilibrium point
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36
Q

What is displacement (x)?

A

The distance from the equilibrium position

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37
Q

What is Simple Harmonic Motion a type of?

A

Oscillation

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38
Q

What is phase difference, ɸ?

A

The fraction of an oscillation between the position of two oscillating objects

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39
Q

What is phase difference given by?

A

Δt/T x2π

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40
Q

What is angular frequency, ω?

A

The rate of change of angular position (given by 2πf)

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41
Q

What is the key equation for SHM?

A

a = -ω²x

42
Q

What does it mean, that an oscillator in SHM is an isochronous oscillation?

A

The period of the oscillation is independent of the amplitude

43
Q

What does isochronous mean?

A

Occupying equal time

44
Q

Graphically, how is the velocity of a pendulum given?

A

The gradient of a displacement-time graph

45
Q

Graphically, how is the acceleration of a pendulum given?

A

By the gradient of a velocity-time graph

46
Q

In SHM, does T depend on A?

A

No

47
Q

When using the equation a=-(2πf)²x, what must be remembered?

A

2πft must be in radians

48
Q

How to prove equation for T=2π√m/k?

A

F = -kx and F = ma

ma = -kx (rearrange for a)

SHM: a = -(2πf)²x

(2πf)² = k/m

1/2π . T = √m/k

T = 2π √m/k

49
Q

How to prove equation for T=2π√l/g?

A

(R) Tcosθ = mg

(R) -Tsinθ = ma

Tsinθ / Tcosθ = ma/mg

-tanθ = a/g

small angles tanθ = sinθ (displacement/length = x/l)

-x/l = a/g

(2πf)² = g/l

T/2π = √l/g

T = 2π√l/g

50
Q

Where is a fiducial marker usually placed in the pendulum experiment?

A

Equilibrium position

51
Q

Which two equations can be used to determine the displacement of a simple harmonic oscillator?

A
  • x = A sinωt

* x = A cosωt

52
Q

What is the difference between waves and oscillations in terms of energy?

A

Waves transmit energy, oscillations do not

53
Q

For the equations used to determine the displacement on a simple harmonic oscillator, when is each used?

A
  • x = A sinωt for when oscillator begins at equilibrium position
  • x = A cosωt for when oscillator begins at amplitude position
54
Q

In SHM, where does maximum velocity occur?

A

At the equilibrium position, with the oscillator being stationary at the amplitude points

55
Q

In SHM, where does the maximum acceleration occur?

A

At the amplitude points, and is 0 when the oscillator is at equilibrium position

56
Q

What is the velocity of the oscillator given by?

A

v = ±ω √A²-x²

57
Q

How is the equation for maximum velocity derived from v = ± ω√A²-x²?

A

Maximum velocity occurs at the equilibrium position, where x=0, so vmax = ωA

58
Q

What is the equation for maximum velocity?

A

ωA

59
Q

In SHM, what forms of energy are involved?

A

Kinetic and potential

60
Q

When does maximum Ek occur in SHM?

A

At the equilibrium point - where velocity is a maximum

61
Q

When does maximum Ep occur in SHM?

A

At the amplitude positions, where displacement is at a maximum

62
Q

In SHM, is total energy conserved?

A

Yes

63
Q

What is damping?

A

The process by which the amplitude of the oscillations decreases over time

64
Q

Why might the amplitude of oscillations decrease over time?

A

Energy loss to resistive force e.g. drag, friction

65
Q

What happens in SHM if there’s no friction?

A

Free oscillation

66
Q

What happens if frictional forces are acting in SHM?

A

The amplitude decreases

67
Q

How does the energy-displacement graph for energy in SHM look?

A
  • Ek - ‘sad’ parabola(max. at displacement = 0)
  • Ep - ‘happy’ parabolamax at either side where displacement is max.)
  • total energy - straight line in line with max. values for Ep and Ek
68
Q

What are the three types of damping?

A
  • critical
  • heavy
  • light
69
Q

What is critical damping?

A

Object returns to equilibrium in shortest possible time and does not overshoot

70
Q

What is heavy damping?

A

Where damping is so strong that object takes a long time to return to equilibrium - oscillation does not happen

71
Q

Does oscillation occur with heavy damping?

A

No

72
Q

How does damping occur in a car suspension system?

A
  • includes spring and damper

* damper provides almost critical damping so that oscillation dies away quickly after going over a bump

73
Q

How does a displacement-time graph look?

A

Oscillations start large and then decrease by the same fraction each cycle

74
Q

What is light damping?

A

Where T stays the same, and amplitude decreases by the same fraction each cycle (exponentially)

75
Q

What happens to T in light damping?

A

Stays the same

76
Q

What happens to amplitude in light damping?

A

Decreases by the same fraction each cycle (exponentially)

77
Q

When does light damping occur?

A

Naturally (e.g. pendulum oscillating in air)

78
Q

What happens to amplitude when heavy damping occurs?

A

Amplitude decreases dramatically

79
Q

Example of when heavy damping may occur?

A

Pendulum oscillating in water

80
Q

Example of when critical damping may occur?

A

Pendulum oscillating in treacle

81
Q

What happens to amplitude in critical damping?

A

The object stops before one oscillation is completed

82
Q

What is natural frequency?

A

Frequency at which a SHM oscillator vibrates when no force is applied

83
Q

What is periodic force?

A

Regular pushes at the right times to make an SHM oscillator to swing high

84
Q

When does a system undergo forced oscillation?

A

When a periodic force is applied

85
Q

What is forced oscillation?

A

The oscillation of a system when a periodic force is applied

86
Q

What happens if applied frequency = natural frequency?

A
  • amplitude of oscillations becomes very big
  • phase difference between displacement and periodic force changes to π/2
  • periodic force is now in phase with velocity
87
Q

What is it called when applied frequency = natural frequency?

A

The system is resonating

88
Q

What happens, in terms of applied and natural frequency, when damping is light?

A

Applied/driving frequency of periodic force = natural frequency of system

89
Q

What happens, in terms of applied and natural frequency, when damping is heavy?

A

Resonant frequency is slightly lower than natural frequency

90
Q

What factors affect resonance?

A
  • when oscillating mass ↑, natural frequency decreases
  • when springs are weaker, natural frequency decreases
  • damping limits oscillations
91
Q

What is the link between free oscillation and natural frequency?

A

When an object is in free oscillation, it vibrates at its natural frequency

92
Q

What is driving frequency the same as?

A

Applied frequency

93
Q

When does resonance occur?

A

When the driving frequency of the external force is the same as the natural frequency of the object

94
Q

What will happen when a system is resonating and there is no damping?

A

The amplitude will continue to increase until the system fails

95
Q

What will happen when a system is resonating and damping increases?

A

The amplitude will decrease at all frequencies, and the maximum amplitude occurs at a lower frequency

96
Q

What is the problem with finding the natural frequency of a system when there is no damping?

A

It is very hard to do

97
Q

How can the resonance of an object be investigated experimentally?

A
  • suspend mass between two springs attached to oscillation generator
  • ruler placed parallel with mass-spring system to record amplitude
  • driver frequency of generator slowly increased from zero - reaching max. amplitude when driver frequency reaches natural frequency of system
  • amplitude of oscillation decreases as frequency is increased further
98
Q

When can a comparatively weak vibration in one object cause a strong vibration in another?

A

Through resonance

99
Q

How is g derived from the pendulum experiment?

A
  • T = 2π √L/g - square both sides
  • Graph T²-L
  • gradient = 4π²/g
  • so g = 4π²/gradient
100
Q

How to verify Hooke’s law from the mass-spring experiment?

A
  • T² = 4π² x m/k
  • graph T²-m
  • gradient = T²/m = 4π²/k
  • draw graph F=kx and see if gradient = 4π²/m

AQA A Level Physics (10 decks)

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