Download 21 Gravitational fields

AQA Physics
21 Gravitational fields
Exam-style questions
Refer to the Physics data sheet for data, formulae and relationships information.
1
a
Define the gravitational potential at a point in a gravitational field.
(2 marks)
1
b Figure 1, which is not drawn to scale, shows the region between the Earth
(E) and the Moon (M).
Figure 1
i
The gravitational potential at the Earth’s surface is 62.6 M J kg1. Point X
shown in Figure 1 is on the line of centres between the Earth and the
Moon. At X the resultant gravitational field is zero, and the gravitational
potential is 1.3 M J kg1.
Calculate the minimum amount of energy that would be required to move
a Moon probe of mass 1.2 × 104 kg from the surface of the Earth to
point X. Express your answer to an appropriate number of significant
figures.
minimum amount of energy .................................. J
(3 marks)
ii
Explain why, once the probe is beyond X, no further energy would have
to be supplied in order for it to reach the surface of the Moon.
(1 mark)
AQA Physics, 2012, Unit 4 (Question 4)
2
Figure 2 shows a satellite in a geostationary orbit around the Earth.
Figure 2
© Oxford University Press 2016 http://www.oxfordsecondary.co.uk/acknowledgements
This resource sheet may have been changed from the original
1
21 Gravitational fields
Exam-style questions
AQA Physics
a
State the time period for a geostationary satellite.
(1 mark)
b The height of a geostationary satellite in orbit is approximately 36 000 km
above the surface of the Earth.
Calculate the radius of a geostationary orbit.
radius ...................................... m
(1 mark)
c
Calculate the speed, in km s1, of a satellite in a geostationary orbit.
speed ...................................... km s1
(3 marks)
d
State a common use for a geostationary satellite.
(1 mark)
e
Explain why a geostationary orbit is necessary for this use.
(1 mark)
AQA Physics B, 2010, Unit 4 (Question 1)
3
The graph in Figure 3 shows how the gravitational potential energy, Ep, of a
1.0 kg mass varies with distance, r, from the centre of Mars. The graph is plotted
for positions above the surface of Mars.
Figure 3
© Oxford University Press 2016 http://www.oxfordsecondary.co.uk/acknowledgements
This resource sheet may have been changed from the original
2
AQA Physics
a
21 Gravitational fields
Exam-style questions
Explain why the values of Ep are negative.
(2 marks)
b Use data from the graph to determine the mass of Mars.
mass of Mars .......................................... kg
(3 marks)
c
Calculate the escape velocity for an object on the surface of Mars.
escape velocity .................................... ms1
(3 marks)
AQA Physics B, 2013, Unit 4 (Question 1)
4
a
State Newton’s law of gravitation.
(2 marks)
b In 1798 Cavendish investigated Newton’s law by measuring the gravitational
force between two unequal uniform lead spheres. The radius of the larger
sphere was 100 mm and that of the smaller sphere was 25 mm.
i The mass of the smaller sphere was 0.74 kg. Show that the mass of the
larger sphere was about 47 kg.
density of lead  11.3 × 103 kg m3
(2 marks)
© Oxford University Press 2016 http://www.oxfordsecondary.co.uk/acknowledgements
This resource sheet may have been changed from the original
3
21 Gravitational fields
Exam-style questions
AQA Physics
ii
Calculate the gravitational force between the spheres when their surfaces
were in contact.
gravitational force ..................................... N
(2 marks)
c
Modifications, such as increasing the size of each sphere to produce a
greater force between them, were considered in order to improve the
accuracy of Cavendish’s experiment. Describe and explain the effect on the
calculations in part b of doubling the radius of both spheres.
(4 marks)
AQA Physics B, 2010, Unit 4 (Question 1)
5
a
The table gives the gravitational potentials, V, at three different distances, r,
from the centre of the Earth.
i
distance from centre of Earth r / km
gravitational potential V / 107 J kg1
7 500
5.36
12 500
3.22
22 500
1.79
Show that the data in the table is consistent with V  r1.
(3 marks)
ii
A satellite of mass 450 kg is moved from an orbit of radius 7500 km
around the Earth to an orbit of radius 12 500 km.
Use data from the table to show that the potential energy of the satellite
increases by about 10 GJ.
(2 marks)
© Oxford University Press 2016 http://www.oxfordsecondary.co.uk/acknowledgements
This resource sheet may have been changed from the original
4
21 Gravitational fields
Exam-style questions
AQA Physics
5
b The kinetic energy of a 450 kg satellite orbiting the Earth with a radius of
7500 km is 12 GJ.
i Calculate the kinetic energy of the 450 kg satellite when it is in an orbit of
radius 12 500 km.
mass of the Earth  6.0 × 1024 kg
kinetic energy ............................................ GJ
(4 marks)
ii
Calculate the change in kinetic energy of the satellite when it moves into
the higher orbit.
change in kinetic energy ............................................ GJ
(1 mark)
iii
Calculate the total energy that has to be supplied to move the 450 kg
satellite from an orbit of radius 7500 km to an orbit of radius 12 500 km.
total energy ............................................ GJ
(1 mark)
© Oxford University Press 2016 http://www.oxfordsecondary.co.uk/acknowledgements
This resource sheet may have been changed from the original
5