Physics 6 - Further Mechanics and Thermal Physics

Question 1

What kind of force is required to keep an object moving in a circle at a constant speed?

Answer 1

A constant centripetal force (A force applied towards the centre of the circle of motion).

Question 2

True or false; “An object moving in a circle at a constant speed is accelerating.”?

Answer 2

True. The direction is always changing, hence the velocity is always changing, where acceleration is defined as the change in velocity over time.

Question 3

What equation(s) can you use to calculate the magnitude of angular speed.

Answer 3

ω=v/r
ω=2πf
Where:
ω=Angular velocity (s⁻¹)
v=Linear velocity (ms⁻¹)
r=Radius of circular motion (m)
f=Frequency of rotation (Hz)

Question 4

What is angular acceleration in terms of angular velocity?

Answer 4

a=ω²r
Where:
a=Angular acceleration (ms⁻²)
ω=Angular velocity (s⁻¹)
r=Radius of circular motion (m)

Question 5

What is angular acceleration in terms of velocity?

Answer 5

a=v²/r
Where:
a=Angular acceleration (ms⁻²)
v=Linear velocity (ms⁻¹)
r=Radius of circular motion (m)

Question 6

What are the equations for centripetal force?

Answer 6

F=mv²/r
F=mω²r
Where:
F=Centripetal force (N)
m=Mass of object (kg)
v= Linear velocity (ms⁻¹)
ω=Angular velocity (s⁻¹)
r=Radius of circular motion (m)

Question 7

What is a radian?

Answer 7

The angle of a circle sector such that the arc length is equal to the radius.
Radians are usually written in terms of π.
2π radians=360°

Question 8

What are the conditions for simple harmonic motion?

Answer 8

Acceleration must be proportional to is displacement from the equilibrium point and it must act towards the equilibrium point.
a∝-x

Question 9

What is the constant of proportionality linking acceleration and displacement in simple harmonic motion?

Answer 9

-ω² or -k/m

Question 10

What is displacement as a trigonometric function of t and ω in simple harmonic motion?

Answer 10

x=Acos(ωt) or x=Asin(ωt)
Where:
x=Displacement (m)
A=Amplitude (m)
ω=Angular speed (s⁻¹)
t=Time (s)

Question 11

How can you calculate the maximum speed in simple harmonic motion using ω and A?

Answer 11

Max speed=ωA
Where:
Max speed (ms⁻¹)
ω=Angular speed (s⁻¹)
A=Amplitude (m)

Question 12

How can you calculate the maximum acceleration using ω and A?

Answer 12

Max acceleration=ω²A
Where:
Max acceleration (ms⁻²)
ω=Angular speed (s⁻¹)
A=Amplitude (m)

Question 13

What is the equation for the time period of a mass-spring simple harmonic system?

Answer 13

T=2π√(m/k)
Where:
T=Time period (s)
m=Mass (kg)
k=Spring (Nm⁻¹)

Question 14

What is the equation for the time period of a simple harmonic pendulum?

Answer 14

T=2π√(l/g)
Where:
T=Time period (s)
l=Length of pendulum (m)
g=Gravitational field strength (ms⁻²)

Question 15

What is the small angle approximation for sin(x)?

Answer 15

sin(x)≈x

Valid in radians

Question 16

What is the small angle approximation for cos(x)?

Answer 16

cos(x)≈1-(x²/2)

Valid in radians

Question 17

Define free vibrations.

Answer 17

The frequency a system tends to vibrate at in a free vibration is called the natural frequency.

Question 18

Define forced vibrations.

Answer 18

A driving force causes the system to vibrate at a different frequency.
For higher driving frequencies, the phase differences between the driver and the oscillations rises to π radians.
For lower frequencies, the oscillations are in phase with the driving force.
When resonance occurs, which is when it most efficiently transfers energy to the system, the phase difference will be π/2 radians.

Question 19

Define damping and explain what critical damping, overdamping and underdamping are.

Answer 19

Damping occurs when an opposing force dissipates energy to the surroundings.
Critical damping reduces the amplitude to zero in the quickest time.
Overdamping is when the damping force is too strong and it returns to equilibrium slowly without oscillation.
Underdamping is when the damping force is too weak and it oscillates with exponentially decreasing amplitude.

Question 20

What happens to a vibration with greater damping?

Answer 20

For a vibration with greater damping, the amplitude is lower at all frequencies due to greater energy losses from the system. The resonant peak is also broader because of the damping.

Question 21

What are some implications of resonance in real life?

Answer 21

Implications of resonance include that soldiers must stop when crossing bridges and vehicles must be designed so there are no unwanted vibrations.

Question 22

What is internal energy?

Answer 22

The sum of potential and kinetic energies of a system.

Question 23

How can you increase the thermal energy of a system?

Answer 23

By heating it up or doing work on the object.

Question 24

Explain the energy changes that occur during a change of state.

Answer 24

During a change of state, the potential energy of the particles change, but their kinetic energies don’t change.

Question 25

What equation can be used to determine the energy required to change the temperature of a substance?

Answer 25

Q=mcΔT
Where:
Q=Energy (J)
m=Mass of substance (kg)
c=Specific heat capacity of substance (Jkg⁻¹K⁻¹)
ΔT=Change in temperature (K)

Question 26

Give the equation to work out the energy required for a change of state?

Answer 26

Q=ml
Where:
Q=Energy (J)
m=Mass of substance (kg)
l=Latent heat capacity (Jkg⁻¹)

Question 27

What is the Ideal gas equation?

Answer 27

pV=nRT
Where:
p=Pressure (pa)
V=Volume (m³)
n=Number of moles
R=The molar gas constant (8.31 Jmol⁻¹kg⁻¹)
T=Temperature (K)

Question 28

What is the first law of thermodynamics?

Answer 28

ΔU=Q-W
Where:
ΔU=Change in internal energy (J)
Q=The heat added to a system (J)
W=The work done by the system (J)

Question 29

What is the specific heat capacity of a substance?

Answer 29

The energy required to raise the temperature of 1kg of a substance by 1K.

Question 30

What is the specific latent heat of a substance?

Answer 30

The energy required to change the state per unit mass of a substance, while keeping the temperature constant.

Question 31

What is an ideal gas?

Answer 31

A gas where:
The gas molecules don’t interact with each other
The molecules are thought to be perfectly spherical.

Question 32

What is the internal energy of and ideal gas equal to?

Answer 32

It is equal to the internal energy of an ideal gas.

Question 33

What is Boyle’s law?

Answer 33

Pressure is inversely proportional to volume, providing temperature is constant.

Question 34

In an ideal gas, how would increasing the volume change the temperature of the gas, while the pressure remains constant?

Answer 34

As you increase the volume, you also increase the temperature.

Question 35

Explain how increasing the temperature of a balloon, while keeping the volume the same will increase the pressure.

Answer 35

As the temperature increases, the average kinetic energy increases.
Therefore the particles are travelling at a higher speed on average.
There are also more frequent collisions.
Which means the particles would exert a greater force.
Which would cause an increased rate of change of momentum.
This would therefore increase pressure.

Question 36

What is absolute zero?

Answer 36

The temperature at which objects have no/minimum kinetic energy. This temperature is -273°C, or 0K.

Question 37

What is Avogadro’s constant?

Answer 37

The number of atoms there are in one mole of a substance (6.02×10²³).

Question 38

True or false: “All collisions between particles and between particles and the wall are elastic.” is an assumption of an ideal gas?

Answer 38

True.

Question 39

Describe some assumptions of the ideal gas equation.

Answer 39

The time for each collision is negligible in comparison to the time taken between collisions.
The particles move randomly.
The particles follow Newton’s laws of motion.
No intermolecular forces act between particles.
The volume of the particles is negligible compared to the volume of the container they are in.

Question 40

What is meant by the root mean square speed?

Answer 40

The square root of the mean of the squares of the speeds of the molecules.

Question 41

What is Brownian motion?

Answer 41

Brownian motion is the idea that very small objects have random motion in a liquid or gas due to random bombardment by the molecules in this substance.
This movement will be fractionally more on one side than the other so a force will push it for an instant as the net forces shift directions.
This random motion is Brownian Motion and gives evidence for the existence of atoms.