Download - Revision Unit 5

Physics: Unit 5 –Revision Exercises. Done by: Nidal Al Halabi

THERMAL ENERGY:

1. (a) What is meant by the absolute zero of temperature?

.....................................................................................................................................

..................................................................................................................................... (1)

(b) (i) The Football Association rules require a football to have a maximum volume of

5.8 × 10–3

m3 and a maximum pressure of 1.1 × 10

5 Pa above atmospheric

pressure (1.0 × 105 Pa). Assuming that the thickness of the material used for the

ball is negligible and that the air inside the ball is at a temperature of 10 °C,

show that the maximum amount of air inside the football is about 0.5 mol.

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...........................................................................................................................

........................................................................................................................... (4)

(ii) One mole of air has a mass of 0.029 kg. Calculate the maximum mass of air

allowed in the football.

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...........................................................................................................................

Maximum mass = .................................. (1)

(iii) A football is also required to have a minimum pressure 0.6 × 105 Pa above

atmospheric pressure. Assuming the volume of the football remains constant,

calculate the lowest temperature to which the air inside this ball could fall to

while still meeting the pressure requirements.

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Lowest temperature = .................................. (3)

(Total 9 marks)


2. A problem with warming milk in a saucepan is that it can suddenly boil over if it is not

watched carefully. A student decides to take some measurements to find the time it takes for

the milk to reach a temperature of 96 °C so he can be ready for it without having to keep a

constant watch.

(a) The student first uses an electric hotplate to warm a saucepan of water from room

temperature to 96 °C. He measures the time taken to be 347 s.

He calculates the heat energy gained by the water to be 1.63 × 105 J.

Show that the rate at which heat energy is supplied to the water by the electric hotplate

is about 500W.

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.....................................................................................................................................

..................................................................................................................................... (2)

(b) The student then uses the following data to calculate the time taken for milk taken

from a refrigerator to reach the temperature of 96 °C.

mass of milk = 0.44 kg

initial temperature of milk = 12 °C

desired final temperature of milk = 96 °C

specific heat capacity of milk = 3800 J kg–1

°C–1

(i) Show that the heat energy the milk needs to gain is about 1 × 105 J.

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...........................................................................................................................

........................................................................................................................... (2)

(ii) Calculate the time it would take for the milk to reach the temperature of 96 °C.

Assume that the student uses the same hotplate as in (a).

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...........................................................................................................................

...........................................................................................................................

Time = ............................................................... (2)


(c) The student warms up the milk and is surprised when the time taken is exactly the

time calculated. He had expected it to take longer because of heat losses.

(i) Explain why he might expect it to take longer.

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........................................................................................................................... (1)

(ii) Suggest why the calculated time was the same as the actual time.

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...........................................................................................................................

........................................................................................................................... (1)

(Total 8 marks)

3. In a radio programme about space tourism, the presenter says that the Earth‟s atmosphere

stops 100 km above the surface. A student decides to put this claim to the test, initially

applying the following equation to gas molecules at this height:

where k is the Boltzmann constant.

(a) (i) State the meanings of the other symbols used in the equation.

m .......................................................................................................................

c2 ....................................................................................................................

T ....................................................................................................................... (3)

(ii) What physical quantity does each side of the equation represent?

...........................................................................................................................

........................................................................................................................... (1)

kTcm2

3

2

1 2


(iii) Calculate a value for the velocity of an oxygen molecule at this height, where

the temperature is −50 °C.

Mass of oxygen molecule = 5.4 × 10–26

kg

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...........................................................................................................................

Velocity = ......................................... (2)

(b) The student decides that if there really is no atmosphere above the height of 100 km

this velocity must be equal to the escape velocity. The escape velocity is the minimum

velocity needed for any particle to escape from the Earth‟s gravitational attraction.

He obtains an expression for the escape velocity, starting with the total energy of a

molecule at this height, i.e. its kinetic energy + its potential energy.

(i) He finds that the potential energy of a mass m at distance r from the centre of

the Earth is given by −GMm/r, where M is the mass of the Earth. Hence show

that the escape velocity is given by:

vesc =

...........................................................................................................................

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...........................................................................................................................

........................................................................................................................... (2)

r

GM2


(ii) Show that the escape velocity for an oxygen molecule from this height is more

than 10 km s–1

.

Mass of Earth = 5.98 × 1024

kg

Radius of Earth = 6.37 × 106 m

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........................................................................................................................... (2)

(iii) Explain whether oxygen molecules are likely to escape.

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........................................................................................................................... (1)

(Total 11 marks)


4. (a) Describe how the concept of an absolute zero of temperature arises from

(i) the ideal gas laws,

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........................................................................................................................... (2)

(ii) the kinetic model of an ideal gas.

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........................................................................................................................... (2)

(b) Name the temperature scale based on absolute zero.

..................................................................................................................................... (1)

(c) The oven of a cooker has a volume of 0.10 m3. The air in the oven is at normal

atmospheric pressure, 1.0 × 105 Pa.

(i) Calculate the mass of air in the oven at 27 °C.

1 mole of air has a mass of 0.029 kg.

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...........................................................................................................................

Mass of air = .............................. (4)


(ii) When the oven is heated the pressure of the air in the oven stays at atmospheric

pressure but the density of the air changes. Calculate the ratio of the density of

air at 227 °C to its density at 27 °C.

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........................................................................................................................... (3)

(Total 12 marks)

5. Water molecules oscillate when stimulated by high-frequency electromagnetic waves. A

microwave oven heats food that contains water by forcing the water molecules to oscillate at

their resonant frequency f0.

(a) Explain what is meant by resonance and suggest why the microwave frequency is

chosen to be about f0.

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..................................................................................................................................... (3)

(b) A microwave oven is used to heat 1.2 kg of meat. The temperature of the meat

increases by 75 K in the first 10 minutes.

The power of the microwave source is 800 W.

Calculate the efficiency of the heating process during this time. Take the specific heat

capacity of the meat to be 3200 J kg–1

K–1

.

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.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

Efficiency = ..........................................


Why does the temperature of the meat not continue to rise at this rate for the next

10 minutes?

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..................................................................................................................................... (4)

(Total 7 marks)

6. The presence of people in a room warms the air in the room.

Use these figures to answer the questions below.

Mass of air in room = 740 kg

Number of people in room = 27

Rate of thermal output from each person = 80 W

Specific heat capacity of air = 960 J kg–1

°C–1

Calculate the amount of thermal energy the people in the room are providing each second.

...............................................................................................................................................

...............................................................................................................................................

Amount of energy = ............................................... (1)

During the first 40 minutes that the people are in the room no window is open. Show that the

temperature of the air might rise by about 7 °C.

...............................................................................................................................................

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...............................................................................................................................................

............................................................................................................................................... (3)

Explain whether the actual rise in temperature (with no window open) is likely to be more or

less than your answer above.

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............................................................................................................................................... (2)


The room can be maintained at a steady temperature by having a window open, so that warm

air from inside changes places with colder air from outside. The desired temperature

difference between the air inside and outside the room is 8 °C.

Show that the air must be exchanged through the open window at a rate of about 0.3 kg s–1

to

maintain this steady temperature difference within the room.

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...............................................................................................................................................

............................................................................................................................................... (2)

Calculate how long it will take at this rate to exchange all the air in the room.

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Time = ............................................... (1)

(Total 9 marks)

7. A student about to fill a paddling pool for her younger brother noticed that the water left in

the hose-pipe had already been warmed by the sun. She carried out an experiment to find the

efficiency of this method of solar heating.

She cut a short length of hose-pipe and filled it with water from the cold tap. After taking the

initial temperature she plugged both ends and placed the hose-pipe in the sunlight. She

measured the temperature of the water at regular intervals for 1 hour during which time the

amount of sunlight was constant. The graph shows her results.


Explain the shape of the graph.

...............................................................................................................................................

............................................................................................................................................... (2)

Use the graph to show that the initial rate of temperature increase was about 0.01 °C s–1.

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............................................................................................................................................... (3)

Hence calculate the maximum amount of thermal energy gained by the water in one second.

Mass of water in hose-pipe = 0.130 kg

Specific heat capacity of water = 4200 J kg–1 °C–1

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Energy gained per second = ......................................... (2)

30

25

20

15

10

Tem

per

ature

/ °

C

0 500 1000 1500 2000 2500 3000 3500 4000

Time / s


The area of hose-pipe exposed to the solar radiation was 0.015 m2. At the time of the

experiment the power delivered by the solar radiation to an area of 1.0 m2 was 500 W.

Calculate the initial efficiency of this process of heating water by solar energy.

...............................................................................................................................................

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...............................................................................................................................................

Efficiency = ............................................ (3)

The student noticed that she spilled a small amount of water each time she removed the

stopper to measure the temperature of the water. State and explain the effect this would have

on the calculated value of efficiency.

...............................................................................................................................................

...............................................................................................................................................

............................................................................................................................................... (2)

(Total 12 marks)

8. A scientist was investigating the effects of extreme pressure, as might be experienced deep in

the ocean. He used a polystyrene cup in his investigation and a total pressure of 3.5 × 107 Pa

was applied to it, squashing the cup.

The volume of the air in the cup‟s polystyrene bubbles was originally 7 × 10–5 m3.

Calculate the new volume in the bubbles in the squashed cup.

Assume that the temperature remains constant.

Atmospheric pressure = 1.0 × 105 Pa.

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Volume = ....................................................... (3)


State one other assumption made in the calculation above.

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............................................................................................................................................... (1)

In reality, the temperature drops when going down into the ocean from 25°C at the surface to

10°C at the depth modelled in the experiment. Calculate the percentage change in the

average kinetic energy of the air molecules as a result of this temperature change.

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............................................................................................................................................... (3)

(Total 7 marks)


NUCLEAR DECAY:

1. Recently, some old human skulls have been found in Mexico. Their age has been established

using radiocarbon, 14

C, dating.

(a) When a 14

C nucleus decays, it emits a β-particle. State how the composition of the

nucleus changes as a result of the decay.

.....................................................................................................................................

..................................................................................................................................... (1)

(b) When examining a small sample of one of these old skulls, scientists found that

2.3 × 10–11

% of the carbon was 14

C, whereas in recent skulls this proportion is

1.0 × 10–10

%.

(i) Calculate the age of this old skull. Half-life of 14

C = 5730 years

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Age = ...................................... (3)

(ii) Give one reason why the value you calculated above may be inaccurate.

...........................................................................................................................

........................................................................................................................... (1)

(iii) Recent bones are dated using the decay of 210

Pb, which has a half-life of 21

years.

Explain why 210

Pb is more suitable than 14

C for dating recent bones.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (1)

(Total 6 marks)


2. As a beta-minus particle travels through air it causes ionisation.

(a) Describe how the beta particle produces ionisation.

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..................................................................................................................................... (1)

(b) Explain how the amount of ionisation determines a beta particle‟s range in air.

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..................................................................................................................................... (3)

(c) Explain why, towards the end of its range, a beta particle will ionise more molecules

per unit length than at the beginning of its range.

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..................................................................................................................................... (2)

(Total 6 marks)

3. (a) Radioactivity involves the spontaneous emission of radiation from unstable nuclei.

Explain the meaning of the words in italics as they apply to the process of

radioactivity.

Spontaneous ................................................................................................................

.....................................................................................................................................


Radiation .....................................................................................................................

.....................................................................................................................................

Unstable .......................................................................................................................

..................................................................................................................................... (3)

(b) The graph shows how the activity of a sample of the radioisotope technetium, which is

used extensively in medicine, varies with time.

(i) Use the graph to determine the half-life of technetium.

...........................................................................................................................

...........................................................................................................................

Half-life = ............................................. (2)

(ii) Hence calculate the decay constant for technetium.

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Decay constant = ............................................. (1)

Activity/10 Bq7

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14 16 18 20 22 24

Time/hours


(iii) Determine the number of technetium atoms remaining in the sample after 24

hours.

...........................................................................................................................

...........................................................................................................................

Number of atoms = .............................................. (2)

(Total 8 marks)

4. In April 1986 an explosion destroyed one of the reactors at Chernobyl Nuclear Power

Station. In the accident, radioisotopes were scattered over the surrounding area and many

were carried large distances by the wind. The contamination included isotopes of strontium,

iodine, caesium and plutonium.

Data on these isotopes are shown below:

Isotope Proton number Half-life Particles emitted

90Sr 38 28 years

131I 53 8.1 days ,

134Cs 55 2.1 years ,

137Cs 30 years ,

239Pu 94 24 000 years α, γ

240Pu 6600 years α, γ

Fill in the missing proton numbers. (1)

The fuel for the power station originally consisted of uranium ( and ).

(i) Name the process which produced strontium and caesium.

.....................................................................................................................................

(ii) Suggest how plutonium was formed in the nuclear reactor.

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (2)

U23592 U238

92


In June 1986, the area around the power station was still dangerously contaminated, with so

much 137

Cs in the ground that it emitted 1.5 × 106 Bq m

–2. Calculate the emission rate which

would be recorded today from this same ground, stating any assumptions which you make.

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Emission rate = ...............................Bq m–2

Assumption: ………………………………………………………………………………..

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Explain which of the scattered isotopes would no longer be of concern today.

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Some politicians say that the Chernobyl accident happened so long ago that it is no longer

dangerous to live in the area. Comment on this statement.

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............................................................................................................................................... (2)

(Total 11 marks)

5. Radioactive isotopes emitting gamma radiation can be used to preserve food. The food is

exposed to the radiation which kills most of the bacteria that occur naturally.

Why is gamma radiation used in this process rather than alpha or beta?

................................................................................................................................................. (1)


The food is passed on a conveyor belt under a radiation source.

State two factors which control the amount of radiation reaching each item of food.

.................................................................................................................................................

................................................................................................................................................. (2)

A thick wall surrounds the irradiation room to prevent the radiation escaping. Suggest a

suitable material and thickness for this wall.

.................................................................................................................................................

................................................................................................................................................. (2)

Many consumers are worried about irradiated food, as they wrongly believe that this makes

it become radioactive. Food does, however, contain a small level of naturally occurring

radiation. Name something other than food that is also a source of natural radiation.

................................................................................................................................................. (1)

(Total 6 marks)

6. Carbon clock could show the wrong time

This was the headline of a news report in Physics Web in May 2001 about some stalagmites

found in a cave in the Bahamas.

Stalagmites are found in limestone caves and are long, thin rocks formed by the deposition of

calcium carbonate from solution. The stalagmites in the news report are a half-metre long.

They contain atoms of the radioactive isotope carbon-14, which has a half-life of 5730 years.

The decay of carbon-14 can be used to determine the age of objects. This process is called

radiocarbon dating.

In one part of the stalagmites, of the carbon-14 atoms have decayed.

Gammasource

Food

Conveyor belt

256

255


Determine the age of this part of the stalagmite.

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Age = .................................... (3)

Some parts were formed much more recently. How would this affect their carbon-14

concentration?

................................................................................................................................................. (1)

However, scientists have found that the level of carbon-14 when the oldest parts of the

stalagmites were formed was twice the modern level. Discuss the effect on the validity of

radio-carbon dating.

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(Total 7 marks)

7. An airport decides to use -radiation to examine luggage.

How are -rays dangerous to people?

...............................................................................................................................................

............................................................................................................................................... (2)

Suggest a material which could be used for the shielding of airport staff, and the minimum

thickness required.

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............................................................................................................................................... (2)


Why is radiation not used to examine luggage?

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............................................................................................................................................... (1)

Explain why air travellers are exposed to increased doses of background radiation.

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(Total 7 marks)

8. The Huygens/Cassini space mission to Titan, a moon of Saturn, left the Earth amid a storm

of protest. The protest was about its nuclear-powered battery which contained plutonium-

238, an alpha emitter. Before launch in 1997, a newspaper article read

PLUTONIUM PROBE PERIL

NASA is going to send up a space probe with 70 pounds of deadly

plutonium on board. The probe is going to be launched using a Titan

IV rocket – the same type of rocket that blew up over the Pacific

Ocean just 4 years ago in 1993.

Plutonium is so deadly that just one pound of it, spread through the

Earth‟s atmosphere, could cause lung cancer in every person on Earth!

Less than one millionth of a gram of it is a deadly dose.

In plutonium-238, what does 238 mean?

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............................................................................................................................................... (1)

Why did the plutonium source cause concern?

...............................................................................................................................................

............................................................................................................................................... (1)


The half-life of plutonium-238 is 88 years and, at launch, the source contained 7.2 × 1025

atoms. Show that the activity of the plutonium source, at the time of launch, was about

2 × 1016

Bq. (1 year = 3.16 × 107 s)

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Each plutonium nucleus releases 5.6 MeV when it decays. Calculate the power (in watts)

delivered by the plutonium at the time of the rocket launch.

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Power = ............................................................. (3)

The textbooks say that nuclear decay is a random process. Explain whether this means that

there is some doubt that the power can be relied upon.

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............................................................................................................................................... (1)

What percentage of the power at launch will still be available 10 years after the launch?

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Percentage = ...................................................... (2)


Suggest why plutonium was chosen for this mission.

............................................................................................................................................... (1)

(Total 12 marks)

9. A radioactive source contains barium-140. The initial activity of the source is 6.4 × 108 Bq.

Its decay constant is 0.053 day–1

.

Calculate the half-life in days of barium-140.

...............................................................................................................................................

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Half-life = .............................................. days

Calculate the initial number of barium-140 nuclei present in the source.

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Number of nuclei = ....................................... (4)

The graph below represents radioactive decay. Add a suitable scale to each axis, so that the

graph correctly represents the decay of this barium source.

A radium-226 source has the same initial activity as the barium-140 source. Its half-life is

1600 years. On the same axes sketch a graph to show how the activity of the radium source

would vary over the same period. (3)

(Total 7 marks)

Activity

Time


10. (i) Define the term binding energy.

.....................................................................................................................................

..................................................................................................................................... (1)

(ii) Use the following data to show that the binding energy of carbon-14 is approximately

100 MeV.

Masses: nucleus = 14.003 24 u

= 1.007 28 u

= 1.008 67 u

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(iii) The binding energy of carbon-12 is 89 MeV. Hence determine which of these two

carbon isotopes is more stable.

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..................................................................................................................................... (3)

(Total 8 marks)

11. The Joint European Torus (JET) was a nuclear fusion experiment near Oxford in England.

JET was the first experiment to produce a controlled nuclear fusion reaction.

(a) Describe the process of nuclear fusion.

.....................................................................................................................................

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..................................................................................................................................... (2)

C146

p11

n10


(b) Explain why it is difficult to maintain the conditions for nuclear fusion in a reactor.

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(c) The nuclei which fused were two isotopes of hydrogen. Why should the fusing of

hydrogen nuclei release energy?

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(Total 6 marks)

12. Fission of 235

U (uranium-235) nuclei is used to provide the energy to heat the core of a

nuclear reactor.

A typical fission reaction is given in the equation

U + n Ru + Cd + 3 n + energy

Write down the number of protons and neutrons in the isotope of cadmium produced, 122

Cd.

Protons ........................................................ Neutrons ........................................................ (2)

Describe briefly the process which occurs in a fission reaction.

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23592

10

11144

12248

10


The fission of one 235

U nucleus in the equation above releases 3.2 × 10–11

J of energy.

Calculate the change in mass which occurs in this reaction.

.................................................................................................................................................

.................................................................................................................................................

................................................................................................................................................. (2)

A nuclear power station, which uses the fission of 235

U nuclei, generates 660 MW of

electrical power and is 30% efficient. Calculate the number of fissions required each second

to produce this power.

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Number of fissions per second = .................................... (2)

This number of atoms has a mass of less than a gram. Give two reasons why it is necessary

to have a lot more fuel than this in a nuclear reactor.

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................................................................................................................................................. (2)

(Total 11 marks)


13. Nuclear power stations use the fission of uranium-235 to produce thermal energy. The

simplified graph below can be used to explain energy transformation by nuclear fission

Use the graph to estimate the binding energy (in eV) of a nucleus of uranium-235.

...............................................................................................................................................

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Binding energy = ....................................... eV (2)

When a uranium-235 nucleus undergoes fission, two smaller nuclei are formed, each with

about half the number of nucleons.

Show that the energy released in the fission of one nucleus of uranium-235 is about

4 × 10–11 J.

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............................................................................................................................................... (3)

0 50 100 150 200 250

Nucleon number

Binding energyper nucleon / Me V

10

5

0


1.0 kg of uranium-235 contains 2.6 × 1024 nuclei.

Calculate the energy released by the fission of 1.0 kg of uranium-235.

...............................................................................................................................................

...............................................................................................................................................

Energy = ........................................ (1)

(Total 6 marks)

14. The equations below represent a typical fission and a typical fusion reaction.

State the values of X and Z for the two nuclear equations above.

...............................................................................................................................................

...............................................................................................................................................

X = ................................... Z = ................................... (2)

Write a short account of the physics of nuclear fission and fusion explaining the similarities

and differences between them.

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...............................................................................................................................................

...............................................................................................................................................

............................................................................................................................................... (5)

(Total 7 marks)

nXRbCsnU 1

0

96

37

138

55

1

0

235

92 pZHeHeHe 4

2

3

2

3

2


OSCILLATIONS

1. A motion sensor, connected through a data logger to a

computer, is used to study the simple harmonic motion

of a mass on a spring.

The data logger records how the height h of the mass

above the sensor varies with the time t. The computer

calculates the velocity v and acceleration a and displays

graphs of h, v and a against t. Idealised graphs of h and

a for two cycles are shown below.

1.1

0.9

0.70 0.4 0.8 1.2 1.6 2.0 2.4

t / s

h / m

0 0.4 0.8 1.2 1.6 2.0 2.4

t / s

5.0

0

–5.0

a / m s –2

0 0.4 0.8 1.2 1.6 2.0 2.4

t / s

v / m s –2

Clamp

To data logger

and computer

Motion

Motion

sensor

h

Mass

Spring


(a) (i) Determine the amplitude and frequency of the motion.

...........................................................................................................................

...........................................................................................................................

Amplitude = ........................................ Frequency = ........................................ (2)

(ii) Show that the maximum velocity of the mass is approximately 0.9 m s–1

.

...........................................................................................................................

........................................................................................................................... (2)

(iii) Complete the above set of graphs by sketching the velocity-time graph for the

same interval. (2)

(b) (i) Define simple harmonic motion.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) Describe how you would use data from the graphs of h and a against t to check

that the motion of the mass was simple harmonic. (Note that you are not

required to actually carry out the check.)

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (4)

(Total 12 marks)


2. When a person walks across a suspended footbridge, the bridge can oscillate with increasing

amplitude.

(a) Name the effect which causes this and state the condition needed for the amplitude to

increase in this situation.

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (2)

(b) In November 1940, the wind caused some alarming movement and twisting of the

road bridge over Tacoma Narrows in the United States. The amplitude of the

oscillations became so large that cars were abandoned on the bridge.

(i) Why can these oscillations be described as forced?

...........................................................................................................................

........................................................................................................................... (1)

(ii) The vertical oscillations of the bridge can be modelled using the equations of

simple harmonic motion. Calculate the maximum acceleration of the bridge

when it was oscillating 38 times per minute and the amplitude of its oscillations

was 0.90 m.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

Maximum acceleration = ......................................... (2)

(iii) Use this value to explain why any car abandoned on the bridge would lose

contact with the road‟s surface at a certain point in the oscillation. Identify this

point.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(Total 7 marks)


3. Buildings situated close to railway lines should be constructed in a manner which minimises

noise and vibrations from passing trains.

(a) Vibrations could cause parts of the building to resonate. Describe the meaning of the

word resonate in this context.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (2)

(b) Some buildings, which are subject to vibrations, are constructed on springs.

(i) Suggest how springs could prevent these buildings from vibrating.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) It is said that such buildings would also suffer less damage in the event of an

earthquake. Comment on this statement.

...........................................................................................................................

........................................................................................................................... (1)

(Total 5 marks)

4. The oscillations of a child on a swing are approximately simple harmonic. State the

conditions which are needed for simple harmonic motion.

...............................................................................................................................................

...............................................................................................................................................

............................................................................................................................................... (2)

Why is the child‟s motion only approximately simple harmonic?

...............................................................................................................................................

............................................................................................................................................... (1)


The child completes six oscillations of amplitude 1.2 m in 20 s.

(i) Calculate the period and the frequency of the oscillations.

.....................................................................................................................................

.....................................................................................................................................

Period = ..................................... Frequency = ..................................................

(ii) The quantity ω in the equations for simple harmonic motion is defined as 2πf, where f

is the frequency of the oscillations. Calculate ω for these oscillations.

.....................................................................................................................................

ω = ....................................................................

(iii) Calculate the child‟s acceleration when the displacement is maximum.

.....................................................................................................................................

.....................................................................................................................................

Acceleration = .................................................. (5)

Explain how pushing a child on a swing can be an example of resonance.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

............................................................................................................................................... (2)

(Total 10 marks)


5. Below are some examples of oscillations. For each, state with a reason whether the motion is

simple harmonic or not.

Oscillation SHM

or

Reason

Mass on end of a spring ..................... ....................................................................

Child jumping up and

down ..................... ....................................................................

Vibrating guitar string ..................... ....................................................................

(Total 4 marks)


6. London‟s Millennium Walkway Bridge across the River Thames was opened in January

2000.

When it was opened, it swayed alarmingly when people walked across.

An engineer commented “The movement of the people walking is forcing the bridge into

worryingly large oscillations. We will need to either stiffen it by welding more steel onto the

structure or damp the oscillations using small weights suspended from the bridge. These

weights can be controlled so that they oscillate out of phase cancelling out the bridge‟s

motion”. (Based on an article in the New Scientist, no. 2243)

Explain each of the engineer‟s comments, outlining the physics principles involved.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

............................................................................................................................................... (Total 7 marks)


7. A mass oscillating on a spring, is an example of simple harmonic motion.

State the conditions required for simple harmonic motion to occur.

...............................................................................................................................................

...............................................................................................................................................

............................................................................................................................................... (2)

The graph shows how the potential energy varies with displacement for a particular mass and

spring,

On the same axes draw a graph showing how the total energy of the mass-spring system

varies with displacement, assuming no energy loss. (1)

Use the graph to calculate

(i) the kinetic energy of the mass when the displacement is 2.0 cm,

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

20

15

10

5

–4 –2 0 2 4

Displacement / cm

PotentialEnergy / J


(ii) the stiffness, k, of the spring.

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (5)

(Total 8 marks)

8. The speaker shown below is used to produce the bass notes in a music system.

The cone moves with simple harmonic motion and it emits a single-frequency sound of 100 Hz.

When it is producing a loud sound, the cone moves through a maximum distance of 2.0 mm.

The equation that mathematically describes the displacement of the cone is

x = 1.0 × 10–3 cos 628 t.

Show that the data for this speaker lead to the numbers in the equation above.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

............................................................................................................................................... (2)

Calculate

(i) the maximum acceleration of the cone

...........................................................................................................................

...........................................................................................................................

Maximum acceleration = ........................................................


(ii) the maximum speed of the cone

...........................................................................................................................

...........................................................................................................................

Maximum speed = ........................................................ (3)

On the grid below sketch the acceleration-time graph for two cycles of vibration of this

speaker cone used under these conditions. Add suitable numerical scales to the two axes.

(3)

Explain why designers ensure that bass speakers have a natural frequency of oscillation

much greater than 100 Hz.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

............................................................................................................................................... (2)

(Total 10 marks)

Acceleration

Time


ASTROPHYSICS & COSMOLOGY

1.* For most of its life (11 billion years) the Sun will burn hydrogen in its core. A chemistry

student might use the word burn to describe a chemical reaction involving oxygen.

Explain fully the meaning of the word burn when used in astrophysics to describe what

happens in the core of a star.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

............................................................................................................................................... (Total 4 marks)

2. (i) Near the end of its life the Sun will decrease in size and become a white dwarf.

State two other ways in which this type of star differs from the Sun as it is today.

1 ..................................................................................................................................

2 .................................................................................................................................. (2)

(ii) Describe what will eventually become of a white dwarf star.

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (2)

(Total 4 marks)


3. A physics teacher uses a simple model to illustrate the behaviour of the Universe. A long

elastic cord, clamped at one end P, has knots Q, R, S and T tied in it at equal intervals.

Initially the cord is straight but unstretched with the knots 0.50 m apart, as shown in part A

of the diagram.

The teacher grasps knot T and pulls it away from P at a steady speed of 0.80 m s–1

. The cord

stretches uniformly.

(a) (i) On part B of the diagram, mark the position of knot T after 0.50 s.

(ii) Hence complete part B by marking the positions of knots Q, R and S after 0.50 s. (2)

(b) Explain how this model represents the Universe and its behaviour.

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (2)

(c) Using values taken from the diagram, show how the model illustrates Hubble‟s law.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (3)

A

B

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Distance / m

Q

P

R S TP

( = 0)t

( = 0.5 )t s


(d) State two ways in which this demonstration is not a good model of the Universe.

1 ..................................................................................................................................

.....................................................................................................................................

2 ..................................................................................................................................

..................................................................................................................................... (2)

(Total 9 marks)

4. On a line between the Earth and the Sun is a point P where the gravitational field strength of

the Sun is equal and opposite to that of the Earth. Point P is a distance R from the centre of

the Sun and a distance r from the centre of the Earth.

The mass of the Sun is MS. The mass of the Earth is ME. The gravitational constant is G.

(a) Using the symbols given, write down an expression for

(i) the gravitational field strength of the Sun at point P

...........................................................................................................................

(ii) the gravitational field strength of the Earth at point P.

........................................................................................................................... (1)

(b) The mass of the Sun is 2.0 × 1030

kg. The mass of the Earth is 6.0 × 1024

kg.

(i) Show that the ratio of R to r is about 600:1.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

Sun EarthP

R r

Not to

scale


(ii) Hence find the value of r, given that the distance from the centre of the Earth to

the centre of the Sun is 1.5 × 108 km.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

r = ....................................... (2)

(c) SOHO, a satellite that monitors the Sun, is positioned at a point on the line between

the Earth and the Sun. The gravitational forces acting on it keep it in the same relative

position, orbiting the Sun at the same rate as the Earth.

On the diagram opposite, mark with a letter L a possible position for SOHO.

With reference to the circular motion of SOHO, explain how you decided on the

position of L. You are not expected to perform any calculations.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (3)

(Total 8 marks)

5.* A star of mass 30 M has a lot more fuel available than our Sun. A student suggests

that this star should therefore spend longer than the Sun on the main sequence.

Criticise this statement.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (Total 4 marks)


6. A line in the hydrogen spectrum from a laboratory source has a wavelength of 656 nm.

(a) In the spectrum of light received from a distant galaxy X, this line appears at a

wavelength of 684 nm. Calculate the speed of recession of galaxy X.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

Speed = ............................................................. (3)

(b) A second galaxy Y is twice as far from the Earth as galaxy X. At what wavelength

would you expect the same line to appear in the spectrum of light received from Y?

Explain your reasoning.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

Wavelength = .................................................... (3)

(Total 6 marks)

7. (a) A brown dwarf is a star-like object that is composed of hydrogen but has insufficient

mass to become a main sequence star. Explain, in terms of nuclear fusion, why stars

need to exceed a certain minimum mass to join the main sequence. You may be

awarded a mark for the clarity of your answer.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (4)


(b) The Hertzsprung-Russell diagram shows the luminosity of a star plotted against its

temperature.

(i) Both scales of the diagram are logarithmic. State what is meant by logarithmic.

Illustrate your answer by referring to the numerical values on the temperature

axis.

...........................................................................................................................

........................................................................................................................... (2)

(ii) Add to the graph to indicate

1) a low mass star which is on the main sequence, marking this point L

2) the area where white dwarf stars occur, marking this area W

3) the region where red giant stars occur, marking this area R

4) the position of the Sun, marking this point S. (4)

(Total 10 marks)

8. Communication satellites are often placed in geostationary orbit. The speed v of a

geostationary satellite is given by the expression

v = ωr

where r is the radius of the orbit.

(a) A student calculates that ω has the numerical value of 7.27 × 10–5

. Show how he

arrives at this figure.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

104

102

100

10 –2

10–4

L/L

40 000 20 000 10 000 5000 2500

T /K


State the unit of ω.

..................................................................................................................................... (3)

(b) Hence, or otherwise, calculate the height of such satellites above the Earth‟s surface,

given that the Earth has a mass of 5.98 × 1024

kg and a radius of 6.38 × 106 m.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

Height above Earth‟s surface = ................................................ (4)

(Total 7 marks)

9. Meteosat is a weather satellite which is in a geostationary orbit around the Earth, i.e. it stays

above the same point on the Earth‟s surface all the time.

The radius r of the geostationary orbit is given by

r3 =

where T is the time for one orbit of the satellite.

(a) The mass and speed of the satellite do not appear in the above equation. Explain

whether a satellite could remain in geostationary orbit with

(i) a greater mass.

...........................................................................................................................

...........................................................................................................................

(ii) a greater speed.

...........................................................................................................................

........................................................................................................................... (2)

2

2

π4

GMT


(b) Explain why a satellite has to be over the equator to remain in a geostationary orbit.

You may use the diagram to help your explanation.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (2)

(Total 11 marks)

10. (a) Edwin Hubble examined the relationship between the recessional speed of galaxies, v,

and their distance, d, from Earth. The graph shows the best-fit line for his results.

80

60

40

20

00 2.0 4.0 6.0

Distance d / 10 ly9

Recessionalspeedv / 10 km s –13


(i) Use the graph to determine a value for the Hubble constant, H, in s–l

. Show your

working.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

Hubble constant = ..........................................s–1

(4)

(ii) What is the main source of uncertainty in the value of H?

........................................................................................................................... (1)

(b) Explain how the Hubble constant provides us with an estimate for the age of the

Universe, t.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (2)

(c) Briefly explain how the value of the average mass-energy density of the Universe will

determine whether the Universe is open or closed.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (2)

(Total 9 marks)


11. The table shows the properties of three main sequence stars.

Star Luminosity/L Surface

temperature/K

α Cen B 0.53 5250

Sirius A 26 9230

Cas 930 000 29 500

State which star would

(i) have the greatest mass ................................................................................................

(ii) spend the greatest time on main sequence .................................................................. (2)

The luminosity of the Sun is 3.9 × 1026

W. Calculate the luminosity of Sirius A.

...............................................................................................................................................

............................................................................................................................................... (2)

Show that the area of Sirius A is approximately 2.5 × 1019

m2.

...............................................................................................................................................

...............................................................................................................................................

............................................................................................................................................... (2)

Hence calculate the diameter of Sirius A.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

............................................................................................................................................... (2)

(Total 8 marks)


12. State three differences between white dwarf stars and red giant stars. One of your answers

should be numerical.

1 ..................................................................................................................................

......................................................................................................................................

2 ...................................................................................................................................

......................................................................................................................................

3 ...................................................................................................................................

...................................................................................................................................... (3)

What determines whether a neutron star will be formed from a supernova?

......................................................................................................................................

...................................................................................................................................... (2)

(Total 5 marks)

13. (a) What is meant by the Doppler effect (electromagnetic Doppler effect) when applied to

light?

.......................................................................................................................................

....................................................................................................................................... (2)

(b) Edwin Hubble reached a number of conclusions as a result of observations and

measurements of red-shift. State two of these conclusions.

.......................................................................................................................................

....................................................................................................................................... (2)

(c) The diagram gives values of wavelength for part of the electromagnetic spectrum.

Wavelength/ 10–9

m

UV Visible IR

200 300 400 500 600 700


A very hot distant galaxy emits violet light just at the edge of the visible spectrum.

Estimate the maximum velocity the galaxy could have so that visible light could still

be detected as it moves away from the Earth.

.......................................................................................................................................

.......................................................................................................................................

....................................................................................................................................... (4)

(d) The fate of the Universe is dependent on the average mass-energy density of the

Universe. What is meant by the critical density of the Universe?

.......................................................................................................................................

.......................................................................................................................................

....................................................................................................................................... (2)

(Total 10 marks)

14. (a) (i) State Newton‟s law for the gravitational force between point masses.

...............................................................................................................................

...............................................................................................................................

............................................................................................................................... (2)

(ii) Use this law to show that the gravitational field strength g at a distance r from

the centre of the Earth, where r is greater than or equal to the radius R of the

Earth, is given by

g =

where M is the mass of the Earth.

............................................................................................................................

............................................................................................................................ (1)

2r

GM


(iii) Use the axes below to plot a graph to show how g varies as the distance r

increases from its minimum value of R to a value of 4R.

(3)

(b) (i) When a satellite, which travels in a circular orbit around the Earth, moves to a

different orbit the change in its gravitational potential energy can be calculated

using the idea of equipotential surfaces. What is an equipotential surface?

............................................................................................................................

............................................................................................................................

............................................................................................................................ (1)

(ii) Add to the diagram below three equipotential surfaces which have equal

changes of potential between them.

(2)

Gravitationalfield strength

g

g

g

g

3 / 4

/ 2

/ 4

0 R 2R 3R 4R

Distance from centre of Earth

Earth


(c) The change in the gravitational potential energy of the satellite when it moves to a

different orbit might be calculated using the expression

„weight of satellite × change in height‟.

(i) What condition must apply for this to be valid?

............................................................................................................................

............................................................................................................................

(ii) Explain your answer.

............................................................................................................................

............................................................................................................................

............................................................................................................................ (2)

(Total 11 marks)

15. (a) On the axes below sketch a graph showing how the intensity I of a star varies with

distance D from the star.

(2)

Give two reasons why measurements of a star‟s intensity are often made from above

the Earth‟s atmosphere.

1. ...........................................................................................................................

2. ........................................................................................................................... (2)

I

00 D


(b) The graph shows the energy distribution in the spectra of two stars Car and And.

What can be deduced about the colours of the two stars from the graph?

.....................................................................................................................................

..................................................................................................................................... (1)

Estimate the surface temperature of And.

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (3)

The luminosity of βCar is 2.0 × 1028

W and it has a surface temperature of 9300 K.

Calculate the surface area of βCar.

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (3)

By comparing the areas under the two graphs, estimate the luminosity of βAnd.

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (2)

(Total 13 marks)

Relativeemittedpower

0 200 400 600 800 1000 1200 1400

visibleWavelength / 10 m

–9

Car

And


16.* Explain what is meant by a main sequence star.

...............................................................................................................................................

............................................................................................................................................... (1)

Outline the life story of a white dwarf star starting from when it was a main sequence star.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

............................................................................................................................................... (4)

What determines whether or not a main sequence star eventually becomes a white dwarf?

Quantify your answer.

...............................................................................................................................................

...............................................................................................................................................

............................................................................................................................................... (2)

(Total 7 marks)

17. Two stars, Deneb and Vega, are similar in colour. What can be deduced about the surface

temperatures of the two stars? Explain your answer.

...............................................................................................................................................

...............................................................................................................................................

............................................................................................................................................... (2)

The table gives some information about the two stars.

Star Luminosity/W Distance from Earth/m

Deneb 2.5 × 1031

1.5 × 1019

Vega 1.9 × 1028

2.3 × 1017


Which star has the greater surface area? Justify your answer.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

............................................................................................................................................... (3)

Which star will have the higher intensity and therefore appear brighter as seen from the

Earth? Show all your working.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

............................................................................................................................................... (4)

(Total 9 marks)

18. Stars much more massive than the Sun may become supernovae. How do astronomers

recognise a supernova?

...............................................................................................................................................

...............................................................................................................................................

............................................................................................................................................... (2)

How is a supernova formed? You may be awarded a mark for the clarity of your answer.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

............................................................................................................................................... (3)

(Total 5 marks)


19. What force holds our Sun together?

............................................................................................................................................... (1)

Explain how the nuclear processes within the Sun are able to release energy.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

............................................................................................................................................... (3)

At the end of the Sun‟s life, when energy can no longer be released in this manner, theory

predicts that the Sun will become a larger star, of about the same mass, called a red giant.

How will this change affect the Sun‟s gravitational pull on an outer planet? Explain your

reasoning.

...............................................................................................................................................

...............................................................................................................................................

............................................................................................................................................... (3)

(Total 7 marks)

20. Use Wien‟s law to explain why these giant stars look red compared with their appearance

when they were on the main sequence.

...............................................................................................................................................

...............................................................................................................................................

............................................................................................................................................... (2)

Use Stefan‟s law to explain why a red giant has greater luminosity than when it was a main

sequence star.

...............................................................................................................................................

...............................................................................................................................................

............................................................................................................................................... (3)

(Total 5 marks)


21. Jupiter is the most massive planet in our Solar System. The diagram shows the orbits of the

Earth and Jupiter around the Sun.

On the diagram

(i) mark the position of Jupiter at which it has maximum gravitational effect on the Earth,

(ii) draw labelled arrows on E to show the directions of the gravitational fields of Jupiter

and the Sun. (2)

Venus (our nearest neighbour in space) is about 400 times less massive than Jupiter, but, at

its nearest, is 15 times closer. Calculate the maximum value of the ratio

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

............................................................................................................................................... (2)

(Total 4 marks)

E

S

Orbit of Jupiter

E = EarthS = Sun

Not to scale

Jupiter todueEarth at thestrength field nalgravitatio

Venus todueEarth at thestrength field nalgravitatio


22. Read the short passage below and answer the questions about it.

In a simple binary system two stars move in circular orbits of different radii about a

common centre. The two stars take the same time T to complete one revolution. If the

binary system is viewed more or less edge-on the stars periodically pass in front of one

another, reducing the amount of light that reaches us. Such a system is called an

eclipsing binary and can be detected from its light curve, which is a plot showing how

the observed light intensity varies with time. Once the orbital period T has been

determined the total mass M of the binary system can be calculated from the

relationship M = 42d

3 / GT

2 where d is the sum of the radii and G is the gravitational

constant.

[Adapted from TRUMP Astrophysics Project]

Explain the meaning of the term binary system.

...............................................................................................................................................

............................................................................................................................................... (1)

The light curve for an eclipsing binary consisting of a small very bright star and a much

larger star is shown below. The system is being viewed edge-on. Diagrams B and D (not to

scale) show the relative positions of the small and large star at two times between the dips in

the light curve.

Complete diagrams A, C and E to show the positions of the small bright star at the times of

the dips in the light curve. (2)

0 4 8 12 16 20 24 Time/hours

Lightintensity

A B C D E


Explain why the dip in the curve at A is smaller than the dip at C.

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............................................................................................................................................... (2)

Estimate the orbital period of this binary.

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Approximately how long does it take the small star to cross the disc of the larger one?

............................................................................................................................................... (1)

On the light curve above show how the observed light intensity varies with time when this

system is viewed perpendicular to the plane of the orbits. (2)

(Total 9 marks)


23. In 1994 the comet Shoemaker-Levy approached the planet Jupiter on a collision course.

Just before the collision, the comet consisted of at least 17 separate fragments as shown in

the picture.

All the fragments had originally been combined in a single comet with a diameter of 9 km.

Comets like this are made of ice with trapped dust and gas and have a typical density of

500 kg m–3.

Show that the minimum mass for the original comet which formed Shoemaker-Levy was

about 2 × 1014 kg.

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As a single comet, Shoemaker-Levy had previously approached Jupiter in 1992. At its

closest, the near side of the comet was 96 000 km from the centre of Jupiter. At this near side

of the comet, Jupiter‟s gravitational field strength was 13.7458 N kg–1.

Calculate Jupiter‟s gravitational field strength at the far side of the comet.

(Mass of Jupiter = 1.8987 × 1027 kg.

G, gravitational constant = 6.6720 × 10–11 N m2 kg–2).

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Explain why the comet broke apart as it passed Jupiter in 1992.

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State one difference and one similarity between gravitational fields and electric fields.

Difference ............................................................................................................................

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Similarity ..............................................................................................................................

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(Total 10 marks)

24. The Cassini spacecraft was launched from Earth in 1997 and is expected to reach Titan, one

of Saturn‟s moons, in 2004. Cassini‟s energy at launch was insufficient for it to reach Titan

without assistance from the gravitational pull of planets like Venus and Jupiter. The diagram

shows the path of Cassini past Venus. Cassini is at its closest approach, just 284 km from the

surface of Venus.

Write an expression for the magnitude of the gravitational force on Cassini at a distance r

from the centre of Venus.

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............................................................................................................................................... (1)

NOT TO SCALE

Orbit of Venus

Path ofCassini


Hence derive an expression for the gravitational field strength at a distance r from the centre

of Venus.

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............................................................................................................................................... (2)

Calculate the maximum acceleration of Cassini caused by Venus.

Mass of Venus = 4.87 × 1024 kg

Radius of Venus = 6100 km

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Maximum acceleration = .......................................... (3)

State and explain the effect of this acceleration on the velocity of Cassini at its closest

distance to Venus.

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............................................................................................................................................... (2)

Communications between Earth and Cassini are by microwaves using a frequency of

7.2 GHz. As the spacecraft approached Jupiter its speed away from the Earth was 12 m s–1.

Calculate the percentage change in frequency of the microwaves received by Cassini from

Earth.

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Percentage change = ............................................ (2)

(Total 10 marks)


25*. The Doppler shift may be used in the study of distant galaxies. Explain what is meant by a

Doppler shift and how it is used to deduce the motion of distant galaxies.

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............................................................................................................................................... (5)

The graph shows the variation of the size S of an open universe against time t.

On the same axes, sketch a second graph showing how S varies with t for a closed universe. (1)

It can be shown that the Universe is closed if its density exceeds a critical value .

This is determined from the Hubble constant H using

= kH2

where k is a known constant.

Size ofuniverse,S

Bigbang

Time

Now


Outline the experimental difficulties in determining accurately.

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(Total 9 marks)

26. Discuss the ultimate fate of the Universe. Your answer should include reference to dark

matter and the reason why the fate of the Universe is uncertain.

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(Total 6 marks)

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