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 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 -
Critical Damping

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