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AQA A-level Physics > Further mechanics > Flashcards

Further mechanics Flashcards

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1
Q

What do we mean by uniform circular motion?

A

motion in a circle at a constant speed

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2
Q

What is a requirement for circular motion to occur?

A

the force must constantly act perpendicular to the objects velocity (towards the centre of the circle)

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3
Q

What is the speed called for an object in uniform circular motion?

A

linear speed

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4
Q

What is something to know about the velocity of an object in circular motion?

A

always acts at a tangent to the objects’ path

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5
Q

What do we mean if the acceleration is centripetal? What are some things to know about the direction of the acceleration?

A

-acts towards the centre of the circular path
-the acceleration is perpendicular to the direction of the linear speed

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6
Q

Is the velocity constant during uniform circular motion?

A

no, velocity is always changing due to changes in direction (as its a vector quantity)

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7
Q

What do we mean if something is centripetal?

A

it acts towards the centre of the circular path

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8
Q

What do we mean when a force is centripetal?

A

a force that acts towards the centre of the circular path

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9
Q

Draw a diagram of a particle undergoing uniform circular motion with the centripetal force, acceleration and velocity acting on it

A

https://cdn.savemyexams.co.uk/cdn-cgi/image/w=1920,f=auto/uploads/2020/09/12.2.1.1-Force-and-acceleration-direction.png

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10
Q

What do we mean by the angular displacement (θ) of a body in circular motion? What is it measured in?

A

-the change in angle of a body as it rotates around a circle
-measured in radians

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11
Q

How can we work out the angular displacement of an object? (2 equations)

A

-https://cdn.savemyexams.co.uk/cdn-cgi/image/w=1920,f=auto/uploads/2021/04/6.1.2-Radians-Equation-1.png

-https://cdn.savemyexams.co.uk/cdn-cgi/image/w=1920,f=auto/uploads/2021/04/6.1.2-Radians-Equation-2.png

where:
Δθ = angular displacement, or angle of rotation (radians)
s = length of the arc, or the distance travelled around the circle (m)
r = radius of the circle (m)

-both distances must be in metres

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12
Q

What is a radian (rad)?

A

the angle subtended at the centre of a circle by an arc equal in length to the radius of the circle

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13
Q

What is a relationship between an angle, a radius and the arc length?

A

https://cdn.savemyexams.co.uk/cdn-cgi/image/w=1920,f=auto/uploads/2020/09/12.1.1.1-Radians-definition.png
-when the angle is equal to one radian, the length of the arc (Δs) is equal to the radius (r) of the circle

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14
Q

How can we work out arc length from an object moving in a circular motion?

A

Δs=r x Δθ

where:
Δs= arc length (m)
r= radius (m)
Δθ= angular displacement (rad)

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15
Q

How can we convert degrees into radians? What about vice cersa?

A

https://cdn.savemyexams.co.uk/cdn-cgi/image/w=1920,f=auto/uploads/2021/04/6.1.2-Radians-Equations-5.png

-rearrange equation to find angle in degrees

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16
Q

What do we mean by angular speed? What is its’ symbol

A

(⍵- omega)
the rate of change in angular displacement with respect to time

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17
Q

Is angular speed a vector or scalar quantity? What is it measured in?

A

-scalar
-rad s^-1

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18
Q

How can we calculate angular speed? (2)

A

-https://cdn.savemyexams.co.uk/cdn-cgi/image/w=1920,f=auto/uploads/2021/04/6.1.3-Angular-Speed-Equation-2.png

where:
Δθ = change in angular displacement (radians)
Δt = time interval (s)

-https://cdn.savemyexams.co.uk/cdn-cgi/image/w=1920,f=auto/uploads/2021/04/6.1.3-Angular-Speed-Equation-1.png

where:
v = linear speed (m s^-1)
r = radius of orbit (m)
T = the time period (s)
f = frequency (Hz)

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19
Q

Draw a diagram showing a particle in uniform circular motion with its angular speed and linear speed

A

https://cdn.savemyexams.co.uk/cdn-cgi/image/w=1920,f=auto/uploads/2020/10/12.1.1.2-Angular-speed-diagram_1.png

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20
Q

What is centripetal acceleration defined as?

A

the acceleration of an object towards the centre of a circle when an object is in motion (rotating) around a circle at a constant speed

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21
Q

How can we calculate centripetal acceleration? (3)

A

-https://cdn.savemyexams.co.uk/cdn-cgi/image/w=1920,f=auto/uploads/2020/09/3.-Calculating-Centripetal-Acceleration-equation-1-1.png

-https://cdn.savemyexams.co.uk/cdn-cgi/image/w=1920,f=auto/uploads/2020/09/3.-Calculating-Centripetal-Acceleration-equation-2.png

-https://cdn.savemyexams.co.uk/cdn-cgi/image/w=1920,f=auto/uploads/2020/09/3.-Calculating-Centripetal-Acceleration-equation-4.png

where:
a = centripetal acceleration (m s^−2)
v = linear speed (m s^−1)
⍵ = angular speed (rad s^−1)
r = radius of the orbit (m)

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22
Q

How can we calculate linear speed?

A

v = r⍵

where:
v= linear speed (ms^-1)
r= radius (m)
⍵= angular speed (rad s^-1)

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23
Q

What is the centripetal force defined as?

A

the resultant force towards the centre of the circle required to keep a body in uniform circular motion
-always directed towards the centre of the body’s rotation.

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24
Q

What would happen if to an object in circular motion if the centripetal force didn’t exist anymore?

A

the object will move in the direction of the velocity at that point and fall in the very same direction no longer moving in a circular path

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25
Q

How can we calculate the centripetal force?

A

https://cdn.savemyexams.co.uk/cdn-cgi/image/w=1920,f=auto/uploads/2020/10/4.-Calculating-Centripetal-Force-equation-1.png

where:
F = centripetal force (N)
v = linear velocity (m s^-1)
⍵ = angular speed (rad s^-1)
r = radius of the orbit (m)

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26
Q

Give examples of centripetal forces in these scenarios:

-car travelling around a roundabout
-ball attached to a rope moving in a circle
-earth orbiting the sun

A

-friction between car tyres and the road
-tension in the rope
-gravitational force

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27
Q

For a car rotating and being able to hold a corner, what is needed?

A

the limiting frictional (centripetal) force must be enough to maintain the motion

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28
Q

How can we work out the limiting frictional (centripetal) force which prevents an object in circular motion (on a flat surface) from slipping?

A

F= µmg

where
f= limiting frictional force
µ= coefficient of friction
mg= weight (on a flat surface)

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29
Q

How can we work out the maximum speed of an object (on a flat surface) in circular motion before it slips?

A

v= õgr

where:
v= max speed of object (ms^-1)
µ= coefficient of friction
g= gravitational field strength (Nkg^-1)
r= radius (m)

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30
Q

Why do banked paths increase the speed of an object compared to flat paths?

A

-flat paths only consist of one centripetal force
-When a car/airplane moves on a banked pathway, the normal reaction force is at an angle so the horizontal component provides some centripetal force meaning less is provided from friction
-this means the car/airplane can move faster around the bend before the max frictional force is reached

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31
Q

How can we find the speed of an object moving on a banked pathway? Derive the equation explaining each step

A

-first split the normal force into its components
-find tanθ by doing sin/cos with the components (1)
-as the weight is equal to the vertical component, substitute the vertical with mg
-rearrange to find the horizontal component (2)
-as the mgtanθ is equal to the horizontal component, it is also equal to the centripetal force equation which can be rearranged to find the speed (3, 4)

1) tanθ= normal horizontal/ normal vertical
2) mgtanθ- normal horizontal force
3) mgtanθ= mv^2/r
4) v= √grtanθ (as the mass cancels out on both sides)

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32
Q

What is simple harmonic motion

A

a specific type of oscillation

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33
Q

What do we mean by equilibrium in SHM?

A

the position of an object where no resultant force is acting on it

34
Q

What do we mean by a restoring force?

A

a force which acts to bring a body back from equilibrium

35
Q

What are the two conditions required for SHM to occur?

A

-acceleration of the oscillating object is proportional to the displacement
-the acceleration of the oscillating object must be in opposite directions to the displacement

36
Q

Give some examples of oscillators which undergo SHM (4)

A

-the pendulum of a clock
-a mass on a spring
-guitar strings
-the electrons in alternating current flowing through a wire

37
Q

What equation can be used to show the relationship between acceleration and displacement in SHM?

A

a ∝ −x

38
Q

What is something to know about the direction of the restoring force in SHM?

A

-always moves in opposite direction to displacement
-the restoring force and acceleration always act in the same direction (towards equlibrium)

39
Q

Draw and label a diagram of an oscillating pendulum consisting of the restoring force, acceleration and displacement

A

https://cdn.savemyexams.co.uk/cdn-cgi/image/w=1920,f=auto/uploads/2021/04/17.1-SHM-pendulum.png

40
Q

How can we find the acceleration of an object oscillating in SHM from a graph?

A

a= -A ⍵^2 cos (⍵t)

where:
a= acceleration (ms^-2)
A= amplitude (m)
⍵= angular frequency (rad s^-1)
t= time (s)

41
Q

How can we find the acceleration of an object oscillating in SHM?

A

a = −⍵^2 x

where:
a = acceleration (m s^-2)
⍵ = angular frequency (rad s^-1)
x = displacement (m)

42
Q

How can we find the acceleration of an object oscillating in SHM when the object is at max displacement?

A

substitute the displacement with the amplitude, don’t multiply equation with the -1

43
Q

How can we find the displacement of an object oscillating in SHM from a graph (from its maximum displacement)?

A

x= A cos (⍵t)

where:
x= displacement (m)
A= amplitude (m)
⍵ = angular frequency (rad s^-1)
t= time (s)

44
Q

How can we find the displacement of an object oscillating in SHM from a graph (from its equilibrium position)?

A

x = A sin (⍵t)

where:
x= displacement (m)
A= amplitude (m)
⍵ = angular frequency (rad s^-1)
t= time (s)

45
Q

How can we find the max displacement for an object in SHM?

A

x max= amplitude

46
Q

How can we find the velocity of an object oscillating in SHM from a graph?

A

v= -A ⍵ sin (⍵t)

where:
where:
v= velocity (ms^-2)
A= amplitude (m)
⍵ = angular frequency (rad s^-1)
t= time (s)

47
Q

How can we find the velocity of an object oscillating in SHM?

A

v= ±⍵√(A^2-x^2)

where:
v = speed (m s^-1)
A = amplitude (m)
⍵ = angular frequency (rad s^-1)
x = displacement (m)

48
Q

How can we find the maximum velocity of an object oscillating in SHM?

A

v max= A⍵

where:
v = speed (m s^-1)
A = amplitude (m)
⍵ = angular frequency (rad s^-1)

49
Q

When is the velocity of an oscillating object in SHM at the maximum?

A

at the equilibrium position (when x=0)

50
Q

What can a mass-spring system be used for in SHM?

A

can be used as a simple harmonic oscillator

51
Q

How can we work out the time period of a mass-spring system in SHM?

A

https://cdn.savemyexams.co.uk/cdn-cgi/image/w=1920,f=auto/uploads/2021/04/6.2.4-Mass-Spring-Time-Period-Equation.png

where:
T = time period (s)
m = mass on the end of the spring (kg)
k = spring constant (N m^-1)

52
Q

What can a simple pendulum be used for in SHM? What is it made of?

A

-another type of simple harmonic oscillator

-the pendulum consists of a string and a bob (a weight, generally spherical) at the end

53
Q

What is something needed to know when oscillating a simple pendulum? Why

A

-the angle by which the pendulum is displaced must be less than 10°
-this is due to the derivation of the time period formula where a small angle approximation is used, so for larger angles this approximation is no longer valid, therefore isn’t a good model

54
Q

How can we work out the time period of a simple pendulum?

A

https://cdn.savemyexams.co.uk/cdn-cgi/image/w=1920,f=auto/uploads/2021/04/6.2.5-Period-of-Pendulum-Equation-_2.png

where:
T = time period (s)
L = length of string (m)
g = gravitational field strength (N kg^-1)

55
Q

What types of energy are exchanged during SHM?

A

-kinetic
-potential (could be in many forms e.g. elastic/gravitational energy)

56
Q

Draw an energy-displacement graph of the kinetic and potential energy during 1/2 a cycle of SHM. Explain at which points the energies are at a maximum

A

https://cdn.savemyexams.co.uk/cdn-cgi/image/w=1920,f=auto/uploads/2021/05/6.2.7-Energy-graph-with-displacement.png

-the kinetic energy is at a maximum when the displacement x = 0 (equilibrium position)
-the potential energy is at a maximum when the displacement is at a maximum x = A (amplitude)

57
Q

What is something to know about the total energy during SHM?

A

the total energy of a simple harmonic system always remains constant and is equal to the sum of the kinetic and potential energies

58
Q

Draw an energy-time graph of the energies during SHM

A

https://cdn.savemyexams.co.uk/cdn-cgi/image/w=1920,f=auto/uploads/2021/04/17.1-Energy-graph.png

59
Q

SHM

RP7: (mass-spring system) Describe this practical

A

-calculate the spring constant of a mass-spring system
-done by investigating how the time period of the oscillations varies with the mass

60
Q

SHM

RP7: (mass-spring system) What is the y=mx equation?

A

https://cdn.savemyexams.co.uk/cdn-cgi/image/w=1920,f=auto/uploads/2021/04/6.2.8-Spring-Constant-from-Graph.png

61
Q

SHM

RP7: (simple pendulum) Describe this practical

A

-calculate the acceleration due to gravity from a simple pendulum
-done by investigating how the time period of its oscillations varies with its length

62
Q

SHM

RP7: (simple pendulum) What is the y=mx equation?

A

https://cdn.savemyexams.co.uk/cdn-cgi/image/w=1920,f=auto/uploads/2021/04/6.2.8-g-from-Graph.png

63
Q

What is damping?

A

where the energy in an oscillator is lost to the environment, leading to reduced amplitude of oscillations

64
Q

What are the three types of damping?

A

-light damping
-critical damping
-heavy damping

65
Q

What do we mean by light damping?

A

-where the amplitude gradually decreases by a small amount each oscillation
-also known as under-damping

66
Q

What do we mean by critical damping?

A

reduces the amplitude to zero in the shortest possible time (without oscillating)

67
Q

What do we mean by heavy damping?

A

-where the amplitude reduces slower than with critical damping, also without oscillating
-also known as over-damping

68
Q

Why does damping occur?

A

due to resistive forces, such as friction or air resistance, which act in the opposite direction to the motion, or velocity, of an oscillator

69
Q

What is a key feature of SHM regarding damping?

A

frequency of damped oscillations don’t change

70
Q

How do free oscillations occur?

A

-when there is no transfer of energy to or from the surroundings
-happens when an oscillating system is displaced and then left to oscillate

71
Q

What is a free oscillation?

A

an oscillation where there are only internal forces acting and there is no energy input

72
Q

Why does damping occur?

A

due to resistive forces, such as friction or air resistance, which act in the opposite direction to the motion, or velocity, of an oscillator

73
Q

What is a key feature of SHM regarding damping?

A

frequency of damped oscillations don’t change

74
Q

What are forced oscillations?

A

oscillations acted on by a periodic external force where energy is given in order to sustain oscillations

75
Q

What is a free oscillation?

A

an oscillation where there are only internal forces acting and there is no energy input

76
Q

What do we mean by the driving frequency?

A

the frequency of forced oscillations

77
Q

What do we mean by the natural frequency?

A

the frequency of an oscillation when the oscillating system is allowed to oscillate freely

78
Q

What is resonance?

A

where the amplitude of oscillations of a system drastically increase due to gaining an increased amount of energy from the driving force

79
Q

How does resonance occur?

A

when the driving frequency is equal to the natural frequency of a system

80
Q

What are some applications of resonance? (3)

A

instruments- an instrument such as a flute has a long tube in which air resonates, causing a stationary sound wave to be formed

radio- these are tuned so that their electric circuit resonates at the same frequency as the desired broadcast frequency

swing- if someone pushes you on a swing they are providing a driving frequency, which can cause resonance if it’s equal to the resonant frequency and cause you to swing higher

81
Q

How does damping affect resonance?

A

-reduces the amplitude of resonance vibrations
-Note: the natural frequency f0 of the oscillator will remain the same

82
Q

What are some negative effects of resonance? Give two examples

A

-can cause damage to a structure

-e.g. on a bridge, when people cross, the driving frequency will be close to the natural frequency meaning the bridge would oscillate violently
-this could be very dangerous and damage the bridge

-e.g. glass tube smashing from a sound wave at a driving frequency close to the natural frequency causing large oscillations

AQA A-level Physics (11 decks)

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