A rocket moving with speed v relative to the ground emits a flash of light in the backward direction. An observer in the rocket measures the speed of the flash of light to be c.
State the speed of the flash of light according to an observer on the ground using Galilean relativity.
State the speed of the flash of light according to an observer on the ground using Maxwell's theory of electromagnetism.
State the speed of the flash of light according to an observer on the ground using Einstein's theory of relativity.
An astronaut is orbiting Earth in a spaceship. Why does the astronaut experience weightlessness?
This question is about relativistic mechanics. A rho meson (ρ) decays at rest in a laboratory into a pion (π+) and an anti-pion (π−) according to ρ → π+ + π− The rest masses of the particles involved are: m_π+ = m_π− = 140 MeV c^−2 m_ρ = 770 MeV c^−2
Show that the initial momentum of the pion is 360 MeV c^−1.
Show that the speed of the pion relative to the laboratory is 0.932 c.
Calculate, in MeV c^−2, the mass that has been converted into energy in this decay.
The pion (π+) emits a muon in the same direction as the velocity of the pion. The speed of the muon is 0.271 c relative to the pion. Calculate the speed of the muon relative to the laboratory.
An electron is emitted from a nucleus with a total energy of 2.30 MeV as observed in a laboratory.
Show that the speed of the electron is about 0.98c.
The electron is detected at a distance of 0.800 m from the emitting nucleus as measured in the laboratory.
For the reference frame of the electron, calculate the distance travelled by the detector.
For the reference frame of the laboratory, calculate the time taken for the electron to reach the detector after its emission from the nucleus.
For the reference frame of the electron, calculate the time between its emission at the nucleus and its detection.
Outline why the answer to (iii) represents a proper time interval.
This question is about relativistic kinematics. The diagram shows a spaceship as it moves past Earth on its way to a planet P. The planet is at rest relative to Earth. The distance between the Earth and planet P is 12 ly as measured by observers on Earth. The spaceship moves with speed 0.60 c relative to Earth. Consider two events: Event 1: when the spaceship is above Earth Event 2: when the spaceship is above planet P Judy is in the spaceship and Peter is at rest on Earth.
State the reason why the time interval between event 1 and event 2 is a proper time interval as measured by Judy.
Calculate the time interval between event 1 and event 2 according to Peter.
Calculate the time interval between event 1 and event 2 according to Judy.
Judy considers herself to be at rest. According to Judy, the Earth and planet P are moving to the left.
Calculate, according to Judy, the distance separating the Earth and planet P.
Using your answers to (ii) and (c)(i), determine the speed of planet P relative to the spaceship.
Comment on your answer to (ii).
At a point half-way between the Earth and planet P, the spaceship passes a space station that is at rest relative to the Earth and planet P. At that instant, radio signals are sent towards the spaceship from the Earth and planet P. The signals are emitted simultaneously according to an observer S at rest on the space station.
Determine, according to Judy in the spaceship, which signal is emitted first.
On reaching planet P, the spaceship circles the planet and begins the return trip back to Earth. This situation leads to the twin paradox.
Describe what is meant by the term twin paradox.
Suggest how this paradox is resolved.
Outline what is meant by escape speed.
A probe is launched vertically upwards from the surface of a planet with a speed
v = ¾ v_esc
where v_esc is the escape speed from the planet. The planet has no atmosphere.
Determine, in terms of the radius of the planet R, the maximum height from the surface of the planet reached by the probe.
The total energy of a probe in orbit around a planet of mass M is E = -GMm/2r where m is the mass of the probe and r is the orbit radius. A probe in low orbit experiences a small frictional force. Suggest the effect of this force on the speed of the probe.
The de Broglie wavelength associated with a car moving with a speed of is of the order of
This question is about kinematics. The graph shows how the acceleration a of a particle varies with time t. At time t=0 the instantaneous speed of the particle is zero.
State the difference between average speed and instantaneous speed.
Calculate the instantaneous speed of the particle at t=7.5 s.
Using the axes below, sketch a graph to show how the instantaneous speed v of the particle varies with t.
One of the two postulates of special relativity states that the speed of light in a vacuum is the same for all observers in inertial reference frames. State the other postulate of special relativity.
A long straight current-carrying wire is at rest in a laboratory. A negatively-charged particle P outside the wire moves parallel to the current with constant velocity v relative to the laboratory. In the reference frame of the laboratory the particle P experiences a repulsive force away from the wire. State the nature of the force on the particle P in the reference frame of the laboratory.
Deduce, using your answer to part , the nature of the force that acts on the particle P in the rest frame of P.
Explain how the force in part (ii) arises.
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.
This question is about relativistic momentum and energy. An electron and a positron travel towards each other in a straight line in a vacuum. A positron is a positively charged electron. The speed of each particle, as measured by an observer in the laboratory, is 0.85 c . The value of the Lorentz factor at this speed is approximately 1.9.
Calculate the speed of the positron as measured in the frame of reference of the electron.
The electron and positron annihilate each other, creating two photons in the process. Each of the photons transfers the same quantity of energy.
Calculate the total energy in the reaction.
Outline why two photons must be released in this collision.
Determine the frequency of one of the photons.