Download 1. The figure below represents the planet Jupiter. The centre of the

1.
The figure below represents the planet Jupiter. The centre of the planet is labelled
as O.
Jupiter
O
(a)
Draw gravitational field lines on the figure above to represent Jupiter’s
gravitational field.
[2]
(b)
Jupiter has a radius of 7.14 × 107 m and the gravitational field strength at its
surface is 24.9 N kg–1.
(i)
Show that the mass of Jupiter is about 2 × 1027 kg.
[3]
M. Manser
1
(ii)
Calculate the average density of Jupiter.
density = ............................................. kg m–3
[2]
[Total 7 marks]
2.
The figure below shows a mass suspended from a spring.
(a)
The mass is in equilibrium. By referring to the forces acting on the mass, explain
what is meant by equilibrium.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
[2]
(b)
The mass in (a) is pulled down a vertical distance of 12 mm from its equilibrium
position. It is then released and oscillates with simple harmonic motion.
(i)
Explain what is meant by simple harmonic motion.
................................................................................................................
................................................................................................................
................................................................................................................
................................................................................................................
[2]
M. Manser
2
(ii)
The displacement x, in mm, at a time t seconds after release is given by
x = 12 cos (7.85 t).
Use this equation to show that the frequency of oscillation is 1.25 Hz.
[2]
(iii)
Calculate the maximum speed Vmax of the mass.
Vmax = ............................................... m s–1
[2]
(c)
Fig. 1 shows how the displacement x of the mass varies with time t.
15
10
5
0
0
0.2
0.4
0.6
0.8
1.0
1.2
t/s
1.4
–5
–10
–15
Fig. 1
M. Manser
3
Sketch on Fig. 2 the graph of velocity against time for the oscillating mass.
Put a suitable scale on the velocity axis.
velocity / ms –1
0
0
0.2
0.4
0.6
0.8
1.0
1.2
t/s
1.4
Fig. 2
[3]
[Total 11 marks]
3.
This question is about an alpha particle making a head on collision with a gold nucleus.
(a)
(i)
When the alpha particle is at a large distance from the gold nucleus it has a
kinetic energy of 7.6 × 10–13 J. Show that its speed is about
1.5 × 107 m s–1.
mass of alpha particle = 6.6 × 10–27 kg
[2]
M. Manser
4
(ii)
As the alpha particle approaches the gold nucleus, it slows down and the
gold nucleus starts to move, Fig. 1.
gold nucleus
alpha particle
Fig.1
Explain this and explain how it is possible to calculate the speed of the gold
nucleus.
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
[3]
(iii)
Fig.2 shows the alpha particle and the gold nucleus at the distance of
closest approach. At this instant the gold nucleus is moving with speed V
and the alpha particle is stationary.
V
gold nucleus
alpha particle
Fig. 2
Calculate the speed V of the gold nucleus.
mass of gold nucleus = 3.0 × 10–25 kg
V = ......................m s–1
[2]
M. Manser
5
(iv)
The alpha particle bounces back. Its final speed approximately equals its
initial speed of approach. Assume that the mean force on the nucleus is 9.0
N during the interaction.
Estimate the time of the collision.
time = ….…………… s
[2]
(b)
15
F/N
10
5
0
0
5
10
15
20
r / 10 –14 m
Fig. 3
M. Manser
6
(i)
Fig. 3 shows two points on the graph of the electrostatic repulsive force F
between the alpha particle and nucleus against their separation r. The
particle and the nucleus are being treated as point charges. Use data from
the graph to calculate the values of the force at distances r = 10 × 10–14 m
and 15 × 10–14 m.
F at 10 × 10–14 m =…………….N
F at 15 × 10–14 m =…………….N
[3]
(ii)
Plot the two points on the graph and draw the curve.
[1]
[Total 13 marks]
4.
The electric motor in a washing machine rotates the drum containing the clothes by
means of a rubber belt stretched around two pulleys, one on the motor shaft and the
other on the drum shaft, as shown in Fig. 1.
X
machine
casing
motor
belt
drum
Fig. 1
M. Manser
7
(a)
The motor pulley of radius 15 mm rotates at 50 revolutions per second. Calculate
(i)
the speed of the belt
speed = ................... m s–1
[2]
(ii)
the centripetal acceleration of the belt at point X.
acceleration = ................... m s–2
[2]
(iii)
When the motor speed is increased, the belt can start to slip on the motor
pulley. Explain why the belt slips.
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
[2]
M. Manser
8
(b)
When the drum is rotated at one particular speed, a metal side panel of the
machine casing vibrates loudly. Explain why this happens.
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
[2]
(c)
A fault develops in the motor, causing the coil to stop rotating. Magnetic flux from
the electromagnet of the motor still links with the now stationary coil. Fig. 2 shows
how the flux linkage of the coil varies with time.
3
flux linkage /
2
Wb turns
1
0 0
5
10
15
20
–1
25
30
time/ms
–2
–3
Fig. 2
(i)
Using Fig. 2 state a time at which the e.m.f. induced across the ends of the
coil is
1
zero
.................................... ms
2
a maximum.
.................................... ms
[2]
M. Manser
9
(ii)
Use the graph of Fig. 2 to calculate the peak value of the e.m.f. across the
ends of the coil.
peak e.m.f. = ............................... V
[2]
[Total 12 marks]
5.
This question is about the atmosphere treated as an ideal gas.
(a)
The equation of state of an ideal gas is pV = nRT. Data about gases are often
given in terms of density  rather than volume V. Show that the equation of state
for a gas can be written as
p = RT/M
where M is the mass of one mole of gas.
[3]
M. Manser
10
(b)
One simple model of the atmosphere assumes that air behaves as an ideal gas
at a constant temperature. Using this model the pressure p of the atmosphere at
a temperature of 20 °C varies with height h above the Earth’s surface as shown
in the graph below.
100
p / kPa
50
0
0
2.0
4.0
6.0
8.0
10.0
12.0
h / km
Use data from the graph to show that the variation of pressure with height follows
an exponential relationship.
[2]
M. Manser
11
(c)
The ideal gas equation in (a) shows that, at constant temperature, pressure p is
proportional to density . Use data from the graph above to find the density of the
atmosphere at a height of 8.0 km.
density  of air at h = 0 is 1.3 kg m–3
 = .............................................. kg m–3
[3]
(d)
In the real atmosphere the density, pressure and temperature all decrease with
height. At the summit of Mt. Everest, 8.0 km above sea level, the pressure is only
0.30 of that at sea level.
Take the temperature at the summit to be –23 °C and at sea level to be 20 °C.
Calculate, using the ideal gas equation, the density of the air at the summit.
density  of air at sea level = 1.3 kg m–3
 = ............................................. kg m–3
[3]
[Total 11 marks]
M. Manser
12
6.
This question is about a simple model of a hydrogen iodide molecule.
Fig. 1 shows a simple representation of the hydrogen iodide molecule. It consists of

two ions, 11 H  and 127
53 I , held together by electric forces.
I–
H+
Fig. 1
(a)
(i)
Draw on Fig. 1 lines to represent the resultant electric field between the
two ions.
[2]
(ii)
Calculate the electrical force F of attraction between the ions.
Treat the ions as point charges a distance 5.0 × 10–10 m apart. Each ion
has a charge of magnitude 1.6 × 10–19 C.
F = ..................................................... N
[4]
M. Manser
13
(b)
The electrical attraction is balanced by a repulsive force so that the two ions are
in equilibrium.
When disturbed the ions oscillate in simple harmonic motion. Fig. 2 shows a
simple mechanical model of the molecule consisting of two unequal masses
connected by a spring of negligible mass.
mH
mI
Fig. 2
Use Newton’s laws of motion and the definition of simple harmonic motion to
explain why the amplitude of oscillation of the hydrogen ion is 127 times the
amplitude of oscillation of the iodine ion.
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
.........................................................................................................................
[4]
M. Manser
14
(c)
The natural frequency of oscillation of the hydrogen ion is 6.7 × 1013 Hz. Take the
amplitude of oscillation to be 8.0 × 10–12 m.
(i)
Sketch on Fig. 3 a displacement against time graph for the hydrogen ion.
15
10
displacement
/ 10–12 m 5
0
0.5
1.0
1.5
–5
2.0
2.5
3.0
time / 10–14s
–10
–15
Fig .3
[3]
(ii)
It is found that infra-red radiation of frequency close to 6.7 × 1013 Hz,
incident on the molecules, can cause this oscillation, but other frequencies
of infra-red do not. Suggest how this result can be explained.
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
[2]
[Total 15 marks]
M. Manser
15
7.
In a distant galaxy, the planet Odyssey is orbited by two small moons Scylla and
Charybdis, labelled O, S, C respectively in the diagram below. The distances of the
moons from the centre of the planet are 5R and 4R, where R is the radius of the planet.
4R
C
O
5R
R
(a)
S
Draw a gravitational field line of the planet passing through moon S.
[1]
(b)
The radius R of the planet is 2.0 × 107 m. The gravitational field strength g at its
surface is 40 N kg–1.
(i)
Write down a formula for the gravitational field strength g at the surface of
the planet of mass M.
...............................................................................................................
[1]
M. Manser
16
(ii)
Use the data above to show that the gravitational field strength at S is
1.6 N kg–1.
[2]
(iii)
Show that the gravitational field strength at C is 2.5 N kg–1.
[1]
(iv)
Using an average value of g, estimate the increase E in gravitational
potential energy of a small space vehicle of mass 3.0 × 103 kg when it
moves from the orbit of C to the orbit of S.
E = ...................................................... J
[3]
M. Manser
17
(c)
Calculate the orbital period of S. Assume that the gravitational effects of the two
moons on each other are negligible in comparison to the gravitational force of O.
gravitational field strength at S = 1.6 N kg–1
radius of orbit = 1.0 × 108 m
period = ....................................................... s
[4]
[Total 12 marks]
M. Manser
18
8.
Under certain conditions, when a liquid cools, the rate of fall of temperature is directly
proportional to Tx, where Tx is the difference between the temperature of the liquid and
the temperature of the surroundings. A graph of temperature against time is shown in
the graph below for an experiment in which the cooling liquid was 0.160 kg of water (a
cup of tea). The temperature of the surroundings was 15 °C.
100
temperature
of liquid
/°C
80
60
40
20
temperature of
surroundings
0
(a)
0
10
20
30
40
50
70
60
time / minute
Calculate the average time taken for Tx, called the temperature excess, to fall to
half its previous value. (The half-life of the temperature of the cup of tea.)
average time = ................................................... min
[3]
M. Manser
19
(b)
The graph obeys the exponential decay equation
Tx = T0e–t
where T0 is the temperature excess at time t = 0
Use your answer to (a) to calculate a value for , the decay constant. Give the
unit for .
λ = …………………… unit ………
[4]
(c)
At the start of this question it was stated that this law applied “under certain
conditions”.
State three conditions which would affect the rate of cooling of the liquid.
1 .....................................................................................................................
........................................................................................................................
2 .....................................................................................................................
........................................................................................................................
3 .....................................................................................................................
........................................................................................................................
[3]
M. Manser
20
(d)
The specific heat capacity of water is 4200 J kg–1 K–1. Calculate how much heat
is lost by the 0.160 kg of water in 70 min.
heat lost = ....................................................... J
[3]
[Total 13 marks]
9.
A cricketer throws a cricket ball of mass 0.16 kg.
(a)
The figure below shows how the force on the ball from the cricketer’s hand varies
with time. The ball starts from rest and is thrown horizontally.
25
force / N
20
15
10
5
0.0
(i)
0.1
0.2 0.3
time / s
0.4
Estimate the area under the graph.
area = ...................... Ns
[1]
M. Manser
21
(ii)
The area under the graph represents a change in a physical quantity for the
ball.
State the name of this quantity.
...............................................................................................................
[1]
(iii)
Calculate the speed of the ball, mass 0.16 kg, when it is released.
speed = ...................... m s–1
[2]
(iv)
Calculate the maximum horizontal acceleration of the ball.
acceleration = ...................... m s–2
[2]
(b)
The ball bounces several times on a hard surface. The maximum height to which
it rises after each bounce is given in the table below.
bounce number, n
maximum height, h/ m
1
0.71
2
0.33
3
0.16
The data given in the table fit a relationship for the variation in maximum height
with bounce number of the form
h = 1.5 e–kn
where k is a constant.
M. Manser
22
(i)
State the name of this form of relationship.
...............................................................................................................
[1]
(ii)
Calculate the value of k.
k = ...................
[2]
(iii)
What is the height from which the ball was thrown?
height = ...................... m
[1]
(iv)
Show that the loss of kinetic energy of the ball at the second bounce is
about 0.6 J.
Assume that the horizontal speed of the ball is unchanged.
[2]
[Total 12 marks]
M. Manser
23
10.
Fig. 1 shows two protons A and B in contact and at equilibrium inside a nucleus.
A
B
Fig. 1
Proton A exerts three forces on proton B. These are an electrostatic force FE, a
gravitational force FG and a strong force FS.
(a)
On Fig. 1, mark and label the three forces acting on proton B. Assume that every
force acts at the centre of the proton.
[2]
(b)
Write an equation relating FE, FG and FS.
[1]
(c)
The radius of a proton is 1.40 × 10–15 m.
Calculate the values of
(i)
FE
FE = ..................................... N
[2]
M. Manser
24
(ii)
FG
FG = ..................................... N
[2]
(iii)
FS.
FS = ..................................... N
[1]
(d)
Comment on the relative magnitudes of FE and FG.
........................................................................................................................
........................................................................................................................
[1]
M. Manser
25
(e)
Fig. 2 shows two neutrons in contact and at equilibrium inside a nucleus.
Fig. 2
Without further calculation, state the values of FE, FG and FS for these neutrons.
(i)
FE = .................................................................................. N
[1]
(ii)
FG = .................................................................................. N
[1]
(iii)
FS = ................................................................................. N
[1]
[Total 12 marks]
11.
This question is about pressing a red hot bar of steel into a sheet in a rolling mill.
(a)
A bar of steel of mass 500 kg is moved on a conveyor belt at 0.60 m s–1.
Calculate the momentum of the bar giving a suitable unit for your answer.
momentum = .................... unit ...................
[2]
M. Manser
26
(b)
From the conveyor belt, the bar is passed between two rollers, shown in the
figure below. The bar enters the rollers at 0.60 m s–1. The rollers flatten the bar
into a sheet with the result that the sheet leaves the rollers at 1.8 m s–1.
steel bar
conveyor belt
v = 0.60 ms–1
(i)
roller
conveyor belt
v = 1.8 ms–1
Explain why there is a resultant horizontal force on the bar at the point
immediately between the rollers.
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
[2]
(ii)
Draw an arrow on the figure at this point to show the direction of the force.
[1]
(iii)
The original length of the bar is 3.0 m. Calculate the time it takes for the bar
to pass between the rollers.
time = ..................... s
[1]
M. Manser
27
(iv)
Calculate the magnitude of the resultant force on the bar during the
pressing process.
force = ..................... N
[3]
(c)
To monitor the thickness of the sheet leaving the rollers, a radioactive source is
placed below the sheet and a detector is placed above the sheet facing the
source. State, with a reason, which radioactive emission would be suitable for
this task. Assume that the thickness of the sheet is about 20 mm.
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
[2]
[Total 11 marks]
12.
(a)
The figure below shows a graph of the variation of the gravitational field strength
g of the Earth with distance r from its centre.
6
0
0
5.0 R
10.0
15.0
r / 10 m
20.0
25.0
2.0
4.0
g / N kg
–1
6.0
8.0
10.0
M. Manser
28
(i)
Define gravitational field strength at a point.
...............................................................................................................
...............................................................................................................
[1]
(ii)
Write down an algebraic expression for the gravitational field strength g at
the surface of the Earth in terms of its mass M, its radius R and the
universal gravitational constant G.
[1]
(iii)
Use data from the figure above and the value of G to show that the mass of
the Earth is 6.0 × 1024 kg.
[2]
(iv)
State which feature of the graph in the figure above indicates that the
gravitational field strength at a point below the surface of the Earth,
assumed to be of uniform density, is proportional to the distance from the
centre of the Earth.
...............................................................................................................
...............................................................................................................
[1]
M. Manser
29
(v)
Calculate the two distances from the centre of the Earth at which
g = 0.098 N kg–1.
Explain how you arrived at your answers.
distance 1 .............................................................................................
...............................................................................................................
...............................................................................................................
[2]
distance 2 .............................................................................................
...............................................................................................................
...............................................................................................................
[2]
(b)
A spacecraft on a journey from the Earth to the Moon feels no resultant
gravitational pull from the Earth and the Moon when it has travelled to a point 0.9
of the distance between their centres. Calculate the mass of the Moon, using the
value for the mass of the Earth in a(iii).
mass = ...................................... kg
[3]
[Total 12 marks]
M. Manser
30
13.
The external wing mirror of a large vehicle is often connected to the body of the vehicle
by a long metal arm. See Fig. 1. The wing mirror assembly sometimes behaves like a
mass on a spring, with the mirror oscillating up and down in simple harmonic motion
about its equilibrium position. The graph of Fig. 2 shows a typical oscillation.
motion of
mirror
body
of vehicle
Fig. 1
displacement / mm
5.0
0
0
0.25
0.5
–5.0
0.75
time/s
Fig.2
(a)
(i)
Define simple harmonic motion .
...............................................................................................................
...............................................................................................................
...............................................................................................................
[2]
(ii)
Calculate the frequency of oscillation of the wing mirror.
frequency = ......................... Hz
[2]
M. Manser
31
(iii)
Calculate the maximum acceleration of the wing mirror.
acceleration = ......................... m s–2
[3]
(b)
With the vehicle at rest and the engine running slowly at a particular number of
revolutions per second, the wing mirror oscillates significantly, whereas at other
engine speeds the mirror hardly moves.
(i)
Explain how this phenomenon is an example of resonance.
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
[3]
M. Manser
32
(ii)
Suggest, giving a reason, one change to the motion of the mirror
1
for a mirror of greater mass
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
[2]
2
for a metal arm of greater stiffness.
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
[2]
[Total 14 marks]
14.
The radioactive radium nuclide 226
88 Ra decays by alpha-particle emission to an isotope
of radon Rn with a half-life of 1600 years.
(a)
State the number of
(i)
neutrons in a radium nucleus ................................................................
[1]
(ii)
protons in the radon nucleus resulting from the decay .........................
[1]
M. Manser
33
(b)
The historic unit of radioactivity is called the curie and is defined as the number of
disintegrations per second from 1.0 g of 226
88 Ra . Show that
(i)
the decay constant of the radium nuclide is 1.4 × 10–11 s–1
1 year = 3.16 × 107 s
[1]
(ii)
1 curie equals 3.7 × 1010 Bq.
[3]
(c)
Use the data below to show that the energy release in the decay of a single
–13
nucleus of 226
J.
88 Ra by alpha-particle emission is 7.9 × 10
nuclear mass of Ra-226 = 226.0254 u
nuclear mass of Rn-222 = 222.0175 u
nuclear mass of He
= 4.0026 u
[3]
M. Manser
34
(d)
Estimate the time it would take a freshly made sample of radium of mass 1.0 g to
increase its temperature by 1.0 °C. Assume that 80% of the energy of the
alpha-particles is absorbed within the sample so that this is the energy which is
heating the sample. Use data from (b) and (c).
specific heat capacity of radium = 110 J kg–1 K–1
time = ......................... s
[4]
[Total 13 marks]
15.
Data can be displayed in graphical form in many different ways. Sometimes it is
necessary to change from one way of displaying data to another. Four graphs are
drawn below.
graph A
velocity / ms–1
30
distance / m
600
500
20
400
300
10
200
100
0
0
0
M. Manser
5
10
15
20
25
30
35 40
time / s
0
5
10
15
20
25
30
35 40
time / s
35
graph B
current I / A
12
1
–– /A–1
I
0.3
10
8
0.2
6
4
0.1
2
0
0
0
20
40
60
80
resistance / 
graph C
g / ms–2
12
0
1.0
8
0.8
6
0.6
4
0.4
2
0.2
0
5x106
(a)
(i)
10x106
40
60
80
resistance / 
lg (g / ms–2)
1.2
10
0
20
15x106
20x106
r/m
0
6.7
6.8
6.9
7.0
7.1
7.2
7.3
7.4 7.5
lg (r / m)
Calculate the total distance travelled from the velocity-time graph A.
distance = ................................. m
[3]
(ii)
M. Manser
Using graph A, draw the corresponding distance-time graph.
36
[3]
(b)
Graph B shows how the current I in a circuit varies with the total circuit
resistance R when the e.m.f. of the supply is kept constant.
(i)
Draw the corresponding graph of 1/I against R.
[2]
(ii)
What is the e.m.f. of the supply?
e.m.f. = ....................................... V
[1]
(iii)
How is the gradient of the graph you have drawn related to your answer to
(b)(ii)?
...............................................................................................................
...............................................................................................................
[1]
M. Manser
37
(c)
Graph C shows how g, the acceleration due to gravity, varies with r, the distance
from the centre of the Earth. A log-log graph showing the same data has been
drawn on new axes.
(i)
Calculate the gradient of the log-log graph.
gradient = .......................................
[2]
(ii)
What can be deduced from the value of the gradient?
...............................................................................................................
...............................................................................................................
[2]
[Total 14 marks]
16.
A mass oscillates on the end of a spring in simple harmonic motion. The graph of the
acceleration a of the mass against its displacement x from its equilibrium position is
shown in Fig. 1.
15
a / m s –2
10
5
–60 –50 –40 –30 –20 –10
0
–5
10
20
30
40
50
60
x/mm
–10
–15
Fig. 1
M. Manser
38
(a)
(i)
Define simple harmonic motion.
...............................................................................................................
...............................................................................................................
...............................................................................................................
[2]
(ii)
Explain how the graph shows that the object is oscillating in simple
harmonic motion.
...............................................................................................................
...............................................................................................................
...............................................................................................................
[2]
(b)
Use data from the graph
(i)
to find the amplitude of the motion
amplitude = ...................... m
[1]
(ii)
to show that the period of oscillation is 0.4 s.
[3]
M. Manser
39
(c)
(i)
The mass is released at time t = 0 at displacement x = 0.050 m. Draw a
graph on the axes of Fig. 2 of the displacement of the mass until t = 1.0 s.
Add scales to both axes.
x/m
0
0
t/s
Fig. 2
[3]
(ii)
State a displacement and time at which the system has maximum kinetic
energy.
displacement .................................. m
time .................................. s
[2]
[Total 13 marks]
17.
(a)
(i)
State the equation that represents Newton’s law of gravitation, defining all
symbols.
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
[1]
M. Manser
40
(ii)
Why did Newton believe that the Universe must be infinitely large?
...............................................................................................................
...............................................................................................................
[1]
(b)
The period and average orbital radius of two Earth-orbiting research satellites are
given in the table below.
(i)
satellite
period
/h
orbital radius
/km
A
1.63
7010
B
48.1
67100
Satellite B has the larger orbital radius. Using Newton’s law of gravitation,
explain why the satellites have such different periods.
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
[2]
(ii)
Using data from the table, calculate the average orbital radius for a satellite
with a period of 57.2 hours.
radius = ..................km
[3]
M. Manser
41
(c)
Suggest three advantages that land–based telescopes have over those which
are on satellites orbiting the Earth.
........................................................................................................................
........................................................................................................................
........................................................................................................................
[3]
[Total 10 marks]
18.
(a)
The table of Fig. 1 shows four particles and three classes of particle.
hadron
baryon
lepton
neutron
proton
electron
neutrino
Fig. 1
Indicate using ticks, the class or classes to which each particle belongs.
[2]
(b)
The neutron can decay, producing particles which include a proton and an
electron.
(i)
State the approximate half-life of this process.
...............................................................................................................
[1]
(ii)
Name the force which is responsible for it.
...............................................................................................................
[1]
M. Manser
42
(iii)
Write a quark equation for this reaction.
...............................................................................................................
...............................................................................................................
[2]
(iv)
Write number equations which show that charge and baryon number are
conserved in this quark reaction.
charge ..................................................................................................
...............................................................................................................
baryon number .....................................................................................
...............................................................................................................
[2]
(c)
Fig. 2 illustrates the paths of the neutron, proton and electron only in a decay
process of the kind described in (b).
proton
neutron
electron
Fig. 2
M. Manser
43
Fig. 3 represents the momenta of the neutron, pn, the proton, pp and the electron,
pe on a vector diagram.
pe
pp
pn
Fig. 3
(i)
Draw and label a line on Fig. 3 which represents the resultant pr of vectors
pp and pe.
[1]
(ii)
According to the law of momentum, the total momentum of an isolated
system remains constant.
Explain in as much detail as you can, why the momentum pr is not the
same as pn.
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
[3]
[Total 12 marks]
M. Manser
44
19.
This question is about kicking a football.
(a)
The diagram below shows how the force F applied to a ball varies with time t
whilst it is being kicked horizontally. The ball is initially at rest.
60
50
F/N
40
30
20
10
0
0
(i)
0.1
0.2
0.3
t/s
Use the graph to find
1
the maximum force applied to the ball
maximum force = ……………………N
2
the time the boot is in contact with the ball.
time = …….…………..s
[1]
M. Manser
45
(ii)
The mean force multiplied by the time of contact is called the impulse
delivered to the ball. Use the graph to estimate the impulse delivered to the
ball.
impulse = …...…………N s
[2]
(b)
The mass of the ball is 0.50 kg. Use your answers to (a) to calculate
(i)
the maximum acceleration of the ball
acceleration = ......................m s–2
[2]
(ii)
the final speed of the ball
speed = ......................m s–1
[2]
(iii)
the kinetic energy of the ball after the kick.
kinetic energy = ......................J
[2]
M. Manser
46
(c)
The ball hits a wall with a speed of 14 m s–1. It rebounds from the wall along its
initial path with a speed of 8.0 m s–1. The impact lasts for 0.18 s. Calculate the
mean force exerted by the ball on the wall.
force = ………………..N
[3]
[Total 12 marks]
20.
(a)
The equation of state of an ideal gas is pV = nRT. Explain why the temperature
must be measured in kelvin.
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
[2]
M. Manser
47
(b)
A meteorological balloon rises through the atmosphere until it expands to a
volume of 1.0 × 106 m3, where the pressure is 1.0 × 103 Pa. The temperature
also falls from 17 °C to –43 °C.
The pressure of the atmosphere at the Earth’s surface = 1.0 × 105 Pa.
Show that the volume of the balloon at take off is about 1.3 × 104 m3.
[3]
(c)
The balloon is filled with helium gas of molar mass 4.0 × 10–3 kg mol–1 at 17 °C at
a pressure of 1.0 × 105 Pa. Calculate
(i)
the number of moles of gas in the balloon
number of moles = ……………..
[2]
(ii)
the mass of gas in the balloon.
mass = ................kg
[1]
M. Manser
48
(d)
The internal energy of the helium gas is equal to the random kinetic energy of all
of its molecules. When the balloon is filled at ground level at a temperature of
17 °C the internal energy is 1900MJ. Estimate the internal energy of the helium
when the balloon has risen to a height where the temperature is –43 °C.
internal energy = ................MJ
[2]
(e)
The upward force on the filled balloon at the Earth’s surface is 1.3 × 105 N. The
initial acceleration of the balloon as it is released is 27 m s–2. The total mass of
the filled balloon and its load is M.
(i)
On the diagram below draw and label suitable arrows to represent the
forces acting on the balloon immediately after lift off.
[2]
M. Manser
49
(ii)
Calculate the value of M.
M = ...............kg
[3]
[Total 15 marks]
21.
(a)
Define magnetic flux density.
........................................................................................................................
........................................................................................................................
........................................................................................................................
[2]
(b)
The figure below shows an evacuated circular tube in which charged particles
can be accelerated. A uniform magnetic field of flux density B acts in a direction
perpendicular to the plane of the tube.
Protons move with a speed v along a circular path within the tube.
evacuated
tube
P
(i)
path of
proton
On the figure above draw an arrow at P to indicate the direction of the force
on the protons for them to move in a circle within the tube.
[1]
M. Manser
50
(ii)
State the direction of the magnetic field. Explain how you arrived at your
answer.
...............................................................................................................
...............................................................................................................
...............................................................................................................
[2]
(iii)
Write down an algebraic expression for the force F on a proton in terms of
the magnetic field at point P.
...............................................................................................................
[1]
(iv)
Calculate the value of the flux density B needed to contain protons of speed
1.5 × 107 m s–1 within a tube of radius 60 m. Give a suitable unit for your
answer.
B = …………………unit………………
[5]
M. Manser
51
(v)
State and explain what action must be taken to contain protons, injected at
twice the speed (2v), within the tube.
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
[2]
[Total 13 marks]
22.
(a)
Fig. 1 shows a toy consisting of a light plastic aeroplane suspended from a long
spring.
Fig. 1
M. Manser
52
(i)
The aeroplane is pulled down 0.040m and released. It undergoes a vertical
harmonic oscillation with a period of 1.0 s. The oscillations are lightly
damped.
Sketch on the axes of Fig. 2 the displacement y of the aeroplane against
time t from the moment of release.
0.05
y/m
0.04
0.03
0.02
0.01
0
1.0
2.0
4.0
3.0
t/s
–0.01
–0.02
–0.03
–0.04
–0.05
Fig. 2
[3]
(ii)
The aeroplane is replaced by a heavier model made of the same plastic
having the same fuselage but larger wings. State and explain two changes
which this substitution will make to the displacement against time graph
that you have drawn on Fig. 2.
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
[4]
M. Manser
53
(b)
The top end of the spring in Fig. 1 is then vibrated vertically with a small constant
amplitude. The motion of the aeroplane changes as the frequency of oscillation of
the top end of the spring is increased slowly from zero through resonance to
2.0 Hz.
Explain the conditions for resonance to occur and describe the changes in the
motion of the aeroplane as the frequency changes from zero to 2.0 Hz.
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
[5]
[Total 12 marks]
M. Manser
54