Module 5: Newtonian World and Astrophysics

Question 1

What are energy levels?

Answer 1

The name of the discrete set of energies that electrons of atoms in a gas can exist in

Question 2

Why are the energy level of gaseous atoms negative?

Answer 2

Energy is required to remove an electron.

Question 3

What does if mean is an electron has an energy of zero?

Answer 3

It’s free from the atom.

Question 4

What is the ground state (Energy levels)?

Answer 4

Most negative energy level.

Question 5

What does it mean when an electron has been “excited”?

Answer 5

It has moved from a lower energy level to a higher energy level.

Question 6

What happens if a photon doesn’t have enough energy to free an electron?

Answer 6

If it has just enough energy to move it up an energy level, it excites the electron. This energy is the difference in energy between the two energy levels.

Question 7

What happens once electrons have been excited?

Answer 7

They go back down to the lowest energy level they can and emit a photon, and when this light is diffracted, you get an emission line spectrum.

Question 8

What is a spectrum?

Answer 8

A graph of intensity vs frequency.

Question 9

What is a line spectrum?

Answer 9

A series of lines against a background formed by the diffraction of light emitted from excited electrons.

Question 10

What are the three types of spectra?

Answer 10

Continuous spectra: The diffraction of white light produces this spectrum.

Emission line spectra: The result of the diffraction of photons emitted when electrons move to lower energy levels, the colourful lines indicate different energies and are against a dark background.

Absorption line spectra: Similar to emission line spectra but there are dark lines against a continuous spectrum.

Question 11

What are the similarities and differences between emission and absorption line spectra?

Answer 11

Similarity: Lines appear at the same frequencies / positions

Difference: Emission is coloured lines against a dark background, while absorption is dark lines against a coloured background

Question 12

What is required for an object to undergo uniform circular motion?

Answer 12

There must be a resultant force of constant magnitude that is always directed radially inward. This force is called the centripetal force.

Acceleration must be perpendicular to velocity.

Question 13

Why is speed constant during uniform circular motion?

Answer 13

Resultant force and motion are perpendicular, so no work is done in the direction of motion.

Question 14

Name some examples of sources of centripetal forces.

Answer 14

• Friction
• Tension
• Gravitational force
• Changes in normal contact force

Question 15

Define simple harmonic motion.

Answer 15

When a system oscillates about its equilibrium position in a periodic manner.

Question 16

What is the defining equation for simple harmonic motion?

Answer 16

a = -ω²𝑥

Question 17

Describe simple harmonic motion.

Answer 17

When displaced from equilibrium, a restoring force acts towards equilibrium, the size of which is directly proportional to displacement but in the opposite direction.

Question 18

What equation can be used to find the time period of a pendulum?

Answer 18

T = 2𝛑 √(l/g)

Where l is the length of the pendulum and g is the acceleration due to gravity.

Question 19

What equation can be used to find the time period of a mass on a spring?

Answer 19

T = 2𝛑 √(m/k)

Where m is the mass of the masses and k is the spring constant of the spring.

Question 20

How is energy transferred in a pendulum system?

Answer 20

At the highest point: Maximum potential energy, zero kinetic energy.

As it swings down: Potential energy turns into kinetic energy.

At the lowest point: Maximum kinetic energy, zero potential energy.

As it swings up: Kinetic energy turns back into potential energy.

Energy continuously shifts between kinetic and potential energy as the pendulum swings, but total energy remains constant.

The graph for this has a sinusoidal shape.

Question 21

How is energy transferred in a horizontal mass-spring system?

Answer 21

At maximum displacement: Maximum elastic potential energy, zero kinetic energy.

Moving toward equilibrium: Elastic potential energy turns into kinetic energy.

At equilibrium: Maximum kinetic energy, zero elastic potential energy.

Moving away from equilibrium: Kinetic energy turns back into elastic potential energy.

Energy continuously shifts between kinetic and elastic potential energy as the mass moves but total energy remains constant.

The graph for this has a sinusoidal shape.

Question 22

How is energy transferred in a vertical mass-spring system?

Answer 22

At maximum displacement (compression): Maximum elastic potential energy and gravitational potential energy, zero kinetic energy.

Moving toward equilibrium (down): Elastic potential energy and gravitational potential energy turn into kinetic energy.

At equilibrium: Maximum kinetic energy, lower elastic potential energy and lower gravitational potential energy.

Moving away from equilibrium (down): Kinetic energy turns back into elastic potential energy (extension) and lower gravitational potential energy unit at maxium extension (EPE is max, KE is 0).

Energy shifts between elastic potential, gravitational potential, and kinetic energy as the mass moves but total energy remains constant.

Question 23

What is damping?

Answer 23

Damping is the process by which a system loses energy over time due to external forces (such as friction or air resistance), causing the amplitude of oscillations to decrease.

Question 24

Describe light damping.

Answer 24

The amplitude of oscillations decreases gradually over time.

The system oscillates for a long time before coming to rest.

The frequency of oscillation remains almost the same.

Question 25

Describe critical damping.

Answer 25

Amplitude of the oscillations is reduced to zero in the shortest possible time, returning the system to the equilibrium point.

This is the ideal case for stopping oscillations without overshooting the equilibrium

Question 26

Describe heavy damping.

Answer 26

When a system returns to equilibrium slowly without oscillating.

Question 27

Describe resonance.

Answer 27

Resonance occurs when a system is driven at its natural frequency, resulting in a large increase in amplitude. This happens because the driving force is applied at the frequency at which the system naturally wants to oscillate.

Question 28

What is natural frequency?

Answer 28

Every oscillating system has a natural frequency, the frequency at which it oscillates when no external driving or damping force is applied.

Question 29

What is a driving force?

Answer 29

An external force applied to the system that keeps it oscillating

Question 30

How are amplitude and frequency related?

Answer 30

The amplitude of oscillations depends on the frequency of the driving force (bell shaped graph). At resonance, this amplitude reaches its maximum as the frequency of the driving force matches the natural frequency of the system.

Question 31

What are the advantages of resonance?

Answer 31

• Efficient energy transfer (e.g., radios, microwaves).
• Enhances performance (e.g., musical instruments, sensors).
• Key in medical imaging (e.g., MRI).
• Useful in engineering applications (e.g., clocks, filters).

Question 32

What are the disadvantages of resonance?

Answer 32

• Structural damage risk (e.g., bridges, buildings).
• Unwanted noise/vibrations in machinery.
• Safety hazards (e.g., aircraft, earthquakes).
• Adds complexity to engineering design.

Question 33

What is Newton’s law of universal gravitation?

Answer 33

Two masses attract each other with a force that is directly proportional to the product of their masses, and inversely proportional to the square of the distance between their centres.

Question 34

Define gravitational field strength.

Answer 34

The force per unit mass

Question 35

Define gravitational potential.

Answer 35

The work done per unit mass to move a small test mass from infinity to a point in the field a distance r from the centre of the attracting mass.

Question 36

Define gravitational potential energy.

Answer 36

The work done to move a test mass from infinity to a distance r from the centre of the attracting mass.

Question 37

What are equipotential surfaces?

Answer 37

Surfaces where the gravitational potential is constant and no work is required to move a mass along an equipotential surface.

Question 38

What is Kepler’s first law?

Answer 38

The orbit of a planet is an ellipse with the Sun at one of the two foci.

Question 39

What is Kepler’s second law?

Answer 39

A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.

This is because planets move faster when they are closer to the Sun and slower when they are farther away, ensuring that the area swept out over a given time remains constant.

Question 40

What is Kepler’s third law?

Answer 40

The square of the orbital period, T, of a planet of mass M, is directly proportional to the cube of the average radius, r, of its orbit.

T² ∝ r³, where k = 4π²/GM