RelativityM - 1(a proper time the time interval measured by...

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1. (a) proper time: the time interval measured by an observer of an event that happens at the same place according to that observer; proper length: the length of an object as measured by an observer who is at rest relative to the object; 2 Do not look for precise wording but look for the understanding of the quantities in the sense of the words. (b) (i) no they will not appear to be simultaneous; Look for a discussion along the following lines. Carmen sees Miguel move away from the signal from A and since Miguel receives the two signals at the same time; and since the speed of light is independent of the motion of the source; Carmen will see the light from A first / light from B will reach Carmen after light from A / OWTTE ; 4 max (ii) γ = 2; to give u = 0.87c (2.6 × 10 8 m s –1 ); 2 (iii) both measure the correct distance; SR states that there is no preferred reference system / laws of physics are the same for all inertial observers; OWTTE ; 2 max [10] 2. (a) v = c V v 0 0 ( N e w t o n ) ( E i n s t e i n ) K e y correct general shape; asymptotic to c ; 2 max 1
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(b) as the speed of the electrons increases SR predicts that the mass of the electrons will increase; SR also predicts that at speed c the mass will be infinite; so effectively the electrons can never reach the speed of light; 3 Look for an answer that shows that mass increases and why the electrons cannot travel at the speed of light. They might quote m = γm 0 and this is fine. (c) (i) γ = 2 2 2 97 . 0 1 1 1 1 - = - c v to give γ = 4.1; m = γ m 0 = 4.1 × 0.51 = 2.1 MeV c –2 ; Accept m = 3.7 × 10 –30 kg. could also solve from KE = 1.5 MeV; rest mass = 0.51 MeV c –2 ; therefore total mass = 2.1MeV c –2 ; 3 max (ii) E = mc 2 ; = 2.1 MeV; 2 Accept 3.20 × 10 –13 J. [10] 2
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3. (a) t i m e x correct labelling of the axes; any sensible straight line path; some sensible brief description eg “particles move in both space and time and so the motion of the particle can be represented by a path in spacetime”; 3 (b) Look for an explanation that contains the following points. all particles follow the shortest path in spacetime; if the Earth were not present the satellite would move in a straight line; the warping of spacetime forces the satellite to follow an orbital path; 3 The description can of course be aided by use of a diagram. (c) if an object is dense enough it will cause extreme warping of spacetime; such that any light leaving the surface will not be able to escape the spacetime surrounding the object; OWTTE ; 2 max If the explanation is given in terms of Newtonian gravity then award 1 mark only. (d) recognize to use R sch = 16 30 11 2 10 9 10 2 10 6 . 6 2 2 × × × × × = - c GM ; 3000 m; 2 [10] 3
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4. (a) (i) proper length the length of an object as measured by an observer at rest with respect to the object / OWTTE ; 1 max (ii) proper time the time interval between two events measured in the reference frame in which the two events occur at the same place; 1 max (iii) inertial observer an observer who is in a reference frame that is moving with constant velocity / in a reference frame in which Newton’s 1 st law is valid; 1 max (b) (i) half-life = c 95 . 0
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