Download Topic 6 and 10 TEST

Year 13 Physics HL
Topic 6/10 TEST
Monday 21st September 2015
90 min
68 marks
You may use a calculator and data booklet
1
1.
The acceleration of free fall of a small sphere of mass 5.0 × 10–3 kg when close to the surface of
Jupiter is 25 ms–2. The gravitational field strength at the surface of Jupiter is
A.
2.0 × 10–4 N kg–1.
B.
1.3 × 10–1 N kg–1.
C.
25 N kg–1.
D.
5.0 × 103 N kg–1.
(1)
2.
The acceleration of free fall of an object of mass m at the surface of Mars is a. The gravitational
field strength at the surface of Mars is
A.
a.
B.
ma.
C.
a
.
m
D.
m
.
a
(1)
3.
The Earth is distance RM from the Moon and distance RS from the Sun. The ratio
gravitatio nal field strength at the Earth due to the Moon
gravitatio nal field strength at the Earth due to the Sun
is proportional to which of the following?
A.
B.
C.
D.
RM
2
RS
2
RM
RS
RS
2
RM
2
RS
RM
(1)
2
4.
Gravitational field strength at a point may be defined as
A.
the force on a small mass placed at the point.
B.
the force per unit mass on a small mass placed at the point.
C.
the work done to move unit mass from infinity to the point.
D.
the work done per unit mass to move a small mass from infinity to the point.
(1)
5.
The diagram below shows lines of electric equipotential. The change in potential on moving
from one line to the next is always the same. At which point does the electric field strength have its
greatest magnitude?
A
B
C
D
(1)
6.
Two satellites of equal mass, S1 and S2, orbit the Earth. S1 is orbiting at a distance r from the
v
Earth’s centre at speed v. S2 orbits at a distance 2r from the Earth’s centre at speed
. The
2
ratio of the centripetal force on S1 to the centripetal force on S2 is
A.
1
.
8
B.
1
.
4
C.
4.
D.
8.
(1)
3
7.
The gravitational potential at point X due to the Earth is –7 kJ kg–1. At point Y, the gravitational
potential is –3 kJ kg–1.
The change in gravitational potential energy of a mass of 4 kg when it is moved from point X to point
Y is
A.
4 kJ.
B.
10 kJ.
C.
16 kJ.
D.
40 kJ.
(1)
8.
Which one of the following graphs best represents the variation of the kinetic energy, KE, and
of the gravitational potential energy, GPE, of an orbiting satellite with its distance r from the
centre of the Earth?
A.
B.
Energy
KE
Energy
KE
0
0
0
r
0
GPE
r
GPE
C.
D.
Energy
GPE
Energy
KE
0
0
r
GPE
0
0
r
KE
(1)
4
9.
The diagram below shows two parallel conducting plates that are oppositely charged.
+
–
+
–
+
X
Y
–
+
+
–
–
The line XY is perpendicular to the plates.
Which of the following diagrams shows the variation along the line XY of the magnitude E of
the electric field strength between the plates?
A.
B.
E
X
E
Y
distance
C.
X
Y
distance
Y
distance
D.
E
X
E
Y
distance
X
(1)
5
10.
A particle P is moving in a circle with uniform speed. Which one of the following diagrams
correctly shows the direction of the acceleration a and velocity v of the particle at one instant of
time?
a
A.
a
B.
v
v
P
P
v
C.
D.
a
P
a
v
P
(1)
11.
The centripetal force that causes a car to go round a bend in the road is provided by
A.
the force produced by the car engine acting on the wheels.
B.
the friction between the tyres and the road.
C.
the weight of the car.
D.
the force exerted by the driver on the steering wheel.
(1)
6
12.
This question is about a spacecraft.
A spacecraft above Earth’s atmosphere is moving away from the Earth. The diagram below
shows two positions of the spacecraft. Position A and position B are well above Earth’s
atmosphere.
A
Earth
B
At position A, the rocket engine is switched off and the spacecraft begins coasting freely. At
position A, the speed of the spacecraft is 5.37  103 m s–1 and at position B, 5.10  103 m s–1.
The time to travel from position A to position B is 6.00  102 s.
(a)
(i)
Explain why the speed is changing between positions A and B.
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(1)
(ii)
Calculate the average acceleration of the spacecraft between positions A and B.
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(2)
(iii)
Estimate the average gravitational field strength between positions A and B.
Explain your working.
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(3)
7
(b)
The diagram below shows the variation with distance from Earth of the kinetic energy Ek
of the spacecraft. The radius of Earth is R.
energy
Ek
0
R
0
distance
On the diagram above, draw the variation with distance from the surface of Earth of the
gravitational potential energy Ep of the spacecraft.
(2)
(Total 8 marks)
13.
This question is about gravitation.
(a)
(i)
Define gravitational potential at a point in a gravitational field.
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(2)
(ii)
Explain why values of gravitational potential have negative values.
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(2)
8
The Earth and the Moon may be considered to be two isolated point masses. The masses of the
Earth and the Moon are 5.98  1024kg and 7.35  1022 kg respectively and their separation is
3.84  108 m, as shown below. The diagram is not to scale.
Earth
mass  5.98 1024kg
Moon
mass  7.35 1022kg
P
3.84 108m
(b)
(i)
Deduce that, at point P, 3.46  108m from Earth, the gravitational field strength is
approximately zero.
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(3)
(ii)
The gravitational potential at P is −1.28  106 J kg–1. Calculate the minimum speed
of a space probe at P so that it can escape from the attraction of the Earth and the
Moon.
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(3)
(Total 10 marks)
9
14.
This question is about gravitation.
A binary star consists of two stars that each follow circular orbits about a fixed point P as shown
below.
star mass
M1
P
R1
star mass
M2
R2
The stars have the same orbital period T. Each star may be considered to act as a point mass
with its mass concentrated at its centre. The stars, of masses M1 and M2, orbit at distances R1
and R2 respectively from point P.
(a)
State the name of the force that provides the centripetal force for the motion of the stars.
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(1)
10
(b)
By considering the force acting on one of the stars, deduce that the orbital period T is
given by the expression
T2 
4 2
2
R1 R1  R2  .
GM 2
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(3)
(c)
The star of mass M1 is closer to the point P than the star of mass M2. Using the answer in
(b), state and explain which star has the larger mass.
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(2)
(Total 6 marks)
15.
This question is about the electric potential due to a charged sphere.
(a)
Define electric potential at a point in an electric field.
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(3)
11
The diagram below shows an isolated, metal sphere in a vacuum that carries a negative electric
charge of 9.0 nC.
–
(b)
On the diagram above draw
(i)
arrows to represent the electric field pattern in the region outside the charged
sphere.
(3)
(ii)
lines to represent three equipotential surfaces in the region outside the sphere. The
potential differences between the lines are to be equal in value.
(2)
(c)
Explain how the lines representing the equipotential surfaces that you have sketched
indicate that the strength of the electric field is decreasing with distance from the centre
of the sphere.
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(2)
(d)
The electric field strength at all points inside the conductor is zero. On the axes below,
draw a graph to show the variation with distance r from the centre of the sphere of the
potential V. The dotted line is drawn at r = a where a is the radius of the sphere. (Note:
this is a sketch graph; you do not need to add values to the axes.)
0
a
r
0
V
(2)
12
(e)
The electric field strength at the surface of the sphere and at points outside the sphere
may be determined by assuming that the sphere acts as though a point charge of
magnitude 9.0 nC is situated at its centre. The radius of the sphere is 4.5 × 10–2 m.
Deduce that the potential at the surface of the sphere is –1800 V.
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(1)
An electron is initially at rest at the surface of the sphere.
(f)
(i)
Describe the path followed by the electron as it leaves the surface of the sphere.
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(1)
(ii)
Determine the speed of the electron when it reaches a point a distance 0.30 m from
the centre of the sphere.
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(4)
(Total 18 marks)
13
16.
This question is about atomic models. The diagram below (not to scale) shows a simple model
of the hydrogen atom in which the electron orbits the proton in a circular path of radius R.
proton
charge +e
electron
charge –e
R
(a)
On the diagram, draw an arrow to show the direction of
(i)
the acceleration of the electron (label this A);
(1)
(ii)
the velocity of the electron (label this V).
(1)
(b)
State an expression for the magnitude of the electrostatic force F acting on the electron.
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(1)
14
(c)
The orbital speed of the electron is 2.2 × 106 m s–1.
Deduce that the radius R of the orbit is 5.2 × 10–11 m.
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(3)
(d)
A more complex model of the atom suggests that the orbital radius can only take certain
discrete values. This leads to the idea of discrete energy levels within the atom. Outline
the evidence that supports the existence of discrete energy levels.
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(3)
(Total 9 marks)
15
17.
This question is about circular motion.
A linear spring of negligible mass requires a force of 18.0 N to cause its length to increase by
1.0 cm.
A sphere of mass 75.0 g is attached to one end of the spring. The distance between the centre of
the sphere M and the other end P of the unstretched spring is 25.0 cm, as shown below.
P
M
25.0 cm
The sphere is rotated at constant speed in a horizontal circle with centre P. The distance PM
increases to 26.5 cm.
(a)
Explain why the spring increases in length when the sphere is moving in a circle.
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(2)
(b)
Determine the speed of the sphere.
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(4)
(Total 6 marks)
16