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[Maximum number: 13]

This question is about time dilation and relativistic mass.

(a)

Two space stations X and Y are at rest relative to each other. The separation of X and Y as measured in their frame of reference is $1.80 \times 10^{11} \mathrm{~m}$ .

State what is meant by a frame of reference.

[ 1 ]

(b)

A radio signal is sent to both space stations in (a) from a point midway between them. On receipt of the signal a clock in X and a clock in Y are each set to read zero. A spaceship S travels between X and Y at a speed of 0.750 c as measured by X and Y . In the frame of reference of S , station X passes S at the instant that X 's clock is set to zero. A clock in S is also set to zero at this instant.

[ 9 ]

(i)

Calculate the time interval, as measured by the clock in X , that it takes S to travel from X to Y .

[ 2 ]

$\frac{1.80\times10^{11}}{0.750\times3\times10^{8}}=800\ \mathrm{s}$

(ii)

Calculate the time interval, as measured by the clock in S , that it takes S to travel from X to Y .

[ 2 ]

$\gamma=\frac{1}{\sqrt{1-0.750^{2}}}=1.51$

time $=\frac{800}{1.51}=530\ \mathrm{s}$

(iii)

Explain whether the clock in X or the clock in S measures the proper time.

[ 2 ]

(iv)

Explain why, according to S , the setting of the clock in X and the setting of the clock in Y does not occur simultaneously.

[ 3 ]

(c)

Muons are produced in the upper atmosphere of Earth and travel towards the surface of Earth where they are detected. Explain how, with reference to the situation described in (b), the production and detection of muons provide evidence for time dilation.

[ 3 ]

[Maximum number: 1]

State a postulate that is the same for both special relativity and Galilean relativity.

[Maximum number: 7]

This question is about the Michelson-Morley experiment.

The diagram shows the basic features of the Michelson-Morley experiment.

(a)

During the experiment, Michelson and Morley slowly rotated the apparatus through $90^{\circ}$ . Discuss, with reference to Galilean transformations, the changes that Michelson and Morley expected to observe during the experiment.

[ 4 ]

(according to a Galilean transformation) speed of light depends on the direction of motion (through the ether);
beam which reflects from mirror $M_{1}$ takes different/less time than the beam reflecting from $\mathrm{M}_{2}$ ;
the time taken to travel each path will change as the apparatus is rotated;
a changing interference pattern is observed;

(b)

Describe how the observations made by Michelson and Morley differed from what was expected.

[ 1 ]

(c)

Explain the importance of the outcome of the Michelson-Morley experiment in support of the special theory of relativity.

[ 2 ]

IB Physics HL A 5 Galilean and Special Relativity Topic Practice

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IB Physics HL A 5 Galilean and Special Relativity Topic Practice

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Question 3

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