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A LEVEL - Physics > Section 7 - Further Mechanics > Flashcards

Section 7 - Further Mechanics Flashcards

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1
Q

What is a radian?

A
  • A unit for angles

* It is the arc-length divided by the radius of the circle

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2
Q

What is 360° in radians?

A

2π radians

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3
Q

Why is the angle in the middle of a circle 2π radians?

A
  • The arc length is the circumference of the circle (2πr)

* Dividing this by the radius (r) gives 2π.

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4
Q

What is 45° in radians?

A

π/4 radians

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5
Q

What is 90° in radians?

A

π/2 radians

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6
Q

What is 180° in radians?

A

π radians

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7
Q

What is angular speed?

A
  • The angle an object rotates through per unit time.

* Unit: rad/s

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8
Q

What is the symbol for angular speed?

A

ω

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9
Q

What is the symbol for angle?

A

θ

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10
Q

What is the symbol for time?

A

t

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11
Q

What is linear speed?

A
  • The speed at which an object is covering distance

* Units: m/s

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12
Q

What is the unit for angular speed?

A

rad/s

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13
Q

What is the unit for linear speed?

A

m/s

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14
Q

What is the symbol for radius?

A

r

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15
Q

What are the two basic equations for angular speed?

A
  • ω = θ / t (NOT GIVEN)

* ω = v / r

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16
Q

In a cyclotron, a beam of particles spirals outwards from a central point. The angular speed of the particles remains constant. The beam of particles in the cyclotrons rotates through 360° in 35μs. Explain why the linear speed of the particles increases as they spiral outwards, even though their angular speed is constant.

A

Linear speed depends on r, the radius of the circle being turned as well as ω (v = ωr). So, as r increases, so does v, even though ω remains constant.

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17
Q

In a cyclotron, a beam of particles spirals outwards from a central point. The angular speed of the particles remains constant. The beam of particles in the cyclotrons rotates through 360° in 35μs. Calculate the linear speed of a particle at a point 1.5m from the centre of rotation.

A
  • First calculate the linear speed:
  • ω = θ / t = 2π / (35 x 10^-6) = 1.7951 x 10^5 rad/s
  • Then substitute ω into v = ωr:
  • v = ωr = 1.7951 x 10^5 x 1.5 = 2.6927 x 10^5 m/s
  • v = 2.7 x 10^5 m/s (to 2 s.f.)
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18
Q

What is angular frequency?

A

The same as angular speed.

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19
Q

In circular motion, what is frequency?

A
  • The number of compete revolutions per second.

* Units: rev/s or Hz

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20
Q

What are the units for frequency?

A

Hertz (Hz)

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21
Q

In circular motion, what is period?

A
  • The time taken for a complete revolution.

* Units: s

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22
Q

What is the unit for period?

A

Seconds (s)

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23
Q

What is the symbol for frequency?

A

f

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24
Q

What is the symbol for time period?

A

T

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25
Q

What is the equation linking time period and frequency?

A

f = 1 / T

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26
Q

What are the three basic equations for angular speed?

A
  • ω = θ / t (NOT GIVEN)
  • ω = v / r
  • ω = 2πf = 2π / T
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27
Q

Derive the equation that links angular speed and frequency.

A
  • ω = θ / t

* ω = 2π / T = 2πf

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28
Q

What is the difference between t and T?

A
  • t is the time

* T is the time period

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29
Q

Are objects travelling in a circle always accelerating?

A

Yes, because:
• They are changing direction, so the velocity is changing constantly
• Acceleration is defined as rate of change of velocity, so the car is accelerating even if the speed isn’t changing

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30
Q

Which way is an object accelerating when it moves in a circle?

A

Towards the centre.

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31
Q

What is the force that causes acceleration in a circle and which way does it act?

A
  • Centripetal force

* It acts towards the centre of the circle

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32
Q

What is the acceleration towards the centre of a circle in circular motion called?

A

Centripetal acceleration

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33
Q

What is the symbol for centripetal acceleration?

A

a

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34
Q

What is centripetal acceleration?

A
  • The acceleration towards the centre of a circle of an object in circular motion
  • Units: m/s²
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35
Q

What are the units for centripetal acceleration?

A

m/s²

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36
Q

What are the two formulas for centripetal acceleration?

A
  • a = v² / r

* a = ω²r

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37
Q

What is centripetal force?

A
  • The force that causes the centripetal acceleration and keeps an object moving in circular motion
  • Units: N
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38
Q

What is the symbol for centripetal force?

A

F

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39
Q

What is the unit for centripetal force?

A

Newtons (N)

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40
Q

What would happen if the centripetal force were removed?

A

The object would fly off at a tangent.

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41
Q

What are the formulas for centripetal force?

A
  • F = mv² / r

* F = mω²r

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42
Q

Which way does the centripetal force act?

A

Towards the centre of the circle.

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43
Q

What does SHM stand for?

A

Simple harmonic motion

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44
Q

What is the point around which simple harmonic motion occurs called?

A

Midpoint

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45
Q

What is displacement in simple harmonic motion?

A

The distance of an object from the midpoint.

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46
Q

What keeps an object in simple harmonic motion?

A

A restoring force pulling the object towards the midpoint at all times.

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47
Q

Describe how the restoring force in SHM changes.

A

It is directly proportional to the displacement.

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48
Q

In SHM, if displacement doubles, what happens to the restoring force?

A

It also doubles.

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49
Q

Describe the acceleration in SHM.

A

It is directly proportional to the displacement and always directed towards the midpoint.

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50
Q

What is the condition for SHM?

A

An oscillation in which the acceleration of an object is directly proportional to its displacement from the midpoint, and is directed towards the midpoint.

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51
Q

Give the condition for SHM as an equation.

A

a ∝ -x

Where a = acceleration and x = displacement.

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52
Q

What is the symbol for potential energy?

A

Ep

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53
Q

What is the symbol for kinetic energy?

A

Ek

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54
Q

What energy exchanges occur in SHM?

A

Potential energy is transferred to kinetic energy and back.

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55
Q

What type of potential energy (Ep) is involved in SHM?

A

It depends on what is providing the restoring force.

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56
Q

For a pendulum in SHM, what type of potential energy is involved?

A

Gravitational

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57
Q

For masses on springs moving horizontally in SHM, what type of potential energy is involved?

A

Elastic

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58
Q

In SHM, what causes the transfer from Ep to Ek?

A

The work done by the restoring force.

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59
Q

Describe energy transfers in SHM.

A
  • At the midpoint, all of the object’s energy is kinetic
  • It is converted to potential energy as it reaches maximum displacement, where all the energy is potential
  • As it returns to the midpoint, the restoring force does work and transfers the potential energy back to kinetic energy
  • This process repeats

NOTE: The sum of the potential and kinetic energy stays constant.

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60
Q

Describe the energy of an object at maximum displacement in SHM.

A
  • Ep is at its maximum

* Ek is zero

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61
Q

Describe the energy of an object at the midpoint in SHM.

A
  • Ek is at its maximum

* Ep is zero

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62
Q

What is the sum of potential and kinetic energy in SHM called?

A

Mechanical energy

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63
Q

What is mechanical energy and what happens to it in SHM?

A
  • It is the sum of the potential and kinetic energy.

* It stays constant (as long as the motion isn’t damped).

64
Q

Describe the graph for Ek and Ep against time in SHM.

A
  • Both curves are the same and are half a cycle out of phase
  • Each curve is like a sine wave that has been shifted above the x-axis.
  • Note that this means that the wave plateaus slightly each time it reaches the x-axis (i.e. it is not a sharp point at the bottom, but a curve)

(See diagram pg 100 of revision guide)

65
Q

Remember to practice drawing out the graph for energy in SHM.

A

Pg 100 of revision guide

66
Q

Describe the graph of displacement against time in SHM.

A
  • It is a cosine wave that goes above and below the x-axis.
  • Starts at the positive maximum.
  • Maximum values are A and -A.

(See graph pg 100 of revision guide)

67
Q

Describe the graph of velocity against time in SHM.

A
  • It is a cosine wave that goes above and below the x-axis.
  • Starts at the origin, then goes down.
  • Maximum values are ωA and -ωA (where ω = angular frequency and A = amplitude.)

(See graph pg 100 of revision guide)

68
Q

Describe the graph of acceleration against time in SHM.

A
  • It is a cosine wave that goes above and below the x-axis.
  • Starts at the negative maximum.
  • Maximum values are ω²A and -ω²A (where ω = angular frequency and A = amplitude.)

(See graph pg 100 of revision guide)

69
Q

Describe how the graphs for displacement, velocity and acceleration against time in SHM are related.

A
  • They are of the same shape, except velocity is 1/4 of a cycle to the left of displacement and acceleration is 1/2 a cycle to the left of displacement.
  • Each graph is the gradient of the previous one.
70
Q

What can be said about the graphs for displacement and acceleration against time in SHM?

A

The acceleration graph is in antiphase with the displacement.

71
Q

What are the maximum and minimum values for displacement in a displacement-time graph in SHM?

A
  • Maximum: A
  • Minimum: -A

(Where A = amplitude)

72
Q

What are the maximum and minimum values for velocity in a velocity-time graph in SHM?

A
  • Maximum: ωA
  • Minimum: -ωA

(Where ω = angular frequency and A = amplitude)

73
Q

What are the maximum and minimum values for acceleration in an acceleration-time graph in SHM?

A
  • Maximum: ω²A
  • Minimum: -ω²A

(Where ω = angular frequency and A = amplitude)

74
Q

Remember to practise drawing out the graphs for displacement, velocity and acceleration against time in SHM.

A

Pg 100 of revision guide

75
Q

What is a cycle in SHM?

A

From maximum positive displacement to maximum negative displacement and back.

76
Q

What is frequency in SHM?

A

The number of cycles per second.

77
Q

What is period in SHM?

A

The time taken for a complete cycle.

78
Q

What is angular frequency?

A
  • The same as angular speed, except in SHM.

* Equal to 2πf.

79
Q

In SHM, are frequency and period dependent on amplitude?

A

No

80
Q

When a pendulum swings, does the amplitude of the swing have any effect on period or frequency?

A

No

81
Q

What is the defining equation of SHM?

A

a = -ω²x

82
Q

How can you convert this into the defining equation of SHM:

a ∝ -x

A

• Introduce a constant of proportionality
• This depends on ω
• So the equation is:
a = -ω²x

83
Q

Add flashcard on how to define angular frequency in SHM.

A

Do it.

84
Q

Give the equation for acceleration in SHM.

A

a = -ω²x

85
Q

Give the equation for the maximum acceleration in SHM.

A

a(max) = ω²A

86
Q

What is the equation for velocity in SHM?

A

v = +-ωsqrt(A² - x²)

87
Q

Why is there a plus or minus in this equation:

v = +-ωsqrt(A² - x²)

A

The object moves in both directions.

88
Q

What is the equation for maximum velocity in SHM?

A

Max velocity = ωA

89
Q

What is the equation for displacement in SHM?

A

x = Acos(ωt)

90
Q

In the equation for displacement in SHM, x = Acos(ωt), at what point is t = 0?

A
  • The object must be at maximum displacement when t = 0.

* i.e. When t = 0, x = A.

91
Q

What type of motion does a mass on a spring demonstrate?

A

Simple harmonic motion

92
Q

In a mass-spring system, what is the equation for the force that is used to displace the mass from its equilibrium position?

A

F = -kx

(Where k = spring constant and x = displacement)

(NOT GIVEN IN EXAM)

93
Q

Give the equation for the period of a mass-spring system.

A

T = 2πsqrt(m/k)

Where m = mass and k = spring constant

94
Q

What is a mass-spring system?

A

A mass on a spring that can be displaced from its equilibrium to show SHM.

95
Q

How do atoms in a solid lattice move?

A

They vibrate in SHM.

96
Q

Describe the experiment to check the formula for the period of a mass-spring system.

A

1) Using string, tie a spring to a clamp.
2) Attach masses under the spring.
3) Place a position sensor below the masses.
4) Pull the masses down a set amount, which will be your initial amplitude, and release.
5) The position sensor measures the displacement over time.
6) Connect the position sensor to a computer and create a displacement-time graph.
7) Read off the period, T, from the graph.

(NOTE: Alternatively, you could also measure the period using a stopwatch. Measure several oscillations and divide by the number to get an average.)

97
Q

In the experiment investigating a mass-spring system, what types of potential energy are involved in the vertical spring?

A

Elastic and gravitational. For a horizontal spring, it would be just elastic.

98
Q

Describe the experimental set-up used to investigate factors that affect the period of a mass-spring system.

A

1) Using string, tie a spring to a clamp.
2) Attach masses under the spring.
3) Place a position sensor below the masses.
4) Pull the masses down a set amount, which will be your initial amplitude, and release.
5) The position sensor measures the displacement over time.
6) Connect the position sensor to a computer and create a displacement-time graph.
7) Read off the period, T, from the graph.
8) Change the mass (m) by using different numbers of springs. Change the spring constant (k) by using different combinations of springs. Change the amplitude (A) by pulling the masses down by different distances.
9) Plot graphs of the period against each variable to see relationships.

(NOTE: Alternatively, you could also measure the period using a stopwatch. Measure several oscillations and divide by the number to get an average.)

99
Q

Describe the relationship between T and m in a mass-spring system and how this can be shown graphically.

A
  • T ∝ √m

* So a graph of T² against m can be plotted, which shows a straight line of positive gradient.

100
Q

Describe the relationship between T and k in a mass-spring system and how this can be shown graphically.

A
  • T ∝ √(1/k)

* So a graph of T² against 1/k can be plotted, which shows a straight line of positive gradient.

101
Q

Describe the relationship between T and A in a mass-spring system and how this can be shown graphically.

A
  • There is no relationship.

* So a graph of T against A can be plotted, which shows a straight horizontal line.

102
Q

Describe what graphs can be plotted in an investigation into factors affecting a mass-spring system. What does each illustrate?

A
  • T² against m -> Illustrates T ∝ √m
  • T² against 1/k -> Illustrates T ∝ √(1/k)
  • T against A -> Shows there is no relationship between T and A.
103
Q

What factors affect the period of a mass-spring system?

A
  • Mass

* Spring constant

104
Q

What type of motion does a simple pendulum show?

A

Simple harmonic motion

105
Q

What examples of SHM do you need to know about?

A
  • Mass-spring system

* Simple pendulum

106
Q

Describe how factors affecting SHM in a simple pendulum can be investigated.

A

1) Attach a pendulum to an angle sensor connected to a computer.
2) Displace the pendulum by a small angle (less than 10°) and let it go.
3) The angle sensor measures how the bob’s displacement from the rest position varies with time.
4) Use the computer to plot a displacement-time graph and read off the period, T, from it. Take the average of several oscillations to reduce percentage uncertainty.
5) Change the mass of the pendulum bob (m), amplitude of displacement (A) and length on the rod (l) independently to see how they affect the period. Plot each graph.

(NOTE: Alternatively, you could also measure the period using a stopwatch. Measure several oscillations and divide by the number to get an average.)

107
Q

What is a pendulum made of?

A
  • Light, stiff rod

* Pendulum bob

108
Q

When measuring the period of a simple pendulum, what reference point should be used to measure the start of each oscillation?

A

The midpoint of the swing, because:
• This is where the pendulum moves fastest, so it is more clear-cut when it reaches the midpoint
• The clamp from which it is hung may be used as a marker

109
Q

Describe the relationship between T and l in a pendulum and how this can be shown graphically.

A
  • T ∝ √l

* So a graph of T² against l can be plotted, which shows a straight line of positive gradient.

110
Q

Describe the relationship between T and m in a pendulum and how this can be shown graphically.

A
  • There is no relationship.

* So a graph of T against m can be plotted, which shows a straight horizontal line.

111
Q

Describe the relationship between T and A in a pendulum and how this can be shown graphically.

A
  • There is no relationship.

* So a graph of T against A can be plotted, which shows a straight horizontal line.

112
Q

What is the formula for the period of a pendulum?

A

T = 2π√(l/g)

Where l = length of pendulum (m) and g = gravitational field strength (N/kg)

113
Q

What are the constraints of the formula for the period of a pendulum?

A

It only works for small angles of oscillation (up to about 10°).

114
Q

Remember to revise SHM graphs.

A

Pgs 102-103 of revision guide.

115
Q

What is a free vibration?

A

One where there is (theoretically) no transfer of energy to or from the surroundings.

116
Q

How does a mass on a spring oscillate when stretched and released?

A
  • At its resonant frequency.
  • It is a free vibration, so if no energy is transferred to or from the surroundings, it will keep oscillating with the same amplitude.
117
Q

What is a forced vibration?

A

When a system is forced to vibrate by a periodic external force.

118
Q

What is the frequency of a driving force causing forced vibrations called?

A

Driving frequency

119
Q

What is driving frequency?

A

The frequency of a driving force causing forced vibrations.

120
Q

What is the resonant frequency of a mass-spring system?

A

The frequency at which a system oscillates when allowed to vibrate freely.

(CHECK THIS!)

121
Q

What happens when the driving frequency is much less than the resonant frequency?

A

The two are in phase since the oscillator just follows the motion of the driver.

122
Q

What happens when the driving frequency is much greater than the resonant frequency?

A

The oscillator can’t keep up with the driver, so the two are completely out of phase.

123
Q

What happens when the driving frequency is equal to the resonant frequency?

A

The system resonates, since the amplitude of vibration is at a maximum.

124
Q

What is resonance?

A
  • When the driving frequency equals the resonant frequency
  • Phase difference between the driver and oscillator is 90°
  • Maximum amplitude of vibration is achieved
125
Q

Describe how amplitude of oscillation changes with driving frequency.

A
  • When the driving frequency is less than the resonant frequency, the amplitude is low
  • As the driving frequency approaches the resonant frequency, the amplitude increases at an increasing rate -> More energy is being transferred from the driving force
  • Peak amplitude is at the resonant frequency
  • As driving frequency increases above the resonant frequency, the amplitude decreases at a decreasing rate -> The driver and oscillator are completely out of phase, so less energy is transferred from the driving force

(See graph pg 104 of revision guide)

126
Q

Practice drawing out the graph of driving frequency against amplitude.

A

Pg 104 of revision guide

127
Q

Practice drawing out the set-up to investigate resonance in a mass-spring system.

A

Pg 104 of revision guide

128
Q

What is the phase difference between the driver and oscillator at resonance?

A

90°

129
Q

Give some examples of resonance.

A
  • Organ pipe
  • Swing
  • Glass smashing
  • Radio
130
Q

What is damping?

A

When an oscillating system loses energy to surroundings.

131
Q

What causes damping?

A

Damping forces, such as air resistance.

132
Q

Give an example of a damping force.

A

Air resistance

133
Q

Is damping always unwanted?

A

No, sometimes systems are deliberately damped to stop them oscillating or to minimise the effect of resonance.

134
Q

How do shock absorbers in a car suspension work?

A

They provide a damping force by squashing oil through a hole when compressed.

135
Q

Is all damping the same?

A

No, there can be different degrees.

136
Q

How can the degree of damping vary?

A

From light damping to overdamping.

137
Q

How does damping affect the amplitude of oscillation and how does the degree of damping change this?

A

The heavier the damping, the quicker the amplitude is reduced.

138
Q

What is critical damping?

A

• Where the amplitude is reduced to equilibrium in the shortest possible time • Only one sharp displacement is seen

139
Q

What is overdamping?

A
  • When the damping is too heavy so the system takes longer to return to equilibrium than a critically damped system
  • Only one long displacement is seen.
140
Q

Give two examples of when critical damping is used.

A
  • Car suspension system

* Moving coil meters

141
Q

Describe the graphs of displacement against time for light damping and heavy damping.

A
  • Light damping is like a sine wave of gradually decreasing amplitude
  • Heavy damping is the same, except the amplitude decreases more sharply

(See graphs pg 105 of revision guide)

142
Q

Describe the graph of displacement against time for critical damping.

A
  • Starts at a positive displacement
  • The curve is like a sine wave until the x-axis, except it starts to flatten out just before
  • The line then continues flat along the axis

(See graph pg 105 of revision guide)

143
Q

Describe the graph of displacement against time for critical damping.

A
  • Starts at a positive displacement
  • The curve is like a gradual and very stretched sine wave until the x-axis, except it begins to flatten out before it reaches the axis
  • The line then continues flat along the axis

(See graph pg 105 of revision guide)

144
Q

Remember to practise drawing out the displacement-time graphs for damping.

A

Pg 105 of revision guide

145
Q

Does damping affect resonance?

A

Yes

146
Q

How does damping affect resonance?

A
  • The heavier the damping, the flatter the graph of amplitude against driving frequency will be.
  • This means the amplitude at the resonant frequency will be lower.
  • The difference in amplitude is most marked near the resonant frequency.

(See diagram pg 105 of revision guide)

147
Q

Remember to practise drawing out the graphs of amplitude against driving frequency for different degrees of damping.

A

Pg 105 of revision guide

148
Q

Describe the set-up used to investigate how damping affects resonance.

A
  • Mass is attached between two springs that are clamped vertically
  • Vibration generator is attached to the bottom of the lower spring
  • Signal generator is connected to the vibration generator
  • Discs of different sizes can be attached to the mass to affect air resistance
  • The amplitude of oscillation is looked at by seeing how far the mass moves
149
Q

Give some used of damping.

A
  • Car suspensions
  • Moving coil meters
  • Skyscrapers
  • Soundproofing
150
Q

Describe how damping can be used to improve sound performance.

A
  • Sound waves reflect off walls and, at certain frequencies, cause stationary waves to be created between walls of a room.
  • This causes resonance and can affect sound quality.
  • Soundproofing walls in music studios absorbs the sound waves and converts their energy to heat energy. This prevents the stationary waves from forming.
151
Q

Add cards on what each letter in the equation sheet represents.

A

Do it.

152
Q

Do all particles in a body travel at the same speed?

A

No

153
Q

How can the speed of particles in a substance be described?

A

Randomly distributed, with the largest proportion travelling at about the average speed.

154
Q

What determines the distribution of particle speeds in a substance?

A

The temperature.

155
Q

How does a high temperature affect the average kinetic energy of particles in a substance?

A

It increases it.

A LEVEL - Physics (14 decks)

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