2018 Sydney Grammar Yr 12 Physics Half Yearly - Advanced Mechanics questions with solutions

2018 Form VI Physics Half-Yearly Examination Page 4 of 30 4. If the cable tethering an astronaut to the shuttle in Earth orbit breaks during a spacewalk, then: (A) she will fly off into space, as the gravitational forces acting on shuttle and astronaut are different. (B) she will remain next to the shuttle as the acceleration of the shuttle and the astronaut are the same. (C) she will remain next to the shuttle as the force of the Sun on the astronaut and shuttle keeps them in orbit. (D) she will fly off into space as the force of the Sun on the astronaut will cause her to fall into the Sun. 5. Which of the following is not correct when comparing these two types of satellites? Property Low Earth Orbit Satellite Geostationary Satellite (A) speed slower faster (B) acceleration higher lower (C) latitude any equatorial (D) orbital period shorter longer

2018 Form VI Physics Half-Yearly Examination Page 9 of 30 Candidate Number Part B Total marks ( 65 ) Attempt ALL Questions Allow about 1 hour and 40 minutes for this Part Answer the questions in the spaces provided. Show all relevant working in questions involving calculations. Question 16 (3 marks) Marks The acceleration due to gravity on Mars is about 1/3 of g on Earth, whereas the radius of Mars is roughly half that of Earth. Estimate the ratio of the mass of Mars to the mass of Earth. ........................................................................................................................................ 3 ........................................................................................................................................ ........................................................................................................................................ ........................................................................................................................................ ........................................................................................................................................ ........................................................................................................................................ ........................................................................................................................................

2018 Form VI Physics Half-Yearly Examination Page 12 of 30 Question 18 (4 marks) Marks A spanner of mass 2 kg is dropped from rest from a distance of 2.737× 10 6 m from the centre of the moon, which has a mass of 7.35 × 10 22 kg and a radius of 1.737× 10 6 m. Determine the speed of the spanner on collision with the moon. ........................................................................................................................................ 4 ........................................................................................................................................ ........................................................................................................................................ ........................................................................................................................................ ........................................................................................................................................ ........................................................................................................................................ ........................................................................................................................................ ........................................................................................................................................ ........................................................................................................................................ ........................................................................................................................................ ........................................................................................................................................ ........................................................................................................................................ ........................................................................................................................................ ........................................................................................................................................

2018 Form VI Physics Half-Yearly Examination Page 17 of 30 Candidate Number Question 22 (5 marks) Marks A boy performs an experiment on a moving train, as shown in the diagram below. When he drops the ball, he finds that its falls diagonally backwards, and lands 0.75 m behind where he was standing. He concludes that the train is a non-inertial frame of reference. Outline the meaning of the term ‘non - inertial frame of reference’. .............................................................................................................................. 1 .............................................................................................................................. Explain the behaviour of the ball, from the perspective of an observer standing on the Earth. .............................................................................................................................. 2 .............................................................................................................................. .............................................................................................................................. .............................................................................................................................. .............................................................................................................................. Estimate t he magnitude of the train’s acceleration. .............................................................................................................................. 2 .............................................................................................................................. .............................................................................................................................. .............................................................................................................................. .............................................................................................................................. motion 1.0 m 0.75 m

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CRIB (AAH) Question 22 (5 marks) Marks A boy performs an experiment on a moving train, as shown in the diagram below. When he drops the ball, he finds that its falls diagonally backwards, and lands 0.75 m behind where he was standing. He concludes that the train is a non-inertial frame of reference. Outline the meaning of the term ‘non-inertial frame of reference’. 1 1 Mark for any sensible outline, e.g.:  A frame of reference that is accelerating.  A frame of reference in which the law of inertia does not hold.  A frame of reference which is experiencing a non-zero net force. Explain the behaviour of the ball, from the perspective of an observer standing on the Earth. 2 Marks Criteria 2  Explains that the ball falls in a parabolic arc (constant horizontal velocity, constant vertical acceleration).  Explains why the ball lands behind the boy (the boy continues to accelerate to the left but the ball does not). 1  Either of the points above. The question asks pupils to explain the “behaviour” of the ball. The most significant (because it is in some sense ‘anomalous’) feature of this behaviour is that the ball falls behind the boy . An explanation of this is therefore essential to gaining full marks in this question. NB 1 : The question required pupils to explain the behaviour, not simply to describe it. Pupils who scored only one mark usually did so because they did not explain why the ball lands behind the boy. NB 2 : Many pupils answered the question from the train’s frame of reference, not that of an external observer. These answers scored no marks . NB 3 : Answers that incorrectly describe the ball’s motion to the stationary observer (e.g. ‘the ball falls straight down’ or ‘the ball falls in a straight line’) usually scored no marks. However, a number of pupils assumed that the ball is dropped when the train is initially at rest, but accelerating to the left (the question makes it clear that this is not the case); these answers scored a maximum of 1 Mark. NB 4 : As the question is only worth two marks, it was not necessary to explain why the ball appears to fall in a straight line. (Though this might have been required if the question had been worth more marks.) motion 1.0 m 0.75 m

Sample Answer to Part (b)  After the boy lets the ball go, it continues with a constant horizontal velocity (to the left) as it accelerates towards the ground, so it falls in a parabolic arc.  After he has let go of the ball, the boy continues to accelerate to the left with the train. He therefore travels a greater horizontal distance than the ball, which ends up somewhere behind him when it hits the floor. Estimate the magnitude of the train’s acceleration. 2 Multiple approaches are possible here, but the simplest was to recognise that, since ݎ ு ൌ ଵ ଶ ܽݐ ଶ and ݎ ௏ ൌ ଵ ଶ ݃ݐ ଶ , a/g are in the same ratio as r H /r V . Thus, a/g = 0.75/1.0 a = 7.4 ms -2 . [2 Marks] [ 1 Mark ] for using ݎ ௏ ൌ ଵ ଶ ݃ݐ ଶ to calculate t = 0.45 s.