M
ULTIPLEC
HOICEQ
UESTIONSChoose the letter A, B, C or D that corresponds to the correct answer.
1 Two bodies of mass m1 and m2 whose centres are separated by a distance d attract each other with a gravitational force of F. If the mass of each body is doubled and their separation reduced to one-quarter of its original value, the new force of attraction is given by:
(A) F (B) 16F
43 Core Topic One: Space (C) 32F
(D) 64F
2 Table 1.7 shows the masses and radii of four imaginary planets expressed as ratios of the Earth’s mass and radius.
Table 1. 7
An astronaut landing on the four planets would have the greatest weight on:
(A) W (B) X (C) Y (D) Z.
3 A satellite of mass m travels with a speed v in a circular path of radius R (between centres) around a planet of mass M. The equation which best describes the motion of the satellite is:
(A) 3
4 In 1610 Galileo discovered four moons of Jupiter — Europa, Callisto, Io and Ganymede.
Their periods are shown in Table 1.8.
Table 1. 8
On the basis of Kepler's Laws, the order of the moons from Jupiter starting with that closest to the planet is:
(A) Callisto, Ganymede, Europa, Io (B) Io, Europa, Ganymede, Callisto (C) Europa, Callisto, Io, Ganymede (D) Io, Callisto, Europa, Ganymede.
5 In Newton’s imaginary analysis of projectile motion, a cannon was used to fire a cannon ball horizontally from the top of a high mountain.
Which of the graphs in Figure 1.28 best
represents the horizontal velocity of the cannon ball against time if we neglect air resistance?
Figure 1. 28
6 As the Space Shuttle orbits the Earth in a circular orbit, it has:
(A) a constant velocity but a changing speed (B) no resultant force acting on it
(C) a constant speed but a changing velocity (D) a constant velocity and a constant
acceleration.
7 As a rocket accelerates from the launch pad, the acceleration:
(A) increases as less fuel is burnt per second (B) increases since the mass of the spacecraft
and rockets decreases
(C) decreases due to air resistance (D) decreases since less fuel is available.
8 A small ‘window’ exists for safe re-entry of spacecraft to Earth. This ‘window’ is determined by:
(A) the size of the spacecraft (B) the landing site
(C) the hole in the ozone layer
(D) a compromise between generating too much heat and keeping within safe g-forces.
9 The rocket pioneer who first suggested multi-stage rockets be used for space flight was:
(A) Tsiolkovsky (B) Goddard (C) Oberth (D) von Braun.
10 According to Galilean-Newtonian relativity, all but one of the following statements is correct.
Which is the incorrect statement?
(A) The laws of mechanics are the same for an observer at rest and one moving at a constant velocity relative to the first.
(B) The velocity of an observer A relative to another observer B is given by
B
(C) The length of a moving object depends upon the reference frame from which it is viewed.
(D) The speed of light c is relative to the ether.
11 The incorrect statement is:
(A) Galileo attempted to measure the speed of light but could only conclude it was
extremely fast.
(B) All measured quantities are relative quantities.
(C) Newton regarded space and time as being dependent.
(D) The ether was believed to be the medium through which light could propagate.
12 For the Michelson-Morley experiment, which statement is incorrect?
(A) No motion of the Earth relative to the ether was detected.
(B) The speed of light depends on the motion of the observer through the ether.
(C) Interference methods were used to look for motion through the ether.
(D) No ether wind was detected.
13 If two separated events are simultaneous for an observer, then the same two events will:
(A) be simultaneous for all other observers.
(B) not be simultaneous for an observer moving with constant velocity relative to the first observer.
(C) be simultaneous only for observers in inertial frames of reference.
(D) be simultaneous for a second observer only if the events are separated by a distance less than one light year.
14 An astronomer measures the speed of recession of a distant galaxy by means of its ‘red shift’ as 3c/4. Radio signals coming from the galaxy reach Earth at:
(A) c (B) 3c/4 (C) c/4 (D) c/2.
15 A metre rule is seen by an observer stationary with respect to the rule, and by a second
observer moving at a speed of c/2 relative to the rule. The second observer observes the rule to be:
In keeping with the format of the HSC sample marks are given for each question.
Answer the following questions in approximately three lines of writing, calculation or diagram.
16 Given that the radius of the Earth is 6380 km, find the acceleration due to gravity at a height of 900 km above the Earth's surface. The following data may be required:
Mass of Earth = 5.983 x 1024 kg G = 6.67 x 10-11 N.m2.kg-2 (2 marks)
17 A ball rolls off a horizontal table with an initial velocity of 2.0 m.s-1. If the table is 70 cm high, how far out from the edge of the table will the ball land? (2 marks)
18 Briefly explain the physical principles that underlie the action of a rocket. (2 marks)
45 Core Topic One: Space 19 Astronauts experience ‘g-forces’ when they are
launched into space.
(a) What are g-forces? (1 mark)
(b) What are the problems of having large g-forces acting on the astronauts? (2 marks) 20 All spacecraft rely on multi-stage rockets to get
them free of the Earth. Why are single-stage rockets not sufficient? (2 marks)
21 The speed of a satellite orbiting the Earth in a circular orbit of radius R is given by
E E
R v2=GM . Show how this equation can be derived.
(3 marks)
22 Neptune has two satellites, Triton and Nereid.
They have periods of 5.8 days and 360 days respectively. Calculate the ratios of their orbital radii. (2 marks)
23 Table 1.9 contains information about four of the planets. Use this data to show that Jupiter obeys Kepler’s Law of Periods. (2 marks) Table 1. 9
Planet Period (years)
24 Table 1.10 contains information about the planets Uranus and Pluto. Use this data to calculate the mass of Pluto. (2 marks) Table 1. 10
Planet Orbital Period
25 Briefly explain the contribution to rocketry of one of the following pioneers:
(a) Tsiolkovsky (b) Goddard
(c) Oberth. (2 marks)
26 (a) What was the purpose of the Michelson-Morley experiment? (1 mark)
(b) What role did the half-silvered mirror serve?
(1 mark)
27 Explain the meaning of the phrase ‘the relativity of simultaneity. (3 marks)
28 Experiments prove that the speed of light is constant and is the same for all observers moving with constant velocity relative to each other. Give three consequences that result from this fact of nature. (3 marks)
29 By reference to a hypothetical ‘light clock’, describe why time is dilated (lengthened) for a moving observer when measured by a stationary observer. (3 marks)
30 An unidentified flying object (UFO) is observed by a stationary observer to be 10 m long and travelling at 0.4c.
(a) What is the length of the UFO as measured by the extraterrestrial pilot? (1 mark) (b) How long does an observer on Earth
measure as having elapsed if the
extraterrestrial pilot measures 1 hour of his time to have passed? (1 mark)
L
ONGERA
NSWERQ
UESTIONSAnswer the following questions in approximately five lines of writing, calculation or diagram.
31 A stone is projected with an elevation of 30 degrees out to sea from the edge of a vertical cliff 49 m high. Given that the stone is thrown with an initial speed of 29.4 m.s-1, find:
(a) the time the stone takes to hit the water.
(1 mark)
(b) the distance from the cliff base at which the stone strikes the water. (1 mark)
(c) the magnitude of the velocity at this instant.
(2 marks)
32 The satellite Phobos describes a nearly circular orbit of radius 9.7 x 106 m round the planet Mars with a period of 2.75 x 104 s. Given that
G = 6.67 x 10-11 N.m2.kg-2 :
(a) What is the mass of Mars from this information? (2 marks)
(b) The period of revolution of the other Martian satellite, Demos, is 1.09 x 105 s. What is the radius of its orbit? (2 marks)
33 The relative slow velocities of current spacecraft affect the feasibility of future space exploration to distant planets.
(a) How do spacecraft gain the escape velocity to leave the Earth? (2 marks)
(b) Approximately how fast do current spacecraft go? (1 mark)
(c) How does the relatively slow speed restrict space exploration? (2 marks)
34 Describe the basic principles behind sending a spacecraft to the moon. (5 marks)
35 Distance, the Van Allen radiation belts and sunspots can all affect communication with distant spacecraft. Explain how each of these affects communication. (5 marks)
36 Figure 1.29 shows a spacecraft re-entering the Earth’s atmosphere after completing its task.
Briefly discuss why the ‘re-entry corridor’ is restricted to 6.2 ± 10 to the horizontal. (4 marks)
Figure 1. 29
37 This question refers to the Michelson-Morley experiment.
(a) List two reasons put forward prior to Einstein to ‘explain’ the negative results of the experiment. (2 marks)
(b) How did Einstein explain the result?
(2 marks)
(c) State one implication that comes from Einstein’s explanation and explain how this occurs. (2 marks)
38 This question refers to relativity.
(a) What was the ether? (1 mark) (b) Mu-mesons (muons) are elementary
particles that come to Earth in cosmic ray
showers. They disintegrate spontaneously after an average lifetime of 2.2 x 10-6 s (in their reference frame). Even allowing for their fast speed (0.999c), in this short lifetime they should not be able to travel more than 600 m. The muons, however, are created at the top of the atmosphere some 10 km up and reach the Earth’s surface (where they are detected in laboratories).
How can this be explained:
(i) in the reference frame of the muon?; (1 mark)
(ii) in the Earth’ reference frame? (1 mark)
39 A spaceship passes you at a speed of 0.80 c.
(a) You measure its length to be 75 m, how long would a member of the spaceships’
crew measure it to be? (2 marks)
(b) If the spaceship were to travel to a star 100 light years away from Earth (as measured by an Earthbound observer) at this speed, how far would the ship’s crew determine the distance to the star to be? (2 marks) 40 Explain how, using the principles of relativity, it
is theoretically possible for astronauts to visit
‘nearby’ stars in their lifetime but it is unlikely that any government would fund such a journey.
(5 marks)