OPTION G SPECIAL AND GENERAL RELATIVITY. 0.5 c

Transcription

1 15 M00/430/H(3) G1. Relativity and simultaneity OPTION G SPECIAL AND GENERAL RELATIVITY (a) State the two postulates of the special theory of relativity. Einstein proposed a thought experiment along the following lines. Imagine a train of proper length 100 m passing through a station at half the speed of light. There are two lightning strikes, one at the front and one at the rear of the train, leaving scorch marks on both the train and the station platform. Observer S is standing on the station platform midway between the two strikes, while observer T is sitting in the middle of the train. Light from each strike travels to both observers. 0.5 c (b) If observer S on the station concludes from his observations that the two lightning strikes occurred simultaneously, explain why observer T on the train will conclude that they did not occur simultaneously. [4] Turn over

2 16 M00/430/H(3) (c) (d) (e) Which strike will T conclude occurred first? What will be the distance between the scorch marks on the train, according to T and according to S? What will be the distance between the scorch marks on the platform, according to T and according to S? [3]

3 16 M01/430/H(3) G1. This question is about time dilation. OPTION G SPECIAL AND GENERAL RELATIVITY (a) One of the two postulates of the Special Theory of Relativity can be stated as the laws of physics are the same for observers in different inertial reference frames. (i) (ii) What does the term inertial reference frame mean? State the other postulate of Special Relativity

4 17 M01/430/H(3) (b) In the diagram below Peter is moving with uniform velocity relative to Jane. A light pulse reflects between the two plane mirrors separated by a distance D as shown in the diagram. To Peter the pulse is seen to traverse a perpendicular path between the mirrors. M 2 " Peter D v M 1 Jane The diagram below shows how the path of the light pulse appears to Jane as it leaves mirror M1, reaches M2 and returns to M1. M 2 M X D M 1 The time for the pulse to move from M1 to M2 and back as measured by Jane is t and the speed of Peter as measured by Jane is v. If the speed of the pulse is c write down expressions for the distances terms of c, v and t. M1X and M1M2 in (i) MX 1 (ii) MM Turn over

5 18 M01/430/H(3) (c) The time for the pulse to move from M to M and back as measured by observer Peter is t. 1 2 (i) Write down an expression for the distance D between the mirrors in terms of c and t. (ii) Show that t = t v 1 c 2 2 [4] (d) Peter and Jane are each wearing a wristwatch with a second hand that takes one minute to make one complete revolution and Peter is moving at a speed of 0.9c with respect to Jane. When Peter observes the second hand on his watch to have made one complete revolution, how many revolutions will Jane observe the second hand of her watch to have made?

6 18 M04/432/H(3)+ Option G Relativity G1. This question is about time dilation. (a) State what is meant by an inertial frame of reference. An observer S in a spacecraft sees a flash of light. The light is reflected from a mirror, distance D from the flash, and returns to the source of the flash as illustrated below. The speed of light is c. X D! S Spaceship speed v "observer E (b) Write down an expression, in terms of D and c, for the time T 0 for the flash of light to return to its original position, as measured by the observer S who is at rest relative to the spaceship. The spaceship is moving at speed v relative to the observer labelled E in the diagram. The speed of light is c. (c) (i) Draw the path of the light as seen by observer E. Label the position F from where the light starts and the position R where the light returns to the source of the flash. (ii) The time taken for the light to travel from F to R, as measured by observer E, is T. Write down an expression, in terms of the speed v of the spacecraft and T, for the distance FR

7 19 M04/432/H(3)+ (iii) Using your answer in (ii), determine, in terms of v, T and D, the length L of the path of light as seen by observer E. (iv) Hence derive an expression for T in terms of T 0, v and c. [4] G2. This question is about the half-life of muons. The half-life of muons is to the muons s as measured in a frame of reference that is stationary relative A pulse of muons is produced such that the muons have a speed of stationary observer ms relative to a Determine the distance travelled by the pulse, as measured by the observer, when half of the muons have decayed. [3] Turn over

8 21 N01/430/H(3) OPTION G SPECIAL AND GENERAL RELATIVITY G1. Two inertial observers, A and B, agree to compare their measurements of time. They each carry an accurate clock. During the experiment, A observes B to be moving at a constant velocity, v, as shown below. B velocity = v A at rest A and B observe two events. For the first event B measured a proper time of 6 seconds while A measured 10 seconds. (a) What is meant by proper time? (b) Calculate the time dilation factor, &, for B s clock as observed by A. (c) (d) According to A, how fast is B moving in order to give this time dilation factor? According to B, how fast is A moving? Turn over

9 22 N01/430/H(3) (e) (f) The second event is at rest with respect to observer A. Observer B measures 6 seconds for this event. What time interval does A measure? Which version of time is correct? Explain your answer. [3]