| Date | May 2019 | Marks available | 1 | Reference code | 19M.3.SL.TZ2.7 |
| Level | Standard level | Paper | Paper 3 | Time zone | 2 |
| Command term | Determine | Question number | 7 | Adapted from | N/A |
Question
A spaceship moves away from the Earth in the direction of a nearby planet. An observer on the Earth determines the planet is 4 ly from the Earth. The spacetime diagram for the Earth’s reference frame shows the worldline of the spaceship. Assume the clock on the Earth, the clock on the planet, and the clock on the spaceship were all synchronized when ct = 0.
Show, using the spacetime diagram, that the speed of the spaceship relative to the Earth is 0.80c.
Label, with the letter E, the event of the spaceship going past the planet.
Determine, according to an observer on the spaceship as the spaceship passes the planet, the time shown by the clock on the spaceship.
Determine, according to an observer on the spaceship as the spaceship passes the planet, the time shown by the clock on the planet.
On passing the planet a probe containing the spaceship’s clock and an astronaut is sent back to Earth at a speed of 0.80c relative to Earth. Suggest, for this situation, how the twin paradox arises and how it is resolved.
Markscheme
Evidence of finding 1/gradient such as:
use of any correct coordinate pair to find v - eg or .
OR
measures tan of angle between ct and ct’ as about 39° AND tan 39 ≈ 0.8 ✔
Answer 0.8c given, so check coordinate values carefully.
E labelled at = 4, ct = 5 ✔
Check that E is placed on the worldline of S.
OR
Allow solutions involving the use of Lorentz equations.
t = 5 years OR ct = 5 ly ✔
On return to Earth the astronaut will have aged less than Earthlings «by 4 years»
OR
time passed on Earth is greater than time passed for the astronaut «by 4 years» ✔
astronaut accelerated/changed frames but Earth did not
OR
for astronaut the Earth clock jumps forward at turn-around ✔
OWTTE
Treat as neutral any mention of both the Earth and astronaut seeing each other’s clock as running slow.
Examiners report
Most candidates could show that the velocity of the spacecraft was 0.8c.
Event E was usually correctly labelled on the space-time diagram.
A very simple time dilation question which most candidates got wrong at SL but the question was better answered at HL.
Many candidates tried to use time dilation again without realising that the clock on P must also read 5 years at event E because that is the time on the Earth clock in P’s frame for the event.
The twin paradox is now well understood and there were some good quality answers. Some candidates even knew that the Earth clock jumps forward when the Astronaut turns around.
Syllabus sections
- 17N.3.SL.TZ0.5e.ii: Deduce, without further calculation, how the time taken for A to meet B, according to an...
- 19M.3.SL.TZ1.3c: State the speed of the flash of light according to an observer on the ground using Einstein’s...
-
18M.3.SL.TZ2.4a:
Calculate the velocity of the spaceship relative to the Earth.
-
18M.3.SL.TZ2.3b:
Outline, with reference to special relativity, which of your calculations in (a) is more likely to be valid.
-
18M.3.SL.TZ2.5a:
Explain what is meant by the statement that the spacetime interval is an invariant quantity.
- 19N.3.SL.TZ0.3a: One of the two postulates of special relativity states that the speed of light in a vacuum is...
-
18M.3.SL.TZ1.3b.i:
Discuss the change in d according to observer Y.
-
18M.3.SL.TZ1.4b.ii:
Discuss how your result in (b)(i) and the outcome of the muon decay experiment support the theory of special relativity.
-
18M.3.SL.TZ1.5c:
Explain whether or not the arrival times of the two flashes in the Earth frame are simultaneous events in the frame of rocket A.
-
18M.3.SL.TZ1.5d:
Calculate the velocity of rocket B relative to rocket A.
- 18N.3.SL.TZ0.5c.i: Using the spacetime diagram, outline without calculation, why observers in frame S′ measure...
-
18N.3.SL.TZ0.4a:
Calculate the speed of the probe relative to the ground.
-
18N.3.SL.TZ0.4b.ii:
Determine the time it takes the probe to reach the front of the rocket according to an observer at rest on the ground.
- 18N.3.SL.TZ0.5c.ii: Using the spacetime diagram, estimate, in m, the length of this rod in the S′ frame.
-
18N.3.SL.TZ0.5a.ii:
ct′ = –1.1 m.
- 19M.3.SL.TZ2.6a: Define proper length.
-
18M.3.SL.TZ2.3a.ii:
Calculate, for the reference frame of rocket A, the speed of rocket B according to the Lorentz transformation.
-
18M.3.SL.TZ2.4b:
The spaceship passes the space station 90 minutes later as measured by the spaceship clock. Determine, for the reference frame of the Earth, the distance between the Earth and the space station.
-
18M.3.SL.TZ2.5b.ii:
determine the time between them according to observer B.
- 17N.3.SL.TZ0.5b: Calculate, according to the observer on Earth, the time taken for A and B to meet.
-
19M.3.SL.TZ1.4b:
Demonstrate how an observer moving with the same velocity as the muons accounts for the answer to (a)(ii).
-
19M.3.SL.TZ1.5c:
Show that the value of the invariant spacetime interval between events 1 and 2 is 9600 ly2.
- 16N.3.SL.TZ0.5c: In the pion reference frame, the Earth moves a distance X before the pion decays. In the...
-
17M.3.SL.TZ2.5b.ii:
which lamp turns on first.
- 16N.3.SL.TZ0.5a: Define proper length.
-
18M.3.SL.TZ1.4b.i:
Calculate, according to the theory of special relativity, the time taken for a muon to reach the ground in the reference frame of the muon.
- 17N.3.SL.TZ0.5a: Define frame of reference.
- 19M.3.SL.TZ2.6bi: In the reference frame of the train a ball travels with speed 0.50c from the back to the...
-
19N.3.SL.TZ0.3b(iii):
Explain how the force in part (b)(ii) arises.
-
19N.3.SL.TZ0.4a(i):
Calculate, for observer A, the length LA of the bridge
-
17N.3.SL.TZ0.5d:
Determine, according to an observer in A, the velocity of B.
-
17M.3.SL.TZ1.4c:
Later the train is travelling at a speed of 0.60c. Observer P measures the length of the train to be 125 m. The train enters a tunnel of length 100 m according to observer Q.
Show that the length of the train according to observer Q is 100 m.
-
17M.3.SL.TZ1.4e:
A second train is moving at a velocity of –0.70c with respect to the ground.
Calculate the speed of the second train relative to observer P.
- 19N.3.SL.TZ0.4b: Outline why LB is the proper length of the bridge.
-
16N.3.SL.TZ0.5b:
A charged pion decays spontaneously in a time of 26 ns as measured in the frame of reference in which it is stationary. The pion moves with a velocity of 0.96c relative to the Earth. Calculate the pion’s lifetime as measured by an observer on the Earth.
-
17M.3.SL.TZ1.4a:
State which of the two time intervals is a proper time.
-
17M.3.SL.TZ2.5a.i:
Calculate the length of the rocket according to X.
-
19N.3.SL.TZ0.3b(iv):
The velocity of P is 0.30c relative to the laboratory. A second particle Q moves at a velocity of 0.80c relative to the laboratory.
Calculate the speed of Q relative to P.
-
19N.3.SL.TZ0.4c(iv):
Determine the time, according to observer A, between X and Y.
-
18M.3.SL.TZ2.4c:
As the spaceship passes the space station, the space station sends a radio signal back to the Earth. The reception of this signal at the Earth is event A. Determine the time on the Earth clock when event A occurs.
-
18M.3.SL.TZ2.5b.i:
calculate the spacetime interval.
-
18M.3.SL.TZ2.5c:
Outline why the observed times are different for A and B.
-
19M.3.SL.TZ1.4a.ii:
Estimate in the Earth frame the fraction of the original muons that will reach the Earth’s surface before decaying according to special relativity.
-
18N.3.SL.TZ0.5a.i:
x′ = 1.5 m.
-
19N.3.SL.TZ0.4a(ii):
Calculate, for observer A, the time taken to cross the bridge.
- 20N.3.SL.TZ0.3b: State a postulate that is the same for both special relativity and Galilean relativity.
-
20N.3.SL.TZ0.4b(ii):
Explain which of the lengths is the proper length.
-
20N.3.SL.TZ0.4c:
Calculate the speed of the probe in terms of , relative to Earth.
-
20N.1.SL.TZ0.4c:
Calculate the speed of the probe in terms of , relative to Earth.
-
20N.3.SL.TZ0.4b(i):
Deduce the length of the probe as measured by an observer in the spaceship.
-
17N.3.SL.TZ0.5e.i:
Determine, according to an observer in A, the time taken for B to meet A.
-
17N.3.SL.TZ0.5c:
Identify the terms in the formula.
u′ =
- 19M.3.SL.TZ2.7ci: Determine, according to an observer on the spaceship as the spaceship passes the planet, the...
- 19M.3.SL.TZ2.6bii: In the reference frame of the train a ball travels with speed 0.50c from the back to the...
-
17M.3.SL.TZ2.5c.iii:
Calculate the value of c 2t 2 – x 2.
-
17M.3.SL.TZ1.4b:
Calculate the speed v of the train for the ratio .
-
17M.3.SL.TZ1.4d.iii:
Apply a Lorentz transformation to show that the time difference between events B and F according to observer P is 2.5 × 10–7 s.
-
17M.3.SL.TZ2.5b.i:
the time interval between the lamps turning on.
-
17M.3.SL.TZ1.4d.iv:
Demonstrate that the spacetime interval between events B and F is invariant.
-
17M.3.SL.TZ2.4:
Muons are unstable particles with a proper lifetime of 2.2 μs. Muons are produced 2.0 km above ground and move downwards at a speed of 0.98c relative to the ground. For this speed = 5.0. Discuss, with suitable calculations, how this experiment provides evidence for time dilation.
-
17M.3.SL.TZ2.5a.ii:
A space shuttle is released from the rocket. The shuttle moves with speed 0.20c to the right according to X. Calculate the velocity of the shuttle relative to the rocket.
