IB Physics HL A.5 Galilean and special relativity questions

Exam-style multiple choice and written questions with full markschemes. Check multiple choice answers straight away, or type, photograph or draw a written answer and get it marked.

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Question 1

Multiple choiceEasy1 mark

A train moves at constant velocity to the right relative to a platform. Light flashes are emitted from its front and rear, and a passenger at the train’s midpoint receives them simultaneously. Which row gives the emission times of the flashes in the train and platform frames?

Show answer and explanation

Answer: A. The passenger is equally distant from both ends in the train frame, so simultaneous arrival means the emissions were simultaneous in that frame. Relativity of simultaneity means they are not simultaneous in the platform frame; for a train moving right, the front emission is later.

B: reverses the event order in the platform frame; the front emission is later, not the rear one.
C: treats simultaneity as unchanged between frames and assigns the front event an earlier time in the train frame.
D: also assigns simultaneity to the platform frame, and reverses the front–rear order in the train frame.
Remember: events simultaneous in one inertial frame need not be simultaneous in another.

Question 2

Paper 2Medium4 marks

In inertial frame $S$ a particle moves along the $x$ -axis as shown in Figure 1. Inertial frame $S'$ moves in the $+x$ -direction at speed $v=0.50c$ relative to $S$ The origins of the frames coincide at $t=t'=0$ Take $c=3.00\times10^8\ \mathrm{m\,s^{-1}}$

The Lorentz transformations are

x'=\gamma(x-vt),\qquad t'=\gamma\left(t-\frac{vx}{c^2}\right), \qquad \gamma=\frac{1}{\sqrt{1-v^2/c^2}}.

(a)

Determine $u/c$ for the particle in frame $S$

[1]

(b)

For two events on the particle’s motion, use the Lorentz transformations to show that

u'=\frac{u-v}{1-uv/c^2}.

[2]

(c)

Use your answers to (a) and (b) to determine $u'/c$ to 2 significant figures.

[1]

Question 3

Paper 2Medium4 marks

A trolley moves at constant velocity in the $+x$ direction relative to the ground. Let $S$ be the ground frame and $S'$ the frame of the trolley. The Galilean transformations are $x'=x-vt$ and $t'=t$ where $v$ is the velocity of $S'$ relative to $S$

(a)

Using the transformations for the positions of an object at two different times, show that its velocity $u'$ measured in $S'$ is related to its velocity $u$ measured in $S$ by $u'=u-v$

[2]

(b)

A puck moves at $+2.5\ \mathrm{m\,s^{-1}}$ relative to the ground while the trolley moves at $+4.0\ \mathrm{m\,s^{-1}}$ relative to the ground. Determine the puck’s velocity relative to the trolley, including its direction.

[2]

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