DO PHYSICS ONLINE
SPACE
QUESTIONS AND PROBLEMS
Under development – early phase only – could be numerous typographical errors until proof read more
carefully
VIEW ANSWERS
How to answer a question: problem solving (t0_372.pdf)
View periodic table (cited Aug 2012)
Numerical values for constants and useful physical quantities)
Review: Displacement, velocity, acceleration (t5_dva)
Review: Rectilinear motion with a uniform acceleration (t5_aconst.pdf)
Review: Forces and Newton’s laws of motion (t5_force.pdf)
Review: Forces, momentum and energy (t5_fme.pdf)
Review: Conservation laws (t5_conservation.pdf)
Gravitational fields (t5_gravity.pdf)
P5117 P5293 P5023 P5086 P5542
P5345
P5489 P5487
P5891
P5738
Gravitational potential energy (t5_gpe.pdf)
P5860 P5188 P5440
Projectile Motion (t5_project.pdf)
P5234 P5921 P5160 P5555 P5682
Motion of rockets (t5_rockets.pdf)
P5697 P5854 P5497 P5876 P5674
Motion of satellites (t5_satellites.pdf)
P5378 P5593 P7777 P5461 P5661
Einstein’s theory of special relativity – frames of reference (t5_fofr.pdf)
P5950 P5886
Concepts of special relativity (t5_sr.pdf)
P5606 P5609
Time dilation (t5_time.pdf)
P5486 P5410
Length contraction (t5_length.pdf)
P5791 P5935 P5176 P5615
Mass and energy (t5_emc2.pdf)
P5456 P5893 P5544
P5023
How could you find the mass of the Earth from its radius and the acceleration due to
gravity at the Earth’s surface?
P5086
What is the gravitational force acting a 2000 kg satellite when it is orbiting the Earth at
twice the Earth’s radius?
Earth’s mass
ME = 5.971024 kg
Earth’s radius RE = 6.38106 m
P5117
A 50 kg person and a 75 kg person are sitting on a bench 500 mm apart. Estimate the
gravitational force acting between the two people.
P5160
A golfer strikes a ball sitting on the ground on a level golf course. The ball hits the
ground 180 m north from where it was struck, 5.6 s later. Assuming air resistance is
negligible find: (a) the maximum height the ball reached, (b) the initial velocity
(direction and magnitude) of the ball as it left the golf club.
P5176
Two clocks are synchronized and then one is sent into space at 0.45c for one hour of its
time. (a) Calculate the time passed for the clock left behind in the stationary frame of
reference. (b) Describe and draw the space of the moving clock as observed from the
stationary clock. Assume they are circular to start. (c) What shape will the moving clock
to an observer moving with the clock? (d) If the moving clock had a mass of 294 g
when stationary, calculate the mass when it is moving at 0.45c.
P5188 (21 22)
(a)
Explain the reason for the selection of infinity as the place of zero gravitational
potential energy.
(b)
How does this selection of zero level result in any point with a gravitational field
having a negative gravitational potential energy value?
P5234 A ball thrown in the air traces a path
as shown. What does the diagram tell
you? (HSC 2005)
P5293
How could you design a pendulum to have a period of 1 s, 1 min, 1 hour?
P5345
Find the net force acting on the Moon from the Earth and the Sun assuming that they are
at right angles to each other.
MM = 7.351022 kg
MS = 1.991030 kg
RME = 3.84105 km RMS = 1.50108 km
P5378
A remote sensing satellite has been placed in a circular orbit with a period of 1.5 h.
Determine the distance above the Earth’s surface and its speed.
Earth’s mass ME = 5.971024 kg Earth’s radius RE = 6.38106 m
universal gravitation constant G = 6.67310-11 N.m2.kg-2
P5410
Astronaut Chris travels to Vega, the fifth brightest star in the night sky, leaving his 35
year old twin Pat behind on Earth. Chris travels at a speed of 0.990c and Vega is 25.3
light-years from Earth. (a) How long does the trip take from the point of view of Pat.
How old is Pat when Chris arrives at Vega? (b) How old is Chris when he arrives at
Vega (use the time dilation effect)? (c) What distance did Chris travel from his point of
view and how old is he at the end of his journey.
P5440 (23 24 25)
(a) Determine the gravitational potential energy of a 1000 kg communications satellite
orbiting the Earth at an altitude of 40 000 km.
(b)
Calculate the change in gravitational potential energy when the 3177 kg space
shuttle is launched from the surface of the Earth into a 400 km altitude low Earth
orbit.
(c)
How much work must be done to increase the altitude of a 1000 kg satellite by
5000 m (assuming its mass is unchanged)?
P5456
An electron with a rest mass of 9.1110-31 kg is travelling at 0.999c. Determine the
relativistic mass of the electron.
P5461
Why would a satellite in low orbit around Earth eventually fall to Earth? (HSC 2005).
P5486
A spacecraft is travelling at 0.99c. An astronaut inside the craft records a time of 1 hour
for a certain event to occur. How long would an observer stationary relative to the craft
record for this event?
P5487
Describe an experiment where a ball is dropped from different heights in a vacuum to
determine the value of the acceleration due to gravity at the surface of the Earth. You
need to describe the equipment used and how it was set up, the results you collected,
how you analyzed them and the conclusion(s) you drew from them. You should use
scientific diagrams where possible to aid your description.
P5489
What is the value of g on the top of Mount Everest, h = 8848 m
P5497
Discuss the effects of the motion of the Earth on the launch of a rocket.
P5542
If an astronaut with all his gear on weights 240 N on the Moon, what is their mass on
the surface of the Earth? Gravitational field strength on the Moon is (1/6)th of that on
Earth.
P5544
A particular radioactive isotope loses 5102 J of energy. Calculate its resultant loss of
mass.
P5555
A cannon fires a shot with a horizontal velocity of 200 m.s-1 from the top of a cliff 30.0
m above the level of the sea. Calculate (a) the time taken for the shot to travel from the
cannon to the sea, (b) the range of the cannon ball hitting the water. (HSC School Exam
2008).
P5593
A spy satellite of mass 1000 kg is orbiting the Earth (RE = 6380 km) at an altitude of
300 km. (a) What is its period? (b) What is its orbital speed? High resolution
photographs on film are sent back to Earth in a special container which can withstand a
maximum acceleration of 8g. The container and contents have a mass of 50 kg. (c)
Calculate the kinetic energy of the container as it traveling with the satellite. (d) The
gravitational potential energy of the container relative to the surface of the Earth is the
difference between the gravitational potential energy of the container in the satellite and
the gravitational potential energy at the Earth’s surface. Calculate this value. (e)
Determine the shortest time the container’s velocity can be brought to zero. (f) If the
total orbital energy = kinetic energy + gravitational potential energy relative to the
surface, determine the rate energy must be lost to remove the orbital energy of the
container by the time it reaches the Earth’s surface.
P5606
A new EFT (extremely fast train) is travelling along the tracks at the speed of light
relative to the Earth’s surface. A passenger is walking towards the front of the train at 5
m/s relative to the floor of the train. Clearly, relative to the Earth’s surface, the
passenger is moving faster than the speed of light. Analyse this situation from the point
of view of Special Relativity.
P5609
Einstein’s 1905 theory of special relativity made several predictions that could not be
verified for many years.
(a 1) State ONE such prediction.
(b 2) Describe an experiment to test this prediction.
(c 3) Explain how technological advances since 1905 have made it possible
to carry out this experiment.
(HSC 2005)
P5615
The radius of our galaxy is 31020 m, or about 3104 light years.
Assume the speed of a spacecraft is 0.99c.
(a)
(b)
(c)
(d)
(d)
From the point of view of an observer on Earth, calculate the time to
travel to the edge of our galaxy?
Use the length contraction formula to calculate the time for a person to
travel from the centre to the edge of our galaxy.
Use the time dilation effect to calculate the time for a person to travel
from the centre to the edge of our galaxy.
How fast would a spaceship have to travel to go from the centre to the
edge of our galaxy in 30 yrs as measured from within the spaceship?
How much time would elapse on Earth during this journey?
What does this tell us about the future of traveling to edge of our galaxy?
P5661
From nearest to furthest, the four satellite moons of Jupiter first observed by Galileo in
the year 1610 are called Io, Europa, Ganymede and Callisto. For the first three moons,
the orbital period T of each is exactly twice the period of the one orbiting immediately
inside it. That is
TEuropa 2 TIo
TGanymede 2 TEuropa
The mass of Jupiter is 1.901027 kg, and the orbital radius of Io is 421 600 km.
(a) Use Kepler’s Law of Periods to calculate Ganymede’s orbital radius.
(b) Calculate Ganymede’s orbital speed. (HSC 2005)
P5674
The initial velocity required by a space probe to just escape the gravitational pull of a
planet is called escape velocity. What quantities affect the magnitude of the escape
velocity?
P5682
Two projectiles are fired at the same initial speed on level ground. Prove that that if one
projectile was launched at an angle of  w.r.t. the ground and the other at an angle 
such that ( + ) = 90o that they have the same range. For the case when  = 60o and  =
30o, which projectile takes the longest time to hit the ground? Sketch for the two
projectiles (a) the trajectory and (b) the vertical displacement against time.
P5697
A rocket takes off from the launch pad with constant thrust. Which choice shows how
the acceleration and velocity changes as it rises?
v
a
A
v
v
B
a
a
a
v
C
D
Explain your answer.
P5738
Given the radius of the Earth is 6400 km, a rocket places a satellite into a stable orbit of
altitude 4020 km. Calculate the period of the satellite,
P5777
A space probe P is in a stable orbit around small, distant planet. Sketch the orbit of the
space probe. The probe fires a forward-facing rocket that reduces its orbital speed by
half. Sketch the subsequent motion of the planet. (HSC 2005).
P5791
A missile travelling at 90% of the speed of light has a rest length of 10 m. Calculate the
length of the moving missile as measured by a stationary observer directly under the
flight path of the missile.
P5854
(a) Give two reasons to explain why the concept of g-force is useful.
(b) Explain why the space shuttle is apparently “weightless” while in orbit.
P5860
Two astronauts landed on a very small asteroid orbiting the Sun between Mars and
Jupiter. They experienced almost negligible weight force. Explain.
P5876
Calculate the escape velocity from the Earth’s surface (m.s-1 and km.h-1).
Earth’s mass ME = 5.971024 kg Earth’s radius RE = 6.38106 m
universal gravitation constant G = 6.67310-11 N.m2.kg-2
P5886
The idea of a universal aether was first proposed to explain the transmission of light
through space. Michelson and Morley attempted to measure the speed of Earth through
the aether. Evaluate the impact of the result of the Michelson and Morley experiment on
scientific thinking.
P5891
In 1970 NASA launched Apollo 13, their third mission planned to land humans on the
Moon. Half-way to the Moon a huge explosion crippled the spacecraft. The only way
home for the astronauts was to fly around the back of the Moon and then fire the rocket
engine to take the craft out of lunar orbit and put it into an Earth-bound trajectory. At
the completion of the rocket engine burn, mission leader Jim Lovell was heard to say,
‘We just put Isaac Newton in the driver’s seat’. Given that the spacecraft returned safely
to Earth, justify Jim Lovell’s statement.
P5893
Energy is radiated by the Sun at the rate of about 3.921026 W. Find the corresponding
decrease in the Sun’s mass for every second that it radiates.
P5899
Compare the orbital radius of a geostationary satellite above Mars with that above the
Earth.
mass of Mars = 6.421023 kg
period of rotation of Mars = 24 h 47 min
radius of Mars = 0.53  radius of Earth
ME = 5.971024 kg Earth’s radius RE = 6.38106 m
P5921
A cannon ball was observed by Isaac Newton to be fired at a velocity of 300 m.s-1 and
at an angle of 30o from the horizontal. Determine: (a) the horizontal and vertical
components of its initial velocity, (b) time taken to reach its maximum height, (c) the
maximum height of the cannon ball, (d) the range of the cannon ball. (HSC School
Exam 2008).
P5935
A spacecraft in the shape of a square box with sides 300 mm long moves away from the
Earth at a velocity of 0.5c. Find the volume of the box as measured from Earth.
P5950
Describe an experiment that you could perform in a reference frame to determine
whether or not the frame was non-inertial.