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.

Type
Multiple choiceWritten
Difficulty
EasyMediumHard

Question 1

Paper 2Medium4 marks

In inertial frame SS a particle moves along the xx-axis as shown in Figure 1. Inertial frame S′S' moves in the +x+x-direction at speed v=0.50cv=0.50c relative to SS The origins of the frames coincide at t=t′=0t=t'=0 Take c=3.00×108 m s−1c=3.00\times10^8\ \mathrm{m\,s^{-1}}

The Lorentz transformations are

x′=γ(x−vt),t′=γ(t−vxc2),γ=11−v2/c2.x'=\gamma(x-vt),\qquad t'=\gamma\left(t-\frac{vx}{c^2}\right), \qquad \gamma=\frac{1}{\sqrt{1-v^2/c^2}}.
01234500.10.20.30.40.50.60.70.80.91t / nsx / m
(a)

Determine u/cu/c for the particle in frame SS

[1]
(b)

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

u′=u−v1−uv/c2.u'=\frac{u-v}{1-uv/c^2}.
[2]
(c)

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

[1]

Question 2

Paper 2Medium4 marks

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

(a)

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

[2]
(b)

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

[2]