IB Physics HL A 5 Galilean and Special Relativity Questions

Practise IB Physics HL A.5 by comparing inertial frames, transforming space-time coordinates and interpreting relativistic motion, clocks, lengths and muon-decay evidence.

Exam points

Apply Galilean transformations x′ = x − vt and t′ = t across inertial frames, including velocity comparisons.
State special-relativity postulates and use Michelson–Morley results to explain invariant light speed.
Combine relativistic velocities with u′ = (u−v)/(1−uv/c²), keeping frame direction and sign consistent.
Apply Lorentz transformations to event coordinates and check the invariant interval between events.
Identify proper time or length in the rest frame, then calculate dilated times or contracted lengths with γ.
Transform time coordinates to decide whether spatially separated events are simultaneous in each frame.
Interpret world-line gradients and light cones on space-time diagrams to compare speeds and event order.
Use muon-survival observations to explain time dilation in Earth and muon frames, including lifetime calculations.

Covered syllabus points

A.5.1 (HL)—Reference frames A.5.2 (HL)—Galilean relativity A.5.3 (HL)—Galilean transformations A.5.4 (HL)—Galilean velocity addition A.5.5 (HL)—Two postulates of special relativity A.5.6 (HL)—Lorentz transformations A.5.7 (HL)—Relativistic velocity addition A.5.8 (HL)—Space-time interval A.5.9 (HL)—Proper time interval and proper length A.5.10 (HL)—Time dilation A.5.11 (HL)—Length contraction A.5.12 (HL)—Relativity of simultaneity A.5.13 (HL)—Space-time diagrams A.5.14 (HL)—World lines and speed A.5.15 (HL)—Muon decay evidence

[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: 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 ]

[Maximum number: 10]

Two rockets, A and B , are moving towards each other on the same path. From the frame of reference of the Earth, an observer measures the speed of A to be 0.6 c and the speed of B to be 0.4 c. According to the observer on Earth, the distance between A and B is $6.0 \times 10^{8} \mathrm{~m}$ .

(a)

Define frame of reference.

[ 1 ]

(b)

Calculate, according to the observer on Earth, the time taken for A and B to meet.

[ 2 ]

(c)

Identify the terms in the formula.

u^{\prime}=\frac{u-v}{1-\frac{u v}{c^{2}}}

[ 1 ]

u and v are velocities with respect to the same frame of reference/Earth AND $u^{\prime}$ the relative velocity

Marking guidance:

Accept 0.4c and 0.6c for u and v

(d)

Determine, according to an observer in A , the velocity of B .

[ 2 ]

(e)

Determine, according to an observer in A , the time taken for B to meet A .

[ 2 ]

$\gamma=1.25$

so the time is t=1.6 «s»

(f)

Deduce, without further calculation, how the time taken for A to meet B , according to an observer in B , compares with the time taken for the same event according to an observer in A .

[ 2 ]

All question bank results loaded

Covered syllabus points

Question 1

Question (a)

Question (b)

Question (i)

Question (ii)

Question (iii)

Question (iv)

Question (c)

Question 2

Question (a)

Question (b)

Question (c)

Question 3

Question (a)

Question (b)

Question (c)

Question (d)

Question (e)

Question (f)