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Physics Paper 1 > Further Mechanics > Flashcards

Further Mechanics Flashcards

1
Q

Describe motion in a circular path at a constant speed

A

Motion in a circular path at constant speed implies there is an acceleration and requires a centripetal force

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2
Q

Which direction does a Centripetal Force act

A

A centripetal force always acts towards the centre of the circle

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3
Q

What is Angular Speed

A

The angle an object moves through per unit time

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4
Q

What are the Equations for Angular Speed

A

ω = v / r

Angular Speed = Velocity / Distance

ω= 2πf

Angular Speed = 2π x Frequecny

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5
Q

What are the Equations for Centripetal Acceleration

A

a = v2 / r = ω2r

Acceleration = Velocity2 / Distance = Angular Speed2 X Distance

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6
Q

What are the Equations for Centripetal Force

A

F = mv2 / r = mω2r

Centripetal Force = Mass x Velocity2 / Distance = Mass x Angular Speed2 x Distance

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7
Q

When is an object experencing simple harmonic motion

A

When its acceleration is directly proportional to displacement from the equilibrium point and is in the opposite direction

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8
Q

What is the equation for accleration in simple harmonic motion

A

a = -ω2x

Accleration = - Angular Speed2 x Displacement

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9
Q

What is the equation for displacement in simple harmonic motion

A

x = A Cos(ωt)

Displacement = Amplitude x Cos(Angular Speed x Time)

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10
Q

What is the equation for velocity in simple harmonic motion

A

v = ± ± ω √(A2 - x2)

Velocity = ± Angular Speed √(Amplitude2 - Displacement2)

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11
Q

When are velocity and acceleration at their maximum and minimum on a pendulm

A
  • Velocity Max = Centre
  • Velcoity Zero = Amplitude
  • Acceleration Max = Amplitude
  • Accleration Zero = Centre
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12
Q

What are the equations for velocity max and acceleration max

A
  • Vmax = ωA
  • amax = ω2A
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13
Q

Describe the displacement-time graph of simple harmonic motion

A
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14
Q

Describe the Velocity-Time Graph of Simple Harmonic Motion

A
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15
Q

Describe the Acceleration-Time Graph of Simple Harmonic Motion

A
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16
Q

Describe the Time Period Equation for a Simple Harmonic Pendulum

A

T = 2π √(L / g)

Time Period = 2π √ (Length of the String / Acceleration due to Gravity)

17
Q

Explain why the simple harmonic pendulum only works for small angles

A
  • The angle by which the pendulum is displaced must be less than 10°
  • This is because during the derivation of the above formula a small angle approximation is used, and so for larger initial angles this approximation is no longer valid, and would not be a good model
  • Therefore the amplitude must be small
18
Q

What are the Limitations of the Simple Harmonic Motion Equations for a Simple Pendulum

A
  • The amplitude is small
  • The string is inextensible
  • The bob used is a point mass
19
Q

How would you measure the time period of the oscillations of a simple pendulum as accurately as possible

A
  • Use a fiducial mark at the centre of oscillations
  • Work out 10 oscillations and then divide by 10 to get the mean
20
Q

Where should you place the fiducial mark

A

The mark should be at the equilibrium position since this is where the mass moves with greatest speed

21
Q

Describe the Time Period Equation for a Mass-Spring Simple Harmonic System

A

T = 2π √ (m / k)

Time Period = 2π √ (Mass / Spring Constant)

22
Q

Describe the Energy Transfers that occur in a Mass-Spring Simple Harmonic System

A
  • There are two types of mass-spring system, where the spring is vertical or horizontal
  • For the vertical system, kinetic energy is converted to both elastic and gravitational potential energy
  • In the horizontal system, kinetic energy is converted only to elastic potential energy
23
Q

Describe the Energy Transfers that occur in any Simple Harmonic System

A
  • Kinetic energy is transferred to potential energy and back as the system oscillates (the type of potential energy depends on the system)
  • At the amplitude = maximum amount of potential energy
  • As it moves towards the equilibrium position, this potential energy is converted to kinetic energy
  • At the centre = maximum kinetic energy
  • Then as the system moves away from the equilibrium again, the kinetic energy is transferred to potential energy until it is at a maximum again
  • The total energy of the system remains constant (when air resistance is negligible, otherwise energy is lost as heat)
24
Q

Describe the graph of potential enegery against kinetic energy for a simple harmonic system

A
25
Q

What is Damping

A

Where the energy in an oscillating is lost to the environment, leading to reduced amplitude of oscillations

26
Q

Describe a Graph of the Effect of Damping

A
27
Q

Describe the three main types of damping

A
  • Light damping - This is also known as under-damping and this is where the amplitude gradually decreases by a small amount each oscillation
  • Critical damping - This reduces the amplitude to zero in the shortest possible time (without oscillating).
  • Heavy damping - This is also known as over-damping, and this is where the amplitude reduces slower than with critical damping, but also without any additional oscillations.
28
Q

What are some of the charactertics of a Damping Force

A
  • The size of the force is directly proportional to the negative velocity
  • F ∝ - v
  • It causes the kinetic energy to be transferred into other forms of energy (such as heat)
29
Q

When do free vibrations/oscillations occur

A

When no external force is continuously acting on the system, therefore the system will oscillate at its natural frequency

30
Q

When do forced vibrations/oscillators occur

A

Forced vibrations are where a system experiences an external driving force which causes it to oscillate

31
Q

What happens when the driving force from a forced oscillator is less than, equal to or higher than the natural frequency

A
  • If the driving frequency is less than the natural frequency it causes a small amplitude
  • If the driving frequency is higher than the natural frequency it causes a small amplitude
  • If the driving frequency is equal to the natural frequency then it causes a very large amplitude (resonance)
32
Q

What is Resonance

A

Resonance occurs when the driving force is equal to the natural frequency so the system experiences max amplitude oscillations due to an increased amount of energy

33
Q

What are some examples of resonance

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
  • Bridge - resonance is a negative effect for a bridge for example when the people crossing a bridge they may provide a driving frequency close to the natural frequency so it will begin to oscillate violently which could be very dangerous and damage the bridge
34
Q

How can the oscillations of a bridge be reduced in order to stop resonace from occuring

A
  • Stiffen the structure (by reinforcement)
  • Install dampers or shock absorbers
35
Q

What is meant by the term forced oscillation

A

When the oscillations are caused by a driving force that is periodic to the free oscillations

Physics Paper 1 (15 decks)

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