Further Mechanics Flashcards
(110 cards)
1
Q
How do you work out an angle in radians?
A
Angle in radians = arc-length / radius of circle
2
Q
How do you convert from angle in degrees to angle in radians?
A
Multiply by 180/π
3
Q
What is 180° equal to in radians?
A
π
4
Q
What is 90° equal to in radians?
A
π/2
5
Q
What is 45° equal to in radians?
A
π/4
6
Q
What is the angular speed of an object?
A
The speed an object rotates through per second
7
Q
What is the units of angular speed?
A
rad s^-1
8
Q
What is the equation for angular speed?
A
ω = θ / t
9
Q
What other equation is there for angular speed, involving radius of circle and linear speed?
A
ω = V / r
10
Q
What is the frequency of circular motion?
A
Number of complete revolutions per second (rev s^-1)
11
Q
What is the period of circular motion?
A
The time taken for a complete revolution
12
Q
What equation links frequency and period for circular motion?
A
Frequency = 1 / Time period
13
Q
Describe the acceleration of objects travelling in circles
A
The object is accelerating because the velocity is changing
14
Q
In what direction is the acceleration of an object towards when travelling in a circle?
A
Acceleration is towards the centre of the circle
15
Q
What is the centripetal acceleration?
A
The acceleration of an object moving in a circle, always directed towards the centre of the circle
16
Q
Why is the linear velocity of an object moving in a circle always changing?
A
Because the direction is constantly changing
17
Q
What are the 2 equations for centripetal acceleration?
A
A = v^2 /r A = ω^2 x r
18
Q
What is a centripetal force?
A
The force on an object moving with circular motion. It’s directed towards the centre of the circle, and is responsible for the object’s curved path
19
Q
What are the 2 equations for centripetal force?
A
F = mv^2 / r
F m x ω^2 x r
20
Q
What happens to the motion of the object is the centripetal force in removed?
A
The object will fly off at a tangent with velocity, V
21
Q
What keeps an object moving in a circle?
A
The centripetal force acting towards the centre
22
Q
What is the trend of the acceleration due to the Earth’s gravity as you move further away?
A
As you move further away from the planet, the acceleration due to gravity decreases
23
Q
What is simple harmonic motion?
A
The oscillation of an object where the object’s acceleration is directly proportional to its displacement from its equilibrium position, and is always directed towards the equilibrium
24
Q
What is an example of something that uses simple harmonic motion?
A
A metronome
25
Describe the force present for simple harmonic motion?
There is always a restoring force pulling or pushing the object back towards the equilibrium position
26
What affects the size of the restoring force?
The displacement
27
What does the restoring force make the object do?
Accelerate back towards the equilibrium
28
What things have to be proportional for simple harmonic motion?
Acceleration ∝ Displacement (a ∝ -x)
| Force ∝ Displacement (f ∝ -x)
29
What does the displacement-time graph look like for simple harmonic motion?
A sine or cosine graph (depending on if starts at amplitude max or 0)
30
How do you work out the velocity from the displacement-time graph of simple harmonic motion?
Velocity is the gradient
31
What is the maximum velocity of simple harmonic motion equal to?
ωA, where ω is the angular frequency and A is the maximum amplitude
32
What is the difference between the meaning of ω for circular motion and the meaning for it in simple harmonic motion?
Circular motion: ω is the angular speed
Simple harmonic motion: ω is angular frequency
Both have same values
33
How do you find the acceleration from a velocity-time graph of simple harmonic motion?
Acceleration is the gradient
34
What is the maximum acceleration of simple harmonic motion equal to?
ω^2 x A
35
What is phase difference?
A measure of how much one wave lags behind another
36
What are the 3 ways that phase difference can be measured?
Radians
Degrees
Fractions of a cycle
37
What is the phase difference of 2 waves that are in phase?
0 or 2π
38
What is the velocity-time graph of simple harmonic motion derived from?
The gradient of the displacement-time graph (which explains why the velocity-time graph is at minimum/maximum point when d-t graph has displacement 0)
39
What is the phase difference between the velocity and the displacement in the v-t and d-t graphs for simple harmonic motion?
π/2 = 1/4 of a cycle
40
What is the phase difference between the acceleration and the velocity in the a-t and v-t graphs for simple harmonic motion?
π/2 = 1/4 of a cycle
41
What is the phase difference between the acceleration and the displacement in the a-t and d-t graphs for simple harmonic motion?
π = 1/2 of a cycle so they are in anti-phase
42
What is the cycle of oscillation of simple harmonic motion?
From maximum displacement to the right (+ve) to maximum displacement to the left (-ve) and back again
43
What is frequency of simple harmonic motion?
The number of oscillation cycles per second
44
What is the period of simple harmonic motion?
The time it takes for 1 oscillation cycle
45
What is the amplitude of an oscillation equal to for simple harmonic motion?
The maximum magnitude of the displacement
46
Describe the forces when an object in simple harmonic motion moves towards the equilibrium position?
The restoring force does work on the object, so transfers some gravitational potential energy to kinetic energy?
47
Why is the velocity of an object in simple harmonic motion at a maximum when at equilibrium position?
Because the potential energy is said to be zero, so kinetic energy is at a maximum
48
Describe the forces when an object in simple harmonic motion moves away from the equilibrium position?
The kinetic energy is transferred to gravitational potential energy
49
Why is the velocity of an object in simple harmonic motion zero when it reaches it's maximum amplitude?
Because the objects potential energy is at a maximum, so its kinetic energy is zero
50
What is mechanical energy?
The sum of the potential and kinetic energy
51
What stays constant during simple harmonic motion?
Mechanical energy
52
What is the equation for displacement of an object in simple harmonic motion?
x = r cosθ = A cos(ωt)
r: Radius of circle
x: Displacement
A: Amplitude
ω: Angular frequency
t: Time
53
For the equation displacement = A cos(ωt), when do you need to start timing for the equation to work?
Start timing when object is at maximum amplitude
54
What is the equation for acceleration of an object in simple harmonic motion?
a = -ω^2 x
55
Why, in the equation a = -ω^2 x, is there a minus sign?
The acceleration is always acting towards the centre of the circle
56
For an object in simple harmonic motion, when does an object's maximum acceleration occur?
When it's at maximum amplitude
57
What is the equation for the magnitude of the max acceleration of an object in simple harmonic motion?
a max = ω^2 A
58
What is the equation for the velocity of an object in simple harmonic motion?
V = ±ω√ (A^2 - x^2)
59
When is the velocity of an object in simple harmonic motion positive and when is it negative?
Positive when moving in the positive direction (left to right) and negative when moving in the negative direction (right to left)
60
What is the equation for maximum velocity of an object in simple harmonic motion?
V max = ωA
As max velocity is at displacement=0
61
What equation links angular speed/frequency (ω) with frequency (f)?
ω = 2πf
62
What is a simple harmonic oscillator?
An oscillator which is neither driven or damped
63
What are 3 properties of a simple harmonic oscillator?
1. Motion is about an equilibrium position where point no net force acts on the system
2. The restoring force is proportional to and oppositely directed to the displacement.
3. Motion is periodic
64
What is the equation for the restoring force?
F = k∆l
65
What is damping?
Restraining of vibratory motion by dissipation of energy
66
What is the equation for the period of oscillations for a simple harmonic oscillator?
T = 2π√(m/k)
m: Mass
k: Spring constant
67
Describe the experiment for investigating the mass-spring system?
Attach a trolley to a spring, pull it to one side and let go. The trolley will oscillate back and forth as the spring pushes and pulls in each direction
68
What could you use to measure the period in the mass-spring system experiment?
Use a computer to plot a displacement-time graph from a data logger connected to a position sensor
69
For the mass-spring system, what is the mass proportional to?
The period squared (T^2)
70
What is the square of period proportional to for the mass-spring system?
Proportional to 1/spring constant
71
What affect does changing the amplitude of the mass-spring experiment have on the period?
No effect, so period is the same
72
What is the simple pendulum an example of?
A simple harmonic oscillator
73
What is the formula for an oscillating pendulum?
T = 2π√(l/g)
l: Length of pendulum
g: gravitational field strength
74
Describe the experiment for investigating the period of a simple pendulum
Use a computer attached to an angle sensor to plot a displacement-time graph for a swinging pendulum, then read the period from the graph
75
What is the length of the pendulum proportional to?
Period^2
76
What 2 things are independent from the period of a swinging pendulum?
Mass of the bob at the bottom and the amplitude of the swing
77
What are free vibrations?
The oscillation of an object with no transfer of energy to or from the surroundings
78
What is the resonant frequency?
The frequency of an object oscillating freely
79
Give 2 examples of free vibrations
Stretch then release a mass on a spring
| Sound caused by striking a metal object
80
If no energy's transferred to or from the surroundings, it will keep...?
Oscillating with the same amplitude forever (in theory)
81
What are forced vibrations?
The oscillation of an object caused by an external driving force
82
What can cause forced vibrations?
A system can be forced to vibrate by a periodic external force
83
What is driving frequency?
The frequency of a periodic external force that causes forced vibrations of an object
84
What is the phase difference if the driving frequency is much less than the resonant frequency?
0 or 2π
85
What is the phase difference if the driving frequency is much greater than the resonant frequency?
π/2 (out of phase)
86
Why is the driving frequency out of phase with the resonant frequency is the driving frequency is greater?
Because the oscillator won't be able to keep up, so the driver ends up out of phase with the oscillator
87
What happens when an object is resonating?
It's vibrating with a rapidly increasing amplitude
88
What causes resonance?
When the driving force approaches the resonant frequency of the object, the system gains more energy from the driving force, so vibrates more with an increasing amplitude
89
What is the phase difference between the driver and oscillator at resonance?
90° = π/4
90
Describe the relationship between displacement of the driver and displacement of the oscillator
When the driver displacement is at a maximum, the oscillator displacement is at its equilibrium point
91
Give 2 examples of resonance
A glass resonates when driven by a sound wave at the right frequency
A swing resonates if driven by someone pushing it at its resonant frequency
92
Why is another name for a damping force: dissipative force?
Because it dissipates the energy of the oscillator into the environment
93
What is damping?
A force which causes an oscillating object to lose energy and so causes the amplitude of the objects oscillations to decrease
94
Why are some systems deliberately dampened?
To stop them oscillating or to minimise the effect of resonance
95
What type of force normally causes am oscillating system to lose its energy to the surroundings?
Frictional forces such as air resistance
96
How do shock absorbers in a car work?
Provide a damping force by squashing oil through a hole when compressed
97
The heavier the damping...?
The quicker the amplitude is reduced to zero (overdamping is an exception)
98
What happens with a lightly damped system?
Takes a long time to stop oscillating, and their amplitude only reduces a small amount each period
99
What happens to a heavily damped system?
Takes a short time to stop oscillating, and their amplitude reduces a large amount every period
100
What type of damping is a pendulum with a small bob?
Light damping
101
Why is a pendulum with a small bob an example of light damping?
Air resistance will cause the pendulum to slow down only very slightly every period
102
What is critical damping?
A damping force that reduces the amplitude in the shortest possible time
103
What type of damping is car suspension?
Critical damping
104
Why are car suspension critical damped?
So they don't oscillate, instead return to equilibrium position as quickly as possible
105
What is overdamping?
Heavy damping that causes the system to take longer to return to equilibrium position than critical damping
106
Give an example of something that is overdamped?
Some doors so they don't slam shut too quickly, instead they close slowly
107
What is ductility?
Physical property of a material associated with the ability to be hammered thin or stretched into a wire without breaking
108
How does plastic deformation of ductile materials have the same effect as damping?
It reduces the amplitude of the oscillations because as the material changes shape, it absorbs energy, so the oscillations are smaller
109
What is plastic deformation?
When a material is permanently stretched beyond its elastic limit
110
How does an organ pipe work?
The column of air resonates in an organ pipe, driven by the motion of air at the base. This creates a stationary wave in the pipe
