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Date November 2018 Marks available 3 Reference code 18N.3.SL.TZ0.5
Level Standard level Paper Paper 3 Time zone 0 - no time zone
Command term Outline Question number 5 Adapted from N/A

Question

The spacetime diagram shows the axes of an inertial reference frame S and the axes of a second inertial reference frame S′ that moves relative to S with speed 0.745c. When clocks in both frames show zero the origins of the two frames coincide.

Event E has coordinates x = 1 m and ct = 0 in frame S. Show that in frame S′ the space coordinate and time coordinate of event E are

A rod at rest in frame S has proper length 1.0 m. At t = 0 the left-hand end of the rod is at x = 0 and the right-hand end is at x = 1.0 m.

x′ = 1.5 m.

[2]
a.i.

ct′ = –1.1 m.

[1]
a.ii.

Label, on the diagram, the space coordinate of event E in the S′ frame. Label this event with the letter P.

[1]
b.i.

Label, on the diagram, the event that has coordinates x′ = 1.0 m and ct′ = 0. Label this event with the letter Q.

[1]
b.ii.

Using the spacetime diagram, outline without calculation, why observers in frame S′ measure the length of the
rod to be less than 1.0 m.

[3]
c.i.

Using the spacetime diagram, estimate, in m, the length of this rod in the S′ frame.

[1]
c.ii.

Markscheme

γ =  « 1 1 0.745 2 = » 1.499 ✔

x′ = « γ ( x v t ) = » 1.499 × (1.0 − 0) ✔

«x′ = 1.5 m»

a.i.

t′ = « γ ( t v x c 2 ) =»  1.499 × ( 0 0.745 c × 1 c 2 ) «= 1.11 c »

«ct′ = –1.1 m»

OR

using spacetime interval 0 − 12 = (ct′)2 − 1.52 ⇒ «ct′ = –1.1» ✔

a.ii.

line through event E parallel to ct′ axis meeting x' axis and labelled P ✔

 

b.i.

point on x' axis about 2 3 of the way to P labelled Q ✔

 

b.ii.

ends of rod must be recorded at the same time in frame S′ ✔

any vertical line from E crossing x’, no label required ✔

right-hand end of rod intersects at R «whose co-ordinate is less than 1.0 m» ✔

 

c.i.

0.7 m ✔

c.ii.

Examiners report

[N/A]
a.i.
[N/A]
a.ii.
[N/A]
b.i.
[N/A]
b.ii.
[N/A]
c.i.
[N/A]
c.ii.

Syllabus sections

Option A: Relativity » Option A: Relativity (Core topics) » A.2 – Lorentz transformations
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Option A: Relativity » Option A: Relativity (Core topics)
Option A: Relativity

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