Fields
Gravitational Fields
Useful things: RE = 6.37 x 106 m, ME = 5.98 x 1024 kg
1) Currently, the space probe, Cassini, is between Jupiter and Saturn. Cassini’s mission is to deliver
a probe to one of Saturn’s moons, Titan, and then orbit Saturn collecting data. Below is
astronomical data that you may find useful when answering the following questions.
Mass of Cassini
2.2 x 103 kg
Mass of Jupiter
1.9 x 1027 kg
Mass of Saturn
5.7 x 1026 kg
Saturn day
10.7 hours
i.
ii.
iii.
iv.
v.
Calculate the magnitude of the total gravitational field experience by Cassini when it is 4.2 x 1011
m from Jupiter and 3.9 x 1011 m from Saturn. [4.68 x 10-7 N/kg]
Indicate the direction of the gravitational field at Cassini in the question above.
When Cassini arrives in the vicinity of Saturn, scientists want it to remain above the same point
on Saturn’s equator throughout one complete day. This is called a stationary orbit.
What is the period in seconds of this stationary orbit? [3.85 x 104 s]
Calculate the radius of this stationary orbit. [1.13 x 108 m]
2) Halley’s comet last passed by Earth in 1986. The path of this comet is elliptical. Part of this
ellipse is shown in the figure below, with P, Q, and R representing three points along the path.
Point P is 1.0 x 1012 m from the sun, Q is 3.0 x 1011 m from the sun, and R is 1.0 x 1011 m.
i.
Calculate the gravitational field strength at point P due to the sun. [1.33 x 10-4 N/Kg [Towards
Sun]]
3) Nato III is a communication satellite that has a mass of 310 kg and orbits Earth at a constant
speed at a radius of 4.22 x 107 m from the centre of the Earth.
i.
Calculate the magnitude of Earth's gravitational field at the orbit radius of Nato III. [0.224 N/kg]
ii.
What is the speed of Nato III in its orbit? [3.07 x 103 m/s]
4) The Russian space Station, MIR, was in a circular orbit around Earth at a height where the
gravitational field strength was 8.7 N/kg.
i.
ii.
iii.
Calculate the magnitude of the gravitational force exerted by Earth on an astronaut of mass 68
kg on board MIR. [590 N]
When the astronaut wishes to rest, he has to lie down and strap himself into bed. What is the
magnitude of the force that the bed exerts on the astronaut before he begins to fasten the
strap? [0 N]
Newspaper articles about astronauts in orbit sometimes speak about zero gravity when
describing weightlessness. Explain why the astronaut orbiting in MIR is not really weightless.
5) The Mir space station orbited Earth at an altitude of 390 km. The total mass of the space station
was 140 tonnes and Mir completed 83 500 orbits in 14.6 years before it crashed to Earth on
March 23 2001.
i.
ii.
iii.
iv.
Calculate the period of Mir’s orbit in seconds. [5.51 x 103 s]
Calculate the speed of Mir while in orbit. [7.70 x 103 m/s]
Calculate the value of the gravitational field strength at 390 km above the Earth’s surface. [8.78
N/kg]
When Mir was in a stable orbit, an object of mass 2.5 kg was placed on a spring balance that was
attached to the inside of the space station. What would be the weight shown on the spring
balance? Explain your reasoning.
6) When people went to the Moon in Apollo 11, the spacecraft was initially placed in a parking
orbit 190km above Earth’s surface. This is show below.
i.
Calculate the speed of Apollo 11 in the parking orbit. [7.8 x 103 m/s]
ii.
iii.
iv.
Two students were discussing the physics of the motion of Apollo 11 in the parking orbit. They
realised that it was travelling at a constant speed but not in a straight line. Jane said that this
can be predicted by Newton’s first law. Maria claimed that this disobeyed Newton’s first law.
Explain, giving reasons, whether Jane is correct or incorrect, and whether Maria is correct or
incorrect.
Which one of the following statements best describes the origin of the centripetal force
required to keep Apollo 11 in its circular parking orbit?
a. Apollo 11’s acceleration towards the Earth
b. The rocket motors of Apollo 11
c. The speed of Apolllo 11 in its orbit
d. The gravitational field of Earth acting on Apollo 11
Apollo 11 then leaves its parking orbit and travels to the moon. Which one of the following
graphs best represent the net gravitational force acting on Apollo 11 as it travels from its
parking orbit to the Moon?
Histories and Theories of Electrostatics
1) Describe a simple experiment that enabled early scientists to determine that there were two
different type of charges.
2) In the 1600s, William Gilbert compared the effects of electricity and magnetism.
i) Describe two similarities between these effects.
ii) Describe two differences between these effects.
3) A negatively charged ebonite rod is brought near a neutral pith ball that is hanging by an insulated
thread from a support. Describe what happens:
i) Before they touch.
ii) After they touch.
Coulomb’s Law
1) Is the force -5.7 x 103 N an attractive or a repulsive force?
2) Two positive charges of 6.0 X 10-6 C are separated by 0.50 m. What force exists between the
charges? [1.3 N]
3) A negative charge of -2.0 x 10-4 C and a positive charge of 8.0 x 10-4 C are separated by 0.30 m. What
is the force between the two charges? [-1.6 x 104 N]
4) An object with charge 7.5 x 10-7 C is placed at the origin. The position of the second object, charge
1.5 x 10-7 C, is varied from 1.0 cm to 5.0 cm. Draw a graph of the force on the object at the origin.
[10 N, 2.5 N, 1.1 N, 0.63 N, 0.41 N]
5) An object, A, with 5.0 X 10-6 C charge, has two other charges nearby. Object B, -2.75 x 10-6 C, is 0.040
m to the right. Object C, 2.0 x 10-6 C, is 0.030 m below. What is the net force on A? [126 N [52° up]]
6) Three charged objects are arranged in a straight line their charges are -4.50 x 10-5 C, 3.50 x 10-5 C,
and -3.6 x 10-5 C respectively. If the first two are 0.50 m apart and the last two are 0.20 m apart,
what is the force felt by the middle object? [227 N [Right]]
7) What is the force of attraction felt by a proton and an electron if they are 1.25 x 10-11 m apart? [1.47 x 10-6 N]
Electric Fields
1) An ion with a charge of 1.60 x10-19 C is placed in an electric field produced by another larger
charge. If the magnitude of the field at this position is 1.00 x 103 N/C, calculate the magnitude
of the electrostatic force on the ion. [1.60 x 10-16 N]
2) The magnitude of the electrostatic force on a small charged sphere is 3.42 x 10-18 N when the
sphere is at a position where the magnitude of the electric field due to another larger charge is
5.34 N/C. What is the magnitude of the charge on the small charged sphere? [6.40 x 10-19 C]
3) The electric field at a position 2.00 cm from a charge is 40.0 N/C directed away from the charge.
Determine the charge producing the electric field. [+1.78 x10-12 C]
4) An electron has a charge of 1.60 x 10-19 C. At what distance from the electron would the
magnitude of the electric field be 5.15 x 1011 N/C? [5.29 x 10-11 m]
5) Two positively charge spheres, A and B, with charges of 1.50 x 10-6 C and 2.00 x 10-6 C,
respectively, are 3.30 x 10-2 m apart. Determine the net electric field at a point P located
midway between the centres of the two spheres. [1.65 x 107 N/C [left]]
6) Calculate the net electric field at a point 2.10 x 10-2 m to the left of the 1.50 x 10-6 C charge in
the previous question. [3.67 x 107 N/C [left]]
7) An electron and a proton are 5.29 x 10-11 m apart in a hydrogen atom. Determine the net
electric field at a point midway between the two charges. [4.11 x 1012 N/C [toward the
electron]]
8) Calculate the net electric field at point P, which is 0.100 m from two similar spheres with
positive charges of 2.00 C and separated by a distance of 0.0600 m, as show in the figure below.
9) At a point in Earth’s atmosphere, the electric field is 150 N/C downwards and the gravitational field
is 9.80 N/kg downward.
a. Determine the electric force on a proton (p+) placed at this point.
b. Determine the gravitational force on the proton at this point. The proton has a mass of
1.67 x 10-27 kg.
Electric Field Lines
1) Describe the difference between an electric field vector and an electric filed line.
2) Sketch the electric field lines around the following charges:
i) A positive charge.
ii) A negative charge
iii)
iv)
v)
vi)
Two positive charges
Two negative charges
A positive charge and a negative charge
Two oppositely charged parallel plates
Magnetic Fields
1) List at least two differences and two similarities between
i) Gravitational and electric fields
ii) Gravitational and magnetic fields
iii) Electric and magnetic fields
2) Draw magnetic field lines for the following situations:
i) A single bar magnet
ii) Two bar magnets with the north poles facing each other
iii) Two bar magnets with the north pole of one magnet facing the south pole of the other.
iv) A U-shaped magnet
3) Indicate the direction of the magnetic field lines and the direction of current in the wire, as required.
4) Sketch the direction of the unknown variable in each situation.
5) An electron and proton, both with the same perpendicular velocity, enter a region with a uniform
external magnetic field. What can you state about the deflection of both particles?
6) Describe the key differences in how magnetic and electric fields affect a moving charge particle.
7) A positively charged lithium ion is travelling horizontally along Earth’s surface. Describe the
deflection due to the magnetic force if the ion travels
i) south to north
ii) east to west
iii) upwards into the atmosphere