A lambda Λ⁰ particle at rest decays into a proton p and a pion π⁻ according to the reaction Λ⁰ → p + π⁻ where the rest energy of p = 938 MeV and the rest energy of π⁻ = 140 MeV. The speed of the pion after the decay is 0.579 c. For this speed γ = 1.2265.
Calculate the speed of the proton.
This question is about mass and energy. The positive kaon K+ has a rest mass of 494 MeVc-2.
Using the grid, sketch a graph showing how the energy of the kaon increases with speed.
The kaon is accelerated from rest through a potential difference so that its energy becomes three times its rest energy. Calculate the potential difference through which the kaon was accelerated.
The neutral kaon is unstable and one of its possible modes of decay is K0 → π0 + π0. The π0 has a rest mass of 135 MeVc-2. The K0 has a rest mass of 498 MeVc-2. The K0 is at rest before it decays. The two π0 particles move apart in opposite directions along a straight line. Determine the momentum of one of the π0 particles.
Muons are created at a height of 3230 m above the Earth's surface. The muons move vertically downward at a speed of 0.980 c relative to the Earth's surface. The gamma factor for this speed is 5.00. The half-life of a muon in its rest frame is 2.20 μs.
Estimate in the Earth frame the fraction of the original muons that will reach the Earth's surface before decaying according to Newtonian mechanics.
Estimate in the Earth frame the fraction of the original muons that will reach the Earth's surface before decaying according to special relativity.
Demonstrate how an observer moving with the same velocity as the muons accounts for the answer to (ii).
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 with total energy 1.50 MeV collides with a positron at rest. As a result two photons are produced. One photon moves in the same direction as the electron and the other in the opposite direction.
Show that the momentum of the electron is 1.41 MeV c^(-1).
The momenta of the photons produced have magnitudes p₁ and p₂. A student writes the following correct equations.
p₁ - p₂ = 1.41 MeV c^(-1) p₁ + p₂ = 2.01 MeV c^(-1)
Explain the origin of each equation.
The momenta of the photons produced have magnitudes p₁ and p₂. A student writes the following correct equations.
p₁ - p₂ = 1.41 MeV c^(-1) p₁ + p₂ = 2.01 MeV c^(-1)
Calculate, in MeV c^(-1), p₁ and p₂.
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.
A proton has a total energy 1050 MeV after being accelerated from rest through a potential difference V.
Define total energy.
Determine the momentum of the proton.
Determine the speed of the proton.
Calculate the potential difference V.
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.
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.