Further Mechanics, Thermal Physics & Gases

Question 1

Amplitude of Oscillations

Answer 1

• The amplitude of the oscillations is the maximum displacement of the oscillating object from equilibrium.
• If amplitude is constant and no frictional forces are present then the object is described as freely oscillating/vibrating.

Question 2

Time period ( Simple harmonic motion)

Answer 2

The time for one complete cycle of oscillation. (starting from a start point and returning back to it)

Question 3

Angular Velocity

Answer 3

The rate of change of angular displacement with time.

Question 4

Angular Displacement

Answer 4

For any object in uniform circular motion, the object turns through an angle of 2π/T radians per second

Question 5

Centripetal acceleration

Answer 5

The acceleration of an object towards the centre of a circle due to a constantly changing velocity at a tangent to the circle.

Question 6

Centripetal Force

Answer 6

F= mv²/r / F= mω²r
The resultant force of an object in circular motion that always acts towards the centre of the circle.

Question 7

How do banked tracks prevent the skidding of an object in circular motion?

Answer 7

• For an object travelling in a circular path, there is a centripetal force pushing the object towards the centre of the circle.
• On an a sloped/banked track, the force from the inwards push of the bank (+ any friction) can be provided by the centripetal force
• The support force ( Horizontal component ) will supply the centripetal force rather than the friction so there is no skidding

Question 8

Why did the object experience a force down on itself when on a big dipper?

Answer 8

On a big dip at high speed you would be pushed in to your seat.
The difference between the support force on the object and it’s weight is the centripetal force
S = mv²/r +mg

Question 9

Oscillating Motion

Answer 9

Oscillation is the motion back and forth about a fixed point in a straight line.

Question 10

Define SHM

Answer 10

Simple Harmonic Motion is an oscillating motion caused by a force that repeatedly acts to restore a moving object to its equilibrium position.

Question 11

Conditions for Simple Harmonic Motion

Answer 11

• The acceleration is proportional to the displacement
• The acceleration is in the opposite direction to the displacement

a = -ω²x

Question 12

Resonance

Answer 12

When within a forced oscillation system the driving frequency is the same as the natural frequency, causing the amplitude to become large

Resonance is achieved when the phase difference between the driving oscillation and oscillating object is pi/2 ( but at the beginning of the motion the force driver and oscillator’s phase difference is 0)

at a systems natural frequency it is the most stable so the amplitude of the oscillations increase massively

Resonance can only occur when damping is small

Question 13

Damping Forces

Answer 13

Damping forces are Fricitonal/Dissipative Forces oppose the motion of the oscillating body; they slow or stop simple harmonic motion from occurring.

ALL UNDAMPED OSCILLATORS ARE CLOSED SYSTEMS (energy does not enter or leave)
thus, TOTAL ENERGY = KE +GPE

Light Damping - slowly reduces amplitude of oscillations but keeps the time period almost constant.
Heavy Damping - occurs when the damping is so strong that the displaced object returns to equilibrium much more slowly than if the system is critically damped, no oscillation motion occurs (e.g mass on a spring in thick oil)
Critical Damping - the oscillating system returns to equilibrium in the shortest possible time, with little to no oscillation (e.g mass-spring system vehicle suspension systems)

Question 14

An object in simple harmonic motion is experiencing light damping due to drag forces, what is the effect of this on the time period?
The object is now 2x in mass how is the frequency of oscillations affected?

Answer 14

T = 2π (L/g) ½

The amplitude of the oscillation does not affect the time period of the oscillation as it is not found in the time period equation.
mass also does not affect the time period because it is independent of the time period for the same reason.

Only things affecting time period are length of pendulum and gravitational field strength.

Question 15

Equilibrium Position

Answer 15

Position of the lowest energy state

Question 16

What is Temperature?

Answer 16

Temperature is a measure of the average kinetic energy of the particles in a substance.

• A substance with a high temperature means the particles are vibrating/moving with higher AVERAGE speeds compared with the same substance at lower temperature

Question 17

What is absolute zero?

Answer 17

When the internal energy of substance is at its minimum (as the kinetic energy u 0)

Question 18

what is internal energy?

Answer 18

The internal energy of an object is the sum of the random distribution of the kinetic and potential energies of its molecules

Question 19

First Law of Thermodynamics

Answer 19

The change in internal energy of the object is the total energy transfer due to work done and heating

• due to this when a substance is not heated or cooled it acts as a closed system because no matter or energy is transferred in and out of the system
• this means the substance has a constant internal energy.
• the average speed of the particles in a substance will stay the same provided a closed system

Question 20

heat transfer

Answer 20

• heat is always transferred from hotter substances to cooler substances
• the particles with more energy transfers some energy to particles with less energy
• heat is transferred by radiation, hotter substance radiate heat quicker than cooler substances

Question 21

Specific heat capacity

Answer 21

The specific heat capacity is the energy needed to raise 1kg of a substance by 1K without changing state

Question 22

Specific latent heat

Answer 22

the energy required to change the state of 1kg of a substance without a change in temperature

specific latent heat of fusion - energy required to change 1kg of sold into liquid without coming temperature

specific latent heat of vaporisation - the energy required to change 1kg of a liquid into a gas without changing temperature

Question 23

Experimental Gas Laws

Answer 23

Boyle’s Law - the inversely proportional relationship between pressure and volume (PV = constant) (isothermal)
P1V1=P2V2

Charles Law - under constant pressure an ideal gas’ volume is proportional to its absolute temperature (PV = T)
work done = pressure x change in volume (on a volume time graph)
V1/T1=V2/T2
any change when pressure stays the same is an isobaric change
any change when pressure is not constant is a

Pressure Law - pressure of a gas of fixed mass and fixed volume is directly proportional to the gas’s absolute temperature (P = kT)
P1/T1=P2/T2

Question 24

Ideal Gas

Answer 24

and ideal gas is a theoretical gas that obeys the experimental gas laws at all pressures and temperatures

ideal gas assumptions
- all gas particles are identical to each other
- all particle motion in a gas is continuous and random
- all particle motion follow a straight line
- all molecules in a gas have a negligible volume compared to the volume of a container
- the gravitational and electrostatic force between the gas particles does not exist
- the internal energy of a gas has no potential energy store, only a kinetic energy store
- the newtonian laws of motion are obeyed and there are enough molecules to apply statistical laws
- all particle-container collisions are elastic
-

avogadro’s law
V/n = V2/n2
equal volumes of different gases at the same pressure and temperature will contain equal numbers of particles

Question 25

Boltzman constant

Answer 25

Question 26

molecular kinetic theory

Answer 26

- the temperature relates to the average speed of the particles within a gas - root mean square speed is different to average speed the average speed of gases in random motion will always be 0 -

Answer 27

- energy is constantly transferred between the particles within a system, through collisions between the particles - however, the total combined beefy of the particles is unchanged - this occurs when a system of particles is isolated/ closed when not heated or cooled

Question 28

If two materials with different specific heat capacities undergo the same temperature will they have the same internal energy? (assume same potential energy)

Answer 28

- No - The object with the higher specific heat capacity will store more kinetic energy per temperature change, so will have more internal energy. - this also means the object will be a larger kinetic energy store and have particles moving, on average at a higher speed

Question 29

How can we make sure the heat energy transfer from a heat is 100% efficient

Answer 29

- use of insulation material (cladding) - insuring good thermal contact i.e in the case of water an a heater, using a small amount of oil between them

Answer 30

- the amount of pressure produced is dependent on the rate of change of momentum ( the no. of collision speed second) - the higher the no. of collisions the greater the pressure

Question 31

How does Brownian motion prove the existence of atoms?

Answer 31

- Brownian motion is the random motion of particles of varying/range of speeds -Brownian motion can be observed under a microscope, - it is observed when small particles (such as pollen or smoke particles) suspended in liquid or gas are observed to move around in a random, erratic fashion. - the collisions between the gas particles and large smoke/pollen particles caused random changes in their speeds and directions - ( the particles are able to effect their speeds because they travel at much larger speeds and have a lot of momentum)

Question 32

Derivation of the kinetic theory of gases equation

Answer 32

The derivation is based on: -the conservation of momentum before an after an elastic collision of a particle ( mv=-mv -> 2mv) - the pressure of a particle P= F/A - the average velocity on the three planes of motion x,y,z and how due to the assumptions made by ideal gas law they all equal each other so Crms^2 = 3V(x)^2 = 1/3N*m*crms^2

Question 33

Outline what is meant by an ideal gas

Answer 33

(for “outline” questions they are looking for combinations of the features of a certain thing) any from: - molecules have negligible volume - collisions are elastic - there are no interactions between molecules - the gas obeys the ideal gas laws/obeys *Boyle’s law* at **ALL pressures and temperatures **

Question 34

What constitutes Free Vibrations?

Answer 34

- If the amplitude is constant and no frictional forces are present, the oscillations are free vibrations

Question 35

How to the find the phase difference of two oscillators in motion

Answer 35

phase difference in radians = 2πΔt/T where Δt is did time between successive instant the two objects are at maximum displacement in the same direction

Question 36

The relationship between the velocity and the displacement

Answer 36

- the magnitude of the velocity is greatest when the gradient of the displacement-time graph is greatest - the velocity is zero when the gradient of the displacement-time graph is zero (max displacement)

Question 37

The relationship between the acceleration and a simple harmonic oscillator

Answer 37

- The acceleration is greatest when the gradient of the velocity-time graph is greatest, (this is when velocity is zero and occurs at maximum displacement in the opposite direction) - the acceleration is zero when the gradient of the velocity-time is zero. This is when the displacement is zero and the velocity is a maximum

Answer 38

The acceleration is always in the opposite direction to the displacement

Question 39

Simple Harmonic motion is defined as oscillating motion in which…

Answer 39

1 - acceleration is proportional to the displacement and 2 - always in the opposite direction to the displacement a = -ω^2 x

Question 41

What is the Restoring Force

Answer 41

- The result force on an on

Answer 42

- Adding Mass - extra mass increases inertia to the system, thus at a given displacement the trolley would be slower. Each cycle of oscillation will therefore take longer - Using Weaker Springs (low spring constant) - The restoring force on the trolley at any given displacement would be less, so the trolley's acceleration and speed at any given displacement would be less. Each cycle of oscillation would therefore take longer (F=ke)

Question 43

How do you find the acceleration for an object in a mass spring-system?

Answer 43

a = restoring force/mass = -kx/m

Question 45

For a Free Oscillator, what is the total energy of the system?

Answer 45

As long as friction is absent, the total energy of the system is constant and is equal to its maximum potential energy Etot = KE + PE

Question 46

Energy-Displacement Graphs for a Oscillating System

Answer 46

Question 47

Natural Frequency and Forced Vibrations

Answer 47

- A system that oscillates without a periodic force being applied to it has a frequency = the natural frequency - when a periodic force is applied to an oscillating system the response depends on the frequency of the periodic force (Forced Vibrations)

Question 48

What is the effect of increasing the Applied Frequency on a mass-spring system under Forced Vibrations

Answer 48

As the frequency increases, - the amplitude of oscillations of the system increases until it reaches a maximum amplitude at a particular frequency, and then the amplitude decreases again - the phase difference between the displacement and the periodic force increases from zero to 1/2 π at the maximum amplitude, the 1/2 π to π as the frequency increases further

Question 49

Resonance

Answer 49

- when a system is oscillating at the maximum amplitude, the phase difference between the displacement and the periodic force is 1/2 π - The periodic force is then exactly in phase with the velocity of the oscillating system - resonance - the frequency at the maximum amplitude is called the resonant frequency - the lighter the damping - the larger the maximum amplitude becomes at resonance - the closer the resonant frequency is to the natural frequency of the system - the applied frequency becomes increasingly larger than the resonant frequency of the mass-spring system: - the amplitude of oscillations decreases more and more - the phase difference between the displacement and the periodic force increases from 1/2 π until the displacement is π radians out of phase with the periodic force if no damping: applied frequency of periodic force = natural frequency at resonance

Question 50

Which of the pendulums will oscillate with the greatest amplitude when the driver pendulum (D) is oscillating

Answer 50

- The effect of the oscillating motion of D is transmitted along the support thread - subjecting each of the other pendulums to **forced oscillations** - Pendulum R due to being the **same length** and **time period** as D, will have a **natural frequency = to the natural frequency of D** - R oscillates in **resonance** with D - the response of each of the pendulums depend on how close its length is to the *length of D*,and whether they r *shorter or longer* than D

Question 51

Motion Over the top of a hill

Answer 51

- At the top of a hill the support force (S) is directly upwards - The resultant force on the vehicle is the different between the weight and the support force mg - S = mv^2/r the vehicle would lose contact with the road if its speed is equal to or greater than a particular speed S = 0

Question 52

What is a Free and Forced Oscillation?

Answer 52

Free - An object oscillates at its natural frequency Forced - An object is made to oscillate by an external driving frequency when the driving frequency = the natural frequency, large amplitude oscillations occur (resonance)

Question 53

How can you prevent resonance from occurring?

Answer 53

- By changing the natural frequency of a system to one that is unlikely to resonate by changing the stiffness of supplies - introducing damping systems, these do not change the resonant frequency but they do alter the sharpness of the resonant peak