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AQA A Level Physics Paper 1 > Further Mechanics > Flashcards

Further Mechanics Flashcards

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1
Q

What is SHM defined in terms of?

A

SHM is defined in terms of acceleration and displacement

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2
Q

Describe the movement of an object moving with SHM

A

An object moving with simple harmonic motion oscillates to and fro either side of a midpoint

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3
Q

What is the distance of an object from the midpoint called?

A

Displacement

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4
Q

Define the term displacement in regards to SHM

A

Displacement is the distance from an object to the midpoint

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5
Q

What is the restoring force in SHM and how does it work?

A

There is always a restoring force pulling or pushing an object back towards the midpoint. The size of the restoring force is directly proportional to the displacement

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6
Q

What is the relationship between the restoring force and acceleration in SHM?

A

As the restoring force causes acceleration towards the midpoint it can be said that acceleration is directly proportional to displacement

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7
Q

What must be true about movement for it to be classed as SHM?

A

SHM occurs when there is 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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8
Q

How can SHM be defined as an equation?

A

a ∝ -x

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9
Q

In SHM what is the relationship between the restoring force and Ep and Ek?

A

The restoring force makes the object undergoing SHM exchange Ep and Ek. The type of potential energy depends on what it is that’s providing the restoring force. This is gravitational potential energy for a pendulum and elastic potential energy for masses on springs moving horizontally

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10
Q

Describe the energy changes that occur on an object undergoing SHM

A

As the object moves towards the midpoint the restoring force does work on the object and so transfers some Ep to Ek. When the object is moving away from the midpoint all that Ek is transferred back to Ep again

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11
Q

At the midpoint what is an objects Ep and Ek?

A

At the midpoint the object’s Ep is zero and its Ek is maximum

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12
Q

At the maximum displacement (amplitude) on both sides of the midpoint what is an object’s Ep and Ek?

A

At the maximum displacement on both sides of the midpoint the object’s Ek is zero and its Ep is as its maximum

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13
Q

In SHM what is the sum of the potential and kinetic energy called?

A

The sum of the potential and kinetic energy is called the mechanical energy and it stays constant as long as the motion isn’t damped

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14
Q

Draw a graph of how Ep and Ek change for one cycle of SHM

A

See page 100 in the revision guide

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15
Q

Draw a graph of displacement against time for an object undergoing SHM

A

See page 100 in the revision guide

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16
Q

What are the maximum and minimum values for the graph of displacement against time for an object undergoing SHM?

A

A and -A (A is amplitude)

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17
Q

Draw a graph of velocity against time for an object undergoing SHM

A

See page 100 in the revision guide

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18
Q

Draw a graph of acceleration against time for an object undergoing SHM

A

See page 100 in the revision guide

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19
Q

What are the maximum and minimum values for the graph of velocity against time for an object undergoing SHM?

A

ωA and ωA

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20
Q

What are the maximum and minimum values for the graph of acceleration against time for an object undergoing SHM?

A

ω^2A and -ω^2A

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21
Q

What is the relationship between the frequency, period and amplitude of an object undergoing SHM?

A

The frequency and period don’t depend on the amplitude

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22
Q

Define the term cycle of oscillation

A

A cycle of oscillation is from maximum positive displacement to maximum negative displacement and back again

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23
Q

What is the frequency of SHM?

A

The frequency ,f, of SHM is the number of cycles per second measured in hertz

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24
Q

What is the period of an object undergoing SHM?

A

The period ,T, is the time taken for a complete cycle in seconds

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25
Q

What is the formula used to calculate the angular frequency?

A

ω = 2πF

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26
Q

In SHM what is the amplitude (A)

A

A is the maximum displacement

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27
Q

In the formula to calculate the acceleration of an object undergoing SHM why is there a minus sign?

A

There is a minus sign as the constant of proportionality depends on ω and the acceleration is always in the opposite direction from the displacement

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28
Q

To use this equation 𝑥 = 𝐴 cos (𝜔t) when must you start timing?

A

When the pendulum is at its maximum displacement

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29
Q

What type of oscillator is a mass on a spring?

A

A mass on a spring is a simple harmonic oscillator

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30
Q

What happens when a mass on a spring is pushed to left or pulled to the right?

A

When a the mass is pushed to the left or pulled to the right of the equilibrium position there is a force exerted on it.

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31
Q

What is the formula used to calculate the force exerted on a mass on a spring when it is moved from its equilibrium position?

A

F = -kx where k is the spring constant and x is the displacement in m

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32
Q

In the formula for the period of a mass oscillating on a spring what are the different variables?

A
  • T is the period of oscillation in seconds
  • m is the mass in kg
  • k is the spring constant
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33
Q

Describe the practical used to find the period of a mass-spring system

A

1- Set up the apparatus
2- Pull the masses down a set amount, this will be your initial amplitude. Let the masses go
3- The masses will now oscillate with simple harmonic motion
4- The position sensor measures the displacement of the mass over time
5- Connect the position sensor to a computer and create a displacement-time graph. Then just read the period from the graph

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34
Q

How could you use a stopwatch in the practical for finding the period of a mass-spring system?

A

You could use the stopwatch to measure the period of an oscillation. Measure the time taken for example 5 oscillations then divide by the number of oscillations to get an average as it will reduce the random error in the result

35
Q

What is the difference in potential energy between a spring hung vertically and a spring hung horizontally?

A

For a spring hung vertically the potential energy is both elastic and gravitational whereas for a spring hung horizontally the potential energy is just elastic

36
Q

How can you use the apparatus from the practical for finding the period of a mass-spring system to investigate factors which affect the period?

A

1- Change the mass by loading more masses onto the spring
2- Change the spring stiffness constant by using different combinations of springs
3- Change the amplitude by pulling the masses down by different distances

37
Q

What type of oscillator is a simple pendulum?

A

A simple harmonic oscillator

38
Q

Explain the practical for finding the period of a simple pendulum

A

1- Attach a pendulum to an angle sensor connected to a computer
2- Displace the pendulum from its rest position by a small angle (less than 10 degrees) and let it go The pendulum will oscillate with simple harmonic motion
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 from it. Make sure you calculate the average period over several oscillations to reduce the percentage uncertainty in your measurements
5- Change the mass of the pendulum bob, the amplitude of displacement and the length of the rod independently to see how they affect the period

39
Q

What are the different variables in the formula for calculating the period of a pendulum?

A
  • T is the period of oscillation in seconds
  • l is the length of the pendulum between the pivot and the centre of mass of the bob in m
  • g is the gravitational field strength
40
Q

What does the formula for calculating the period of a pendulum only work for?

A

It only works for small angles of oscillation up to about 10 degrees from the equilibrium point

41
Q

What are the two different types of vibration?

A

Free vibrations and Forced vibrations

42
Q

What is a free vibration?

A

A free vibration is a vibration in which there is no transfer of energy to or from the surroundings

43
Q

Describe an example of a free vibration

A

1- If you stretch and release a mass on a spring it oscillates at its resonant frequency
2- If no energy is transferred to or from the surroundings, it will keep oscillating with the same amplitude forever
3- In practice this never happens but a spring vibrating in air is called a free vibration anyway

44
Q

What is a forced vibration?

A

A forced vibration happens when there is an external driving force

45
Q

What is the relationship between the driving and resonant frequencies in a forced vibration?

A

If the driving frequency is much less than the resonant frequency then the two are in phase - the oscillator just follows the motion of the driver. If the driving frequency is much greater than the resonant frequency the oscillator wont be able to keep up which means you end up with the driver completely out of phase with the oscillator.

46
Q

What is the driving force in a forced vibration?

A
  • A system can be forced to vibrate by a periodic external force
  • The frequency of this force is called the driving frequency
47
Q

At resonance what is the phase difference between the driver and the oscillator?

A

90 degrees

48
Q

When does resonance occur?

A

Resonance happens when the driving frequency = resonant frequency

49
Q

Define the term resonance

A

When the driving frequency approaches the resonant frequency the system gains more and more energy from the driving force and so vibrates with a rapidly increasing amplitude. This is called resonance and the system is resonating

50
Q

What is damping?

A

Damping happens when energy is lost to the surroundings by reducing the amplitude of an oscillation over time.

51
Q

What are damping forces?

A

In practice any oscillating system loses energy to its surroundings usually due to frictional forces like air resistance. These are called damping forces

52
Q

Why are systems often deliberately damped?

A

Systems are often deliberately damped to stop them oscillating or to minimise the effect of resonance

53
Q

The heavier the damping…

A

the quicker the amplitude is reduced to zero

54
Q

What are the four different types of damping?

A
  • Light damping
  • Heavy damping
  • Critical damping
  • Overdamping
55
Q

What is critical damping?

A

Critical damping reduces the amplitude in the shortest possible time

56
Q

Why are car suspension systems and moving coil meters critically damped?

A

Car suspension systems and moving coil meters are critically damped so that they don’t oscillate but return to equilibrium as quickly as possible

57
Q

What effect does overdamping have on a system?

A

Overdamped systems take longer to return to equilibrium than a critically damped system.

58
Q

What is the relationship between plastic deformation and damping?

A

Plastic deformation of ductile materials reduces the amplitude of oscillations in the same way as damping. As the material changes shape it absorbs energy so the oscillation will be smaller

59
Q

Draw graphs of displacement against time for the different types of damping

A

See page 105 in the revision guide

60
Q

Explain how light damping affects resonance

A

Lightly damped systems have a very sharp resonance peak. Their amplitude only increases dramatically when the driving frequency is very close to the resonant frequency

61
Q

Explain how heavy damping affects resonance

A

Heavily damped systems have a flatter response. Their amplitude doesn’t increase very much near the resonant frequency and they aren’t as sensitive to the driving frequency

62
Q

Why are some structures damped?

A

Structures are damped to avoid being damaged by resonance

63
Q

Explain how damping can be used to improve sound quality in enclosed spaces

A

Loudspeakers in a room create sound waves in the air. These reflect off of the walls of the room and at certain frequencies stationary sound waves are created between the walls of the room. This causes resonance and can improve the quality of the sound - some frequencies are louder than they should be

64
Q

Define a radian

A

A radian is defined as the angle at the centre of a circle that subtends an arc equal to a radius

65
Q

What is an angle in radians defined as?

A

The angle in radians, θ, is defined as the arc-length divided by the radius of the circle

66
Q

Why is there 2π radians in a complete circle?

A

For a complete circle the arc length is the circumference of the circle (2πr). Dividing this by the radius gives 2π, so there are 2π radians in a complete circle

67
Q

How do you convert from degrees to radians?

A

Multiply by π/180

68
Q

How do you convert from radians to degrees?

A

Multiply by 180/π

69
Q

Define the term Angular speed (ω)

A

Angular speed is the angle turned per unit time

70
Q

What is the formula for calculating angular speed and what are its units?

A
  • ω = θ/t
  • Units are radians per second
71
Q

What is the formula linking angular speed with linear speed/ tangential velocity

A

ω = v/r
- r is the radius of the circle being turned in metres

72
Q

What is the relationship between circular motion and frequency and period

A

Circular motion has a frequency and a period

73
Q

Define the frequency of circular motion

A

The frequency is the number of complete revolutions per second measured in hertz

74
Q

Define the period of circular motion

A

The period is the time taken for a complete revolution in seconds

75
Q

What is the equation linking the frequency and the period of circular motion?

A

f = 1/T

76
Q

What is the formula used to calculate angular speed when an object turns through a complete circle?

A

ω = 2π/T = 2πf

77
Q

Are objects travelling in circles accelerating?

A

Objects travelling in circles are accelerating since their velocity is changing

78
Q

What is centripetal acceleration and what is its relevance to an object travelling in a circle?

A

1- If an object travelling in a circle is moving with a constant speed its velocity is changing since its direction is changing
2- Since acceleration is defined as the rate of change of velocity the car is accelerating even though it isn’t going any faster
3- This acceleration is called the centripetal acceleration and is always directed towards the centre of the circle

79
Q

What are the two formulas used to calculate centripetal acceleration?

A

1- a = v^2/r
2- a = ω^2*r

80
Q

What is the centripetal acceleration produced by?

A

The centripetal acceleration is produced by a centripetal force. From Newton’s laws if there is a centripetal acceleration there must be a centripetal force acting towards the centre of the circle

81
Q

What is the centripetal force?

A

The centripetal force is what keeps the object moving in a circle, remove the force and the object would fly off at a tangent

82
Q

Why does the speed of an object moving in a circle stay constant?

A

The speed of the object moving in a circle stays constant even though it is accelerating because the force on the object is at right angles to the velocity and so does no work on the mass. The force just changes the direction but not the magnitude of the velocity

83
Q
A

AQA A Level Physics Paper 1 (9 decks)

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