Gravitational Fields and Oscillations

Question 1

How are gravitational fields represented by field lines?

Answer 1

Arrows show direction of the field, and separation of lines show field strength

Question 2

What is Newton’s Law of Gravitation?

Answer 2

Any two point masses attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of their separation.

Question 3

Express Newton’s Law of Gravitation mathematically

Answer 3

F= -GMm/r^2

The minus sign shows the force is attractive

Question 4

What is gravitational field strength?

Answer 4

The gravitational field strength at a point is the gravitational force exerted per unit mass on a small object placed at that point.

Question 5

Derive a formula for gravitational field strength from the formula for gravitational force.

Answer 5

g=F/m
As F= -GMm/r^2,
g= -GM/r^2

Question 6

How can you find orbital velocity?

Answer 6

By equating centripetal and gravitational force:
mv^2/r = GMm/r^2
v^2=GM/r

Question 7

How can you find the orbital period?

Answer 7

As speed= distance/time
v= 2pi x r/ T (where T is the orbital period)
so 4pi^2r^2/T^2 = GM/r (from equating centripetal and gravitational force)
T^2 = 4pi^2r^3 / GM

Question 8

What is Kepler’s Third Law of Planetary Motion?

Answer 8

The square of the orbital period is proportional to the cube of the planet’s distance from the Sun

Question 9

Describe the features of a geostationary orbit.

Answer 9

24 hours
Remains above a fixed point on the Earth
Used for television broadcasting and telecommunications transmissions

Question 10

Give two examples of oscillations.

Answer 10

A swinging pendulum

A trolley tethered to two springs displaced from its equilibrium position

Question 11

Define the terms: displacement, amplitude, period and frequency

Answer 11

Displacement x- distance from equilibrium position
Amplitude a- maximum displacement
Period T- time for one complete oscillation
Frequency f- Number of oscillations per unit time (1/T)

Question 12

Define the terms phase and phase difference

Answer 12

Phase- the point an oscillating mass has reached within the complete cycle of an oscillation
Phase difference-the fraction of oscillation that two oscillations are out of step with each other (only applicable for identical oscillations)

Question 13

Give some examples of simple harmonic motion

Answer 13

Vibrating string of a guitar
The vibrating electrons when an alternating current flows in a wire
The vibrating air molecules when a pure sound wave travel through them

Question 14

What are the three requirements for simple harmonic motion?

Answer 14

1. An oscillating mass
2. An equilibrium position
3. A restoring force that acts to return the mass to its equilibrium position, directly proportional to the displacement x and directed towards the equilibrium position

Question 15

What is angular frequency?

Answer 15

As an oscillation can be represented by 2pi radians, there must be 2pi x f oscillations in one unit time. This is the angular frequency of oscillation. As f = 1/T, angular frequency also = 2pi/T

Question 16

Define simple harmonic motion.

Answer 16

A body executes simple harmonic motion if its acceleration is directly proportional to its displacement from its equilibrium position, and is always directed towards the equilibrium position.

Question 17

Give the equation that defines simple harmonic motion.

Answer 17

a = -(2pi f)^2x (where a is acceleration, f is frequency and x is displacement)

Question 18

When does a mass executing simple harmonic motion have maximum speed?

Answer 18

When it passes through the equilibrium position

Question 19

What is the formula for the maximum speed of a mass executing simple harmonic motion?

Answer 19

V= 2pifA (where A is amplitude)

Question 20

Between which two forms is energy interchanging during simple harmonic motion?

Answer 20

Potential and kinetic energy

Question 21

How are the amounts of potential and kinetic energy affected by displacement?

Answer 21

Potential energy is at its maximum when displacement is maximum( +/- A), and kinetic energy is at its maximum at the equilibrium position. At all values of displacement, total energy (KE + PE) is the same.

Question 22

What is damping?

Answer 22

When resistive forces remove energy from an oscillating system, causing amplitude to decay exponentially with time, as well as the decrease of the maximum speed.

Question 23

Why does damping cause amplitude to decay exponentially rather than linearly?

Answer 23

Velocity is proportional to amplitude, so at first the mass is moving rapidly as the amplitude is large. Energy is lost quickly and the amplitude decays at a high rate. As the amplitude decreases, the mass is moving more slowly and so energy is lost more slowly, so the amplitude decreases at a lower rate.

Question 24

How are frequency and amplitude of a simple harmonic oscillator related?

Answer 24

The frequency and amplitude are independent of each other.

Question 25

Give an example of a use of damping.

Answer 25

Shock absorbers damp the oscillating springs in cars to prevent long-term vibration after going over a bump

Question 26

What is resonance?

Answer 26

When a system capable of oscillating freely is forced to oscillate, and the forcing frequency matches the natural frequency of the system, the amplitude of the oscillations grow dramatically.

Question 27

Give an example of how damping can reduce the effects of resonance.

Answer 27

During earthquakes, resonance can occur, resulting in serious damage to buildings. In order to reduce this effect, the buildings may be built on foundations that absorb the energy of the shock waves, damping the oscillations.

Question 28

Describe how damping and resonance are related.

Answer 28

As the degree of damping increases, the amplitude of the resonant vibrations decreases.

Question 29

Describe the use of resonance in microwave cooking

Answer 29

Microwaves used in cooking have a frequency that matches the natural frequency of the vibration of water molecules. The water molecules vibrate and absorb the energy of the microwave radiation. The molecules get hotter and the energy spreads through the food, cooking it.

Question 30

Describe the use of resonance in radio

Answer 30

Radio aerials pick up many different frequencies, and the tuner can be adjusted to resonate at the frequency of the transmitting station you are interested in, and its circuit produces a large-amplitude signal for this frequency only.