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A-Level Physics > 6: Further Mechanics & Thermal Physics > Flashcards

6: Further Mechanics & Thermal Physics Flashcards

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1
Q

Motion in a circular path at a constant speed implies ____

A

There is an acceleration and requires a centripetal force

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2
Q

Magnitude of Angular Speed

A

ω = v / r = 2 π f

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3
Q

Centripetal Acceleration

A

a = v² / r = ω² r

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4
Q

Centripetal Force

A

F = m v² / r = m ω² r

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5
Q

Analysis of Characteristics of SHM

A

SHM is an oscillation in which the acceleration of an object is directly proportional to its displacement from its equilibrium position, and is directed towards the equilibrium

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6
Q

Condition for SHM

A

a ∝ -x

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7
Q

Defining Equation for SHM

A

a = -ω² x

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8
Q

SHM Displacement Equation

A

x = A cos(ω t)

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9
Q

SHM Speed Equation

A

v = ±ω √(A² - x²)

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10
Q

Internal Energy

A

The sum of the kinetic energies and potential energies of the particles in a body

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11
Q

First Law of Thermodynamics

A

The internal energy of a system is increased when energy is transferred to it by heating or when work is done on it

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12
Q

Graphical Representation Linking Variation of x with Time

A

https://revise.im/content/02-physics/03-unit-4/03-simple-harmonic-motion/displacement_time.jpg

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13
Q

Graphical Representation Linking Variation of v with Time

A

https://revise.im/content/02-physics/03-unit-4/03-simple-harmonic-motion/velocity_time.jpg

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14
Q

Graphical Representation Linking Variation of a with Time

A

https://revise.im/content/02-physics/03-unit-4/03-simple-harmonic-motion/acceleration_time.jpg

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15
Q

Maximum Speed

A

ω A

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16
Q

Maximum Acceleration

A

ω² A

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17
Q

Variation of Eₖ, Eₚ & Total Energy with Displacement (5)

A
  • As the object moves towards the equilibrium, the restoring force does work on the object so transfers Eₚ to Eₖ
  • As the object moves away from equilibrium, Eₖ is transferred to Eₚ
  • At equilibrium, Eₚ is 0 and Eₖ is a maximum
  • At maximum displacements, Eₖ is 0 and Eₚ is a maximum
  • The sum of Eₖ and Eₚ, total energy, stays constant
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18
Q

Study of Mass-Spring System

A

T = 2 π √(m / k)

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19
Q

Study of Simple Pendulum

A

T = 2 π √(l / g)

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20
Q

Effects of Damping on Oscillation

A

Oscillating systems lose energy to their surroundings, which reduces the amplitude of oscillation over time. This is due to damping forces, usually frictional forces

21
Q

Change of State

A

The potential energies of the particle ensemble are changing but not the kinetic energies

22
Q

Energy to Change Temperature Equation

A

Q = m c Δθ where c is specific heat capacity

23
Q

Energy to Change State Equation

A

Q = m l where l is the specific latent heat

24
Q

Boyle’s Law

A

At a constant temperature, the pressure p and volume V of a gas are inversely proportional

25
Q

Charle’s Law

A

At a constant pressure, the volume V of a gas is directly proportional to its absolute temperature T

26
Q

Pressure Law

A

At a constant volume, the pressure p of an ideal gas is directly proportional to its absolute temperature T

27
Q

Required Practical 8

A

Investigation of Boyle’s law (constant temperature) and Charles’s law (constant pressure) for a gas

28
Q

Required Practical 8: Charle’s Law Method (6)

A
  1. Record the volume of the conical flask and tubing between the gas syringe and conical flask by pouring water into them and then pouring that volume of water into a measuring cylinder
  2. Set the volume of the gas syringe to 40 cm³ and attach the tubing and conical flask to it
  3. Place the conical flask into a water bath and leave it for 3 minutes to reach thermal equilibrium
  4. Record the volume of the gas syringe
  5. Using a thermometer, record the temperature of the water bath
  6. Repeat steps 3 to 5 changing the temperature of the water bath
29
Q

Types of Damping (4)

A
  • Light damping: Systems take a long time to stop oscillating and their amplitude only reduces by a small amount each period
  • Heavy damping: Systems take a short time to stop oscillating and their amplitude reduces by a large amount each period
  • Critical damping reduces the amplitude in the shortest possible time
  • Overdamping is even heavier damping and systems take longer to return to equilibrium than a critically damped system
30
Q

Free Vibrations

A

No transfer of energy to or from the surroundings - the system oscillates at its natural frequency

31
Q

Forced Vibrations (5)

A
  • A system can be forced to vibrate by a periodic external force
  • The oscillations are at the frequency of the driver
  • The amplitude is high at small frequencies and low at large frequencies
  • When frequency of driver » natural frequency of driven, displacements are in antiphase
  • When frequency of driver « natural frequency of driven, displacements are in phase
32
Q

Resonance (4)

A
  • Frequency of the driver is equal to the natural frequency of the driven
  • Large amplitude oscillations
  • Maximum energy transfer from driver to driven
  • Displacement of driver leads on displacement of driven by π / 2 radians
33
Q

Required Practical 7

A

Investigation into simple harmonic motion using a mass–spring system and a simple pendulum

34
Q

Required Practical 7: Mass–Spring System Method (4)

A

https: //3.bp.blogspot.com/-GbqbC_4lAEE/VdA8U9hlaUI/AAAAAAAAIi8/uGgO6aX5bQE/s1600/mass-spring-system-oscillations-nov2002p4q3.png
1. Set up the apparatus in the diagram with a 100 g mass and a pin in the equilibrium position as a fiducial marker
2. Pull the mass hanger vertically downwards a few centimetres and release
3. Record the time taken for 10 complete oscillations
4. Repeat steps 2 and 3 increasing the mass

35
Q

Avogadro Constant

A

N_A is 6.02 x 10²³ Particles per Mole

36
Q

Molecular Mass

A

The sum of the atomic masses of the atoms making up a molecule

37
Q

Molar Mass

A

The mass of 1 mole of a substance in grams and is equal to the molecular mass

38
Q

Ideal Gas Equations (2)

A
  • p V = n R T for n moles

- p V = N k T for N molecules

39
Q

Molar Gas Constant

A

R is the value of p V / T for 1 mole of a gas

40
Q

Boltzmann Constant

A

k is equivalent to R / N_A

41
Q

Work Done on an Ideal Gas

A

p ΔV

42
Q

Required Practical 7: Simple Pendulum Method (5)

A

https: //i.ytimg.com/vi/jneLdSsGlpE/hqdefault.jpg
1. Set up the apparatus as show in the diagram clamping the pendulum between two blocks
2. Measure the length of the pendulum from the point of suspension to the centre of mass of the pendulum bob
3. Pull the bob to the side and release it
4. Using a stopwatch, measure the time taken for 10 oscillations
5. Repeat steps 2 to 4 changing the length of the pendulum

43
Q

Brownian Motion (3)

A
  • Brownian motion is where large particles suspended in a fluid move randomly
  • Large, heavy particles are moved by collisions with smaller, lighter particles travelling randomly at high speeds
  • This is evidence that fluids are made up of tiny atoms moving really quickly
44
Q

Relationships between p, V, T (3)

A
  • As temperature increases, the average speed of the molecules increases. Hence, the rate of change of momentum of the molecules colliding with the walls increases and the number of collisions per second so force and pressure increase
  • Increasing temperature will increase volume. This is because there are less molecules-wall collisions per second, reducing the NET force. However, the molecules have more kinetic energy so are faster so there’s more momentum change per collision. Hence, pressure is kept constant
  • Increasing volume reduces the number of molecule-wall collisions per second. This decreases the NET force and increases the wall surface area. Hence, pressure decreases
45
Q

Derivation of Kinetic Theory Model (8)

A
  • Imagine a cubic box with sies of length l containing N molecules each of mass m
  • Say molecule Q travels towards a wall with velocity u. During the collision, its momentum changes by -2 m u
  • Assuming Q doesn’t collide with other molecules, the time between the collisions is 2 l / u. Hence, the rate of change of momentum is -2 m u × u / 2 l
  • Force equals the rate of change of momentum and the force exerted on the wall by the molecules is equal and opposite so is m u² / l
  • Let the mean square speed be ̅u² = (u₁² + u₂² + … + u_N²) / N
  • Hence the pressure on one wall is:
    p = total force / area = N m ̅u² / l ÷ l² = N m ̅u² / l³ = N m ̅u² / V
  • Q can move in 3 dimensions – x, y and z. So the overall mean square speed ̅c² = ̅u² + ̅v² + ̅w². Since the molecules move randomly, ̅u² = ̅v² = ̅w² so ̅c² = 3 ̅u²
  • Substituting the above equation:
    p = 1/3 N m ̅c² / V
    p V = 1/3 N m ̅c² or 1/3 N m (cᵣₘₛ)² where cᵣₘₛ is the root mean square speed
46
Q

Assumptions in Kinetic Theory (8)

A
  • All molecules of the gas are identical
  • The gas contains a large number of molecules so statistical laws apply
  • The molecules have negligible volume compared to the container
  • The molecules continually move about randomly
  • Newtonian mechanics apply
  • Collisions are perfectly elastic
  • Intermolecular forces are negligble
  • The forces that act during collisions last for much less time than the time between collisions
47
Q

Average Molecular Kinetic Energy

A

1/2 m (cᵣₘₛ)² = 3/2 k T = 3 R T / 2 N_A

48
Q

Required Practical 8: Boyle’s Law Method (4)

A
  1. Measure the internal diameter of the syringe using vernier callipers
  2. Set the volume on the syringe to 40 cm³, seal it and clamp it to the desk. Connect a string from the plunger, over a pulley to a vertical hook with a 100 g hanging mass on it
  3. Record the volume of the syringe
  4. Repeat steps 2 and 3, increasing the mass on the hook

A-Level Physics (9 decks)

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