Rocket A and rocket B are travelling in opposite directions from the Earth along the same straight line.
In the reference frame of the Earth, the speed of rocket A is 0.75c and the speed of rocket B is 0.50c.
a.i.Calculate, for the reference frame of rocket A, the speed of rocket B according to the Galilean transformation.[1]
▶️Answer/Explanation
Markscheme
a.i.
1.25c
[1 mark]
ALTERNATIVE 1
\(u’ = \frac{{(0.50 + 0.75)}}{{1 + 0.5 \times 0.75}}c\)
0.91c
ALTERNATIVE 2
\(u’ = \frac{{ – 0.50 – 0.75}}{{1 – ( – 0.5 \times 0.75)}}c\)
–0.91c
[2 marks]
nothing can travel faster than the speed of light (therefore (a)(ii) is the valid answer)
OWTTE
[1 mark]
Muons are created in the upper atmosphere of the Earth at an altitude of 10 km above the surface. The muons travel vertically down at a speed of 0.995c with respect to the Earth. When measured at rest the average lifetime of the muons is 2.1 μs.
a.i.
Calculate, according to Galilean relativity, the time taken for a muon to travel to the ground[1]
Discuss how your resultin (b)(i) and the outcome of the muon decay experiment support the theory of special relativity.[2]
▶️Answer/Explanation
Markscheme
a.i.
«\(\frac{{{{10}^4}}}{{0.995 \times 3 \times {{10}^8}}} = \)» 34 «μs»
Do not accept 104/c = 33 μs.
[1 mark]
time is much longer than 10 times the average life time «so only a small proportion would not decay»
[1 mark]
\(\gamma = 10\)
\(\Delta {t_0} = \) «\(\frac{{\Delta t}}{\gamma } = \frac{{34}}{{10}} = \)» 3.4 «μs»
[2 marks]
the value found in (b)(i) is of similar magnitude to average life time
significant number of muons are observed on the ground
«therefore this supports the special theory»
[2 marks]
The diagram shows the motion of the electrons in a metal wire carrying an electric current as seen by an observer X at rest with respect to the wire. The distance between adjacent positive charges is d.
Observer Y is at rest with respect to the electrons.
a.State whether the field around the wire according to observer X is electric, magnetic or a combination of both[1]
▶️Answer/Explanation
Markscheme
a.
magnetic field
[1 mark]
«according to Y» the positive charges are moving «to the right»
d decreases
For MP1, movement of positive charges must be mentioned explicitly.
[2 marks]
positive charges are moving, so there is a magnetic field
the density of positive charges is higher than that of negative charges, so there is an electric field
The reason must be given for each point to be awarded.
[2 marks]
Outline the conclusion from Maxwell’s work on electromagnetism that led to one of the postulates of special relativity.
▶️Answer/Explanation
Markscheme
light is an EM wave
speed of light is independent of the source/observer
a.State one prediction of Maxwell’s theory of electromagnetism that is consistent with special relativity.[1]
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.[3]
▶️Answer/Explanation
Markscheme
a.
the speed of light is a universal constant/invariant
OR
c does not depend on velocity of source/observer
electric and magnetic fields/forces unified/frame of reference dependant
[1 mark]
observer X will measure zero «magnetic or electric» force
observer Y must measure both electric and magnetic forces
which must be equal and opposite so that observer Y also measures zero force
Allow [2 max] for a comment that both X and Y measure zero resultant force even if no valid explanation is given.
[3 marks]
A long current-carrying wire is at rest in the reference frame S of the laboratory. A positively charged particle P outside the wire moves with velocity v relative to S. The electrons making up the current in the wire move with the same velocity v relative to S.
a.
State what is meant by a reference frame.[1]
▶️Answer/Explanation
Markscheme
a.
a set of coordinate axes and clocks used to measure the position «in space/time of an object at a particular time»
OR
a coordinate system to measure x,y,z, and t / OWTTE
[1 mark]
magnetic only
there is a current but no «net» charge «in the wire»
[2 marks]
electric only
P is stationary so experiences no magnetic force
relativistic contraction will increase the density of protons in the wire
[3 marks]
An electron X is moving parallel to a current-carrying wire. The positive ions and the wire are fixed in the reference frame of the laboratory. The drift speed of the free electrons in the wire is the same as the speed of the external electron X.
a.Define frame of reference.[1]
(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.[4]
▶️Answer/Explanation
Markscheme
a.
a coordinate system
OR
a system of clocks and measures providing time and position relative to an observer
OWTTE
i
electric
OR
electrostatic
ii
«as the positive ions are moving with respect to the charge,» there is a length contraction
therefore the charge density on ions is larger than on electrons
so net positive charge on wire attracts X
For candidates who clearly interpret the question to mean that X is now at rest in the Earth frame accept this alternative MS for bii
the magnetic force on a charge exists only if the charge is moving
an electric force on X , if stationary, only exists if it is in an electric field
no electric field exists in the Earth frame due to the wire
and look back at b i, and award mark for there is no electric or magnetic force on X
Two protons are moving with the same velocity in a particle accelerator.
Observer X is at rest relative to the accelerator. Observer Y is at rest relative to the protons.
Explain the nature of the force between the protons as observed by observer X and observer Y.
▶️Answer/Explanation
Markscheme
Y measures electrostatic repulsion only
protons are moving relative to X «but not Y» OR protons are stationary relative to Y
moving protons create magnetic fields around them according to X
X also measures an attractive magnetic force OR relativistic/Lorentz effects also present
One of the postulates of special relativity states that the laws of physics are the same in all inertial frames of reference.
a.State what is meant by inertial in this context.[1]
(i) Maxwell’s theory.
(ii) Galilean transformation.[2]
▶️Answer/Explanation
Markscheme
a.
not being accelerated
OR
not subject to an unbalanced force
OR
where Newton’s laws apply
(i) c
(ii) c+v
This question is about relativistic kinematics.
A spacecraft is flying in a straight line above a base station at a speed of 0.8c.
Suzanne is inside the spacecraft and Juan is on the base station.
Suzanne’s spacecraft is on a journey to a star. According to Juan, the distance from the base station to the star is 11.4 ly. Show that Suzanne measures the time taken for her to travel from the base station to the star to be about 9 years.[2]
▶️Answer/Explanation
Markscheme
1.6c;
(one of the) postulates states that the speed of light in a vacuum is the same for all inertial observers;
Galilean transformation will give a relative speed greater than the speed of light;
\(\gamma = \frac{1}{{\sqrt {1 – {{0.976}^2}} }}{\text{ }}( = 4.59)\);
\({l_0} = (4.56 \times 8.00 = ){\text{ 36.7 (m)}}\);
Note: the final answer for SP3 is different to the HP3.
\(t = \frac{s}{v} = \frac{{11.4}}{{0.8}} = 14.25{\text{ (years)}}\);
\(\Delta {t_0} = \frac{{\Delta t}}{\gamma } = \frac{{14.25}}{{1.67}} = 8.6{\text{ (years)}}\);
Allow ECF from (b).
Accept length contraction with the same result.
Examiners report
Only HL Questions 12(a), (b)(i) and (c) were common with SL questions 12(a), (b)(i) and (c). Many did not address “frame of reference”, only explaining “inertial”. Most could identify the postulate relevant to Galilean transformations but few could earn full marks. The calculation was well done by those who attempted the question.
Only HL Questions 12(a), (b)(i) and (c) were common with SL questions 12(a), (b)(i) and (c). Many did not address “frame of reference”, only explaining “inertial”. Most could identify the postulate relevant to Galilean transformations but few could earn full marks. The calculation was well done by those who attempted the question.
Only HL Questions 12(a), (b)(i) and (c) were common with SL questions 12(a), (b)(i) and (c). Many did not address “frame of reference”, only explaining “inertial”. Most could identify the postulate relevant to Galilean transformations but few could earn full marks. The calculation was well done by those who attempted the question.
Only HL Questions 12(a), (b)(i) and (c) were common with SL questions 12(a), (b)(i) and (c). Many did not address “frame of reference”, only explaining “inertial”. Most could identify the postulate relevant to Galilean transformations but few could earn full marks. The calculation was well done by those who attempted the question.
This question is about relativistic kinematics.
Speedy is in a spacecraft being chased by Police Officer Sylvester. In Officer Sylvester’s frame of reference, Speedy is moving directly towards Officer Sylvester at 0.25c.
a.Describe what is meant by a frame of reference.[2]
Officer Sylvester is at a point midway between the flashing lamps, both of which he can see. At the instant when Officer Sylvester and Speedy are opposite each other, Speedy observes that the blue lamps flash simultaneously.
State and explain which lamp is observed to flash first by Officer Sylvester.[4]
the light to return to the source as 1.2 × 10–8s.
(i) Outline why the time interval measured by Officer Sylvester is a proper time interval.
(ii) Determine, as observed by Speedy, the time taken for the light to travel across the police spacecraft and back to its source. [4]
▶️Answer/Explanation
Markscheme
a.
a coordinate system / set of rulers / clocks;
in which measurements of distance/position and time can be made;
light travels at same speed for both observers;
during transit time Officer Sylvester moves towards point of emission at front/away from point of emission at back;
light from front arrives first as distance is less / light from back arrives later as distance is more;
Officer Sylvester observes the front lamp flashes first;
Award [0] for a bald correct answer without correct explanation
(i) the two events occur at the same place (in the same frame of reference) / shortest measured time;
(ii) \(y = \left( {\frac{1}{{\sqrt {1 – \frac{{{v^2}}}{{{c^2}}}} }} = } \right)1.15\);
Δt=1.15 x Δt0;
1.48 x 10-8(s);
This question is about time dilation.
Two space stations X and Y are at rest relative to each other. The separation of X and Y as measured in their frame of reference is 1.80×1011m.
a.State what is meant by a frame of reference.[1]
(i) Calculate the time interval, as measured by the clock in X, that it takes S to travel from X to Y.
(ii) Calculate the time interval, as measured by the clock in S, that it takes S to travel from X to Y.
(iii) Explain whether the clock in X or the clock in S measures the proper time.
(iv) Explain why, according to S, the setting of the clock in X and the setting of the clock in Y does not occur simultaneously.[9]
▶️Answer/Explanation
Markscheme
a.
a set of coordinates that can be used to locate events/position of objects;
(i) \(\frac{{1.80 \times {{10}^{11}}}}{{0.750 \times 3 \times {{10}^8}}}\);
=800(s);
Award [2] for a bald correct answer.
(ii) \(\gamma = \left( {\frac{1}{{\sqrt {1 – {{0.750}^2}} }} = } \right)1.51\);
\({\rm{time}} = \left( {\frac{{800}}{{1.51}} = } \right)530\left( {\rm{s}} \right)\);
Watch for ECF from (b)(i) or first marking point in (b)(ii).
Award [2] for a bald correct answer.
(iii) only S’s clock measures proper time;
because S’s clock is at both events / events occur at same place in S’s frame;
(iv) according to S, Y moves towards/X moves away from the radio signal;
the signal travels at the same speed/at the speed of light in each direction;
therefore according to S’s clock the signal reaches Y before it reaches X/X after reaching Y;
or
S’s frame is different/moving relative to the X and Y frame;
the two events/arrival of signals are separated in space;
so if simultaneous for XY, cannot be simultaneous for S;