DP Physics Questionbank

Description

Nature of science:

Pure science: Einstein based his theory of relativity on two postulates and deduced the rest by mathematical analysis. The first postulate integrates all of the laws of physics including the laws of electromagnetism, not only Newton’s laws of mechanics. (1.2)

Understandings:

• The two postulates of special relativity
• Clock synchronization
• The Lorentz transformations
• Velocity addition
• Invariant quantities (spacetime interval, proper time, proper length and rest mass)
• Time dilation
• Length contraction
• The muon decay experiment

Applications and skills:

• Using the Lorentz transformations to describe how different measurements of space and time by two observers can be converted into the measurements observed in either frame of reference
• Using the Lorentz transformation equations to determine the position and time coordinates of various events
• Using the Lorentz transformation equations to show that if two events are simultaneous for one observer but happen at different points in space, then the events are not simultaneous for an observer in a different reference frame
• Solving problems involving velocity addition
• Deriving the time dilation and length contraction equations using the Lorentz equations
• Solving problems involving time dilation and length contraction
• Solving problems involving the muon decay experiment

Guidance:

• Problems will be limited to one dimension
• Derivation of the Lorentz transformation equations will not be examined
• Muon decay experiments can be used as evidence for both time dilation and length contraction

Data booklet reference:

Utilization:

• Once a very esoteric part of physics, relativity ideas about space and time are needed in order to produce accurate global positioning systems (GPS)

Aims:

• Aim 2: the Lorentz transformation formulae provide a consistent body of knowledge that can be used to compare the description of motion by one observer to the description of another observer in relative motion to the first
• Aim 3: these formulae can be applied to a varied set of conditions and situations
• Aim 9: the introduction of relativity pushed the limits of Galilean thoughts on space and motion

Directly related questions

• 18M.3.SL.TZ2.5c: Outline why the observed times are different for A and B.
• 18M.3.SL.TZ2.5b.ii: determine the time between them according to observer B.
• 18M.3.SL.TZ2.5b.i: calculate the spacetime interval.
• 18M.3.SL.TZ2.5a: Explain what is meant by the statement that the spacetime interval is an invariant quantity.
• 18M.3.SL.TZ2.4c: As the spaceship passes the space station, the space station sends a radio signal back to the...
• 18M.3.SL.TZ2.4b: The spaceship passes the space station 90 minutes later as measured by the spaceship clock....
• 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...
• 18M.3.SL.TZ2.3a.ii: Calculate, for the reference frame of rocket A, the speed of rocket B according to the Lorentz...
• 18M.3.SL.TZ1.5d: Calculate the velocity of rocket B relative to rocket A.
• 18M.3.SL.TZ1.5c: Explain whether or not the arrival times of the two flashes in the Earth frame are simultaneous...
• 18M.3.SL.TZ1.4b.ii: Discuss how your result in (b)(i) and the outcome of the muon decay experiment support the theory...
• 18M.3.SL.TZ1.4b.i: Calculate, according to the theory of special relativity, the time taken for a muon to reach the...
• 18M.3.SL.TZ1.3b.i: Discuss the change in d according to observer Y.
• 17N.3.SL.TZ0.5e.ii: Deduce, without further calculation, how the time taken for A to meet B, according to an observer...
• 17N.3.SL.TZ0.5e.i: Determine, according to an observer in A, the time taken for B to meet A.
• 17N.3.SL.TZ0.5d: Determine, according to an observer in A, the velocity of B.
• 17N.3.SL.TZ0.5c: Identify the terms in the formula. u′ = \(\frac{{u - v}}{{1 - \frac{{uv}}{{{c^2}}}}}\)  
• 17N.3.SL.TZ0.5b: Calculate, according to the observer on Earth, the time taken for A and B to meet.
• 17N.3.SL.TZ0.5a: Define frame of reference.
• 17M.3.SL.TZ2.5c.iii: Calculate the value of c 2t 2 – x 2.
• 17M.3.SL.TZ2.5b.ii: which lamp turns on first.
• 17M.3.SL.TZ2.5b.i: the time interval between the lamps turning on.
• 17M.3.SL.TZ2.5a.ii: A space shuttle is released from the rocket. The shuttle moves with speed 0.20c to the right...
• 17M.3.SL.TZ2.5a.i: Calculate the length of the rocket according to X.
• 17M.3.SL.TZ2.4: Muons are unstable particles with a proper lifetime of 2.2 μs. Muons are produced 2.0 km above...
• 17M.3.SL.TZ1.4e: A second train is moving at a velocity of –0.70c with respect to the ground. Calculate the...
• 17M.3.SL.TZ1.4d.iv: Demonstrate that the spacetime interval between events B and F is invariant.
• 17M.3.SL.TZ1.4d.iii: Apply a Lorentz transformation to show that the time difference between events B and F according...
• 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...
• 17M.3.SL.TZ1.4b: Calculate the speed v of the train for the ratio...
• 17M.3.SL.TZ1.4a: State which of the two time intervals is a proper time.
• 16N.3.SL.TZ0.5c: In the pion reference frame, the Earth moves a distance X before the pion decays. In the Earth...
• 16N.3.SL.TZ0.5b: A charged pion decays spontaneously in a time of 26 ns as measured in the frame of reference in...
• 16N.3.SL.TZ0.5a: Define proper length.
• 16M.3.HL.TZ0.5b: The electron is detected at a distance of 0.800 m from the emitting nucleus as measured in the...
• 16M.3.SL.TZ0.5d: Outline why the answer to (c) represents a proper time interval.
• 16M.3.SL.TZ0.5c: For the reference frame of the electron, calculate the time between its emission at the nucleus...
• 16M.3.SL.TZ0.5b: For the reference frame of the laboratory, calculate the time taken for the electron to reach the...
• 16M.3.SL.TZ0.5a: For the reference frame of the electron, calculate the distance travelled by the detector.
• 15M.3.HL.TZ1.14a: An observer at rest relative to Earth observes two spaceships. Each spaceship is moving with a...
• 15M.3.HL.TZ1.14b: The observer on Earth in (a) watches one spaceship as it travels to a distant star at a speed of...
• 15M.3.SL.TZ1.11b: The observer on Earth in (a) watches one spaceship as it travels to a distant star at a speed of...
• 15M.3.SL.TZ1.11a: An observer at rest relative to Earth observes two spaceships. Each spaceship is moving with a...
• 15M.3.SL.TZ2.11a: Determine the time, in years, that it takes the spacecraft to reach the planet according to...
• 15M.3.SL.TZ2.11c: F and B are two flashing lights located at the ends of the space station, as shown. As the...
• 15M.3.SL.TZ2.11b: The spacecraft passes a space station that is at rest relative to the Earth. The proper length of...
• 15N.3.HL.TZ0.12b.i: A light on the base station flashes regularly. According to Suzanne, the light flashes every 3...
• 15N.3.HL.TZ0.12b.ii: While moving away from the base station, Suzanne observes another spacecraft travelling towards...
• 15N.3.HL.TZ0.12c.i: Suzanne’s spacecraft is on a journey to a star. According to Juan, the distance from the base...
• 14M.3.SL.TZ1.8c: Explain which of the time measurements in (b)(i) and (b)(ii) is a proper time interval.
• 14M.3.SL.TZ1.8a: State what is meant by an inertial frame of reference.
• 14M.3.SL.TZ1.8b: A spaceship travels from space station Alpha to space station Zebra at a constant speed of 0.90c...
• 14M.3.SL.TZ1.8d: The spaceship arrives at Zebra and enters an airlock at constant speed. O is an observer at rest...
• 15N.3.SL.TZ0.12b.iv: Using relativistic kinematics, the relative speeds of the two spacecraft is shown to be 0.976c....
• 15N.3.SL.TZ0.12c: Suzanne’s spacecraft is on a journey to a star. According to Juan, the distance from the base...
• 14N.3.HL.TZ0.18b.i: Calculate the average decay time of a muon as observed by an observer on the surface of the Earth.
• 14N.3.HL.TZ0.19a: Calculate the speed of the positron as measured in the frame of reference of the electron.
• 14N.3.HL.TZ0.18a: Deduce that few muons would be expected to arrive at the surface of the Earth if non-relativistic...
• 14N.3.HL.TZ0.18b.ii: Explain, with a calculation, why many muons reach the surface of the Earth before they have decayed.
• 14N.3.SL.TZ0.11a: State and explain the order of arrival of X and Y at the mirrors according to Jaime.
• 14N.3.SL.TZ0.11b: Outline whether the return of X and Y to Daniela are simultaneous according to Jaime.
• 14N.3.SL.TZ0.12a: One of the postulates of special relativity refers to the speed of light. State the other...
• 14M.3.SL.TZ2.10a: State the reason why the time interval between event 1 and event 2 is a proper time interval as...
• 14M.3.SL.TZ2.10c: (i)     Calculate, according to Judy, the distance separating the Earth and planet P. (ii)   ...
• 14M.3.SL.TZ2.10b: (i)     Calculate the time interval between event 1 and event 2 according to Peter. (ii)   ...
• 13M.3.SL.TZ1.10b: At a later time the police spacecraft is alongside Speedy’s spacecraft. The police spacecraft is...
• 13M.3.SL.TZ1.10c: The police spacecraft is travelling at a constant speed of 0.5c relative to Speedy’s frame of...
• 13M.3.HL.TZ1.14b: Officer Sylvester switches on the blue flashing lamps on his police spacecraft. (i) Calculate,...
• 13M.3.HL.TZ2.16a: Show that, if the muons move at non-relativistic speed, the number of muons detected at sea level...
• 13M.3.HL.TZ2.16b: The muons in (a) move toward the surface of Earth with a relativistic speed of 0.968c. (i)...
• 12M.3.SL.TZ1.11a: State and explain whether the pendulum period is a proper time interval for observer T, observer...
• 12M.3.SL.TZ1.11c: Observer T is standing in the middle of a train watched by observer G at the side of the track....
• 12M.3.SL.TZ1.11b: Observer T measures the period of oscillations of the pendulum to be 0.850s. Calculate the period...
• 12M.3.HL.TZ1.11e: Observer G sees a second train moving towards the first train (i.e. towards the left) at a speed...
• 12M.3.HL.TZ1.12a: In an experiment at CERN in 1964, a neutral pion moving at a speed of 0.99975c with respect to...
• 11M.3.HL.TZ2.10d: Carrie and Louise, two observers in a spaceship, view a light source placed close to Carrie. When...
• 11M.3.SL.TZ2.10a: Carrie measures her spaceship to have a length of 100m. Peter measures Carrie’s spaceship to have...
• 11M.3.SL.TZ2.10b: According to Carrie, it takes the star ten years to reach her. Using your answer to (a)(ii),...
• 11M.3.SL.TZ2.10c: According to Peter, as Carrie passes the star she sends a radio signal. Determine the time, as...
• 11N.3.SL.TZ0.9b: In a thought experiment to illustrate the concept of simultaneity, Vladimir is standing on the...
• 11N.3.HL.TZ0.12f: Suggest how your answers to (e)(i) and (e)(ii) provide evidence that supports the theory of...
• 12M.3.SL.TZ2.10b: A rocket moving at a relativistic speed passes an observer who is at rest on the...
• 12N.3.SL.TZ0.12b: (i) Calculate the time interval t between event 1 and event 2 according to an observer in the...
• 12N.3.SL.TZ0.12c: Relative to an observer on the ground, (i) calculate the distance between S and D. (ii) state...
• 11N.3.SL.TZ0.9a: One of the two postulates of special relativity may be stated as: “The laws of physics are the...
• 11N.3.SL.TZ0.9c: The speed v of the carriage is 0.70c. Vladimir measures the length of the table at which Natasha...
• 11N.3.HL.TZ0.12e: Evidence for time dilation comes from the decay of muons. A pulse of muons produced by cosmic...
• 12M.3.SL.TZ2.10a: State the postulate of special relativity that is related to the speed of light.
• 12N.3.SL.TZ0.12a: In the context of the theory of relativity, state what is meant by an event.
• 12M.3.HL.TZ2.14a: Calculate the time it takes the pulse to travel from S to D, according to (i) an observer in the...
• 12M.3.HL.TZ2.14b: Calculate the distance between the source S and the detector D according to observer Q.
• 12M.3.HL.TZ2.14c: A particular nucleus in the pulse decays by emitting an electron in the same direction as that of...
• 12M.3.HL.TZ2.14d: The laboratory observer and observer Q agree that by the time the pulse arrives at D, half of the...
• 12N.3.HL.TZ0.16a: (i) Define the rest mass of a particle. (ii) The rest mass of a particle is said to be an...
• 13N.3.HL.TZ0.12d: Muons are produced in the upper atmosphere of Earth and travel towards the surface of Earth where...
• 13N.3.HL.TZ0.12b: A radio signal is sent to both space stations in (a) from a point midway between them. On receipt...
• 13N.3.SL.TZ0.9b: A radio signal is sent to both space stations in (a) from a point midway between them. On receipt...
• 11M.3.SL.TZ1.11a: Define proper length.
• 11M.3.SL.TZ1.11b: A spaceship is travelling to the right at speed 0.75 c, through a tunnel which is open at both...
• 11M.3.SL.TZ1.11c: Two sources of light are located at each end of the tunnel. The diagram below shows...
• 11M.3.HL.TZ1.17a: Calculate the velocity of rocket 2 relative to the Earth, using the (i) Galilean transformation...
• 11M.3.HL.TZ1.17b: Comment on your answers in (a).
• 10N.3.SL.TZ0.D1d: The time for the pulse to travel from \({{\text{M}}_{\text{2}}}\) to \({{\text{M}}_{\text{1}}}\)...
• 10N.3.SL.TZ0.D1a: On the diagram, sketch the path of the light pulse between \({{\text{M}}_{\text{1}}}\) and...
• 10N.3.SL.TZ0.D1c: State, according to special relativity, the length of the path of the light between...
• 10N.3.HL.TZ0.H1g: The questions (e) and (f ) introduce the concepts of time dilation and length contraction....
• 10N.3.SL.TZ0.D1b: (i)     State, according to Jill, the distance moved by the spaceship in time \(\Delta t\). (ii)...
• 10N.3.SL.TZ0.D1e: According to a clock at rest with respect to Jill, a clock in the spaceship runs slow by a factor...