| Date | May 2019 | Marks available | 1 | Reference code | 19M.3.SL.TZ2.4 |
| Level | Standard level | Paper | Paper 3 | Time zone | 2 |
| Command term | Calculate | Question number | 4 | Adapted from | N/A |
Question
The speed of a spaceship is measured to be 0.50c by an observer at rest in the Earth’s reference frame.
Define an inertial reference frame.
As the spaceship passes the Earth it emits a flash of light that travels in the same direction as the spaceship with speed c as measured by an observer on the spaceship. Calculate, according to the Galilean transformation, the speed of the light in the Earth’s reference frame.
Use your answer to (a)(ii) to describe the paradigm shift that Einstein’s theory of special relativity produced.
Markscheme
a coordinate system which is not accelerating/has constant velocity/Newtons 1st law applies ✔
OWTTE
Both “inertial” and “reference frame” need to be defined
1.5c ✔
c is the same in all frames
OR
c is maximum velocity possible ✔
velocity addition frame dependent ✔
length/time/mass/fields relative measurements ✔
Newtonian/Galilean mechanics valid only at low speed ✔
Examiners report
In defining an inertial frame of reference far too many candidates started with the words ‘ a frame of reference that...... ’ instead of ‘a coordinate system that.....’
Almost no incorrect answers were seen.
Most candidates correctly stated that in special relativity the velocity of light, c, is the maximum possible velocity or is invariant. Only a few added that Galilean relativity only applies at speeds much less than the speed of light.
Syllabus sections
- 17N.3.SL.TZ0.4: Outline the conclusion from Maxwell’s work on electromagnetism that led to one of...
- 19M.3.SL.TZ1.3b: State the speed of the flash of light according to an observer on the ground using Maxwell’s...
- 19M.3.SL.TZ1.3a: State the speed of the flash of light according to an observer on the ground using Galilean...
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18M.3.SL.TZ1.4a.i:
Calculate, according to Galilean relativity, the time taken for a muon to travel to the ground.
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18M.3.SL.TZ2.3a.i:
Calculate, for the reference frame of rocket A, the speed of rocket B according to the Galilean transformation.
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17M.3.SL.TZ2.3b:
A current is established in a long straight wire that is at rest in a laboratory.
A proton is at rest relative to the laboratory and the wire.
Observer X is at rest in the laboratory. Observer Y moves to the right with constant speed relative to the laboratory. Compare and contrast how observer X and observer Y account for any non-gravitational forces on the proton.
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17M.3.SL.TZ2.3a:
State one prediction of Maxwell’s theory of electromagnetism that is consistent with special relativity.
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18N.3.SL.TZ0.4b.i:
Determine the time it takes the probe to reach the front of the rocket according to an observer at rest in the rocket.
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18N.3.SL.TZ0.3b.ii:
hence show that the space coordinate of E in frame S is .
- 18N.3.SL.TZ0.3a: State what is meant by a reference frame.
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18M.3.SL.TZ1.3b.ii:
Deduce whether the overall field around the wire is electric, magnetic or a combination of both according to observer Y.
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17M.3.SL.TZ1.3a:
State what is meant by a reference frame.
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17M.3.SL.TZ1.3b.ii:
State and explain whether the force experienced by P is magnetic, electric or both, in the rest frame of P.
- 16N.3.SL.TZ0.4a: Define frame of reference.
- 19N.3.SL.TZ0.3b(i): State the nature of the force on the particle P in the reference frame of the laboratory.
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19N.3.SL.TZ0.3b(ii):
Deduce, using your answer to part (a), the nature of the force that acts on the particle P in the rest frame of P.
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19N.3.SL.TZ0.3b(iii):
Explain how the force in part (b)(ii) arises.
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17M.3.SL.TZ1.3b.i:
State and explain whether the force experienced by P is magnetic, electric or both, in reference frame S.
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19M.3.SL.TZ1.4a.i:
Estimate in the Earth frame the fraction of the original muons that will reach the Earth’s surface before decaying according to Newtonian mechanics.
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18M.3.SL.TZ1.3a:
State whether the field around the wire according to observer X is electric, magnetic or a combination of both.
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18N.3.SL.TZ0.3b.i:
explain why the time coordinate of E in frame S is .
- 20N.3.SL.TZ0.3b: State a postulate that is the same for both special relativity and Galilean relativity.
- 20N.3.SL.TZ0.3c(i): Identify the nature of the attractive force recorded by an observer stationary with respect...
- 20N.3.SL.TZ0.4a: The Lorentz transformations assume that the speed of light is constant. Outline what the...
- 20N.3.SL.TZ0.3a: Maxwell’s equations led to the constancy of the speed of light. Identify what Maxwell’s...
- 20N.3.SL.TZ0.3c(ii): A second observer moves at the drift velocity of the electron current in the wires. Discuss...
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16N.3.SL.TZ0.4b:
In the reference frame of the laboratory the force on X is magnetic.
(i) State the nature of the force acting on X in this reference frame where X is at rest.
(ii) Explain how this force arises.
- 19M.3.SL.TZ2.5b: Explain why there is no magnetic force on each proton in its own rest frame.
- 19M.3.SL.TZ2.5c: Explain why there must be a resultant repulsive force on the protons in all reference frames.
- 19M.3.SL.TZ2.4ai: Define an inertial reference frame.
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19M.3.SL.TZ2.4b:
Use your answer to (a)(ii) to describe the paradigm shift that Einstein’s theory of special relativity produced.
- 19M.3.SL.TZ2.5a: Outline why there is an attractive magnetic force on each proton in the laboratory frame.
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18M.3.SL.TZ1.4a.ii:
Deduce why only a small fraction of the total number of muons created is expected to be detected at ground level according to Galilean relativity.
