State one prediction of Maxwell's theory of electromagnetism that is consistent with special relativity.
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.
A rocket of proper length 450 m is approaching a space station whose proper length is 9.0 km. The speed of the rocket relative to the space station is 0.80 c. (not to scale) X is an observer at rest in the space station.
Calculate the length of the rocket according to X.
A space shuttle is released from the rocket. The shuttle moves with speed 0.20 c to the right according to X. Calculate the velocity of the shuttle relative to the rocket.
Two lamps at opposite ends of the space station turn on at the same time according to X. Using a Lorentz transformation, determine, according to an observer at rest in the rocket, the time interval between the lamps turning on.
Two lamps at opposite ends of the space station turn on at the same time according to X. Using a Lorentz transformation, determine, according to an observer at rest in the rocket, which lamp turns on first.
The rocket carries a different lamp. Event 1 is the flash of the rocket's lamp occurring at the origin of both reference frames. Event 2 is the flash of the rocket's lamp at time ct'=1.0 m according to the rocket. The coordinates for event 2 for observers in the space station are x and ct.
On the diagram label the coordinates x and ct.
State and explain whether the ct coordinate in (i) is less than, equal to or greater than 1.0 m.
Calculate the value of c²t² - x².
Define proper length.
A charged pion decays spontaneously in a time of 26 ns as measured in the frame of reference in which it is stationary. The pion moves with a velocity of 0.96 c relative to the Earth. Calculate the pion's lifetime as measured by an observer on the Earth.
In the pion reference frame, the Earth moves a distance X before the pion decays. In the Earth reference frame, the pion moves a distance Y before the pion decays. Demonstrate, with calculations, how length contraction applies to this situation.
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.
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.
Two rockets, A and B, are moving towards each other on the same path. From the frame of reference of the Earth, an observer measures the speed of A to be 0.6c and the speed of B to be 0.4c. According to the observer on Earth, the distance between A and B is 6.0 × 10^8 m.
Define frame of reference.
Calculate, according to the observer on Earth, the time taken for A and B to meet.
Identify the terms in the formula.
Determine, according to an observer in A, the velocity of B.
Determine, according to an observer in A, the time taken for B to meet A.
Deduce, without further calculation, how the time taken for A to meet B, according to an observer in B, compares with the time taken for the same event according to an observer in A.
This question is about kinematics.
Fiona drops a stone from rest vertically down a water well. She hears the splash of the stone striking the water 1.6 s after the stone leaves her hand. Estimate the distance between Fiona's hand and the water surface.
Estimate the speed with which the stone hits the water.
After the stone in hits the water surface it rapidly reaches a terminal speed as it falls through the water. The stone leaves Fiona's hand at time t=0. It hits the water surface at t₁ and it comes to rest at the bottom of the water at t₂. Using the axes below, sketch a graph to show how the speed v of the stone varies from time t=0 to just before t=t₂. (There is no need to add any values to the axes.)
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.
A lambda Λ^0 particle at rest decays into a proton p and a pion π^- according to the reaction Λ^0 → 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 0.579c. For this speed γ = 1.2265.
Calculate the speed of the proton.
The diagram shows the axes for two inertial reference frames. Frame S represents the ground and frame S' is a box that moves to the right relative to S with speed v.
State what is meant by a reference frame.
When the origins of the two frames coincide all clocks show zero. At that instant a beam of light of speed c is emitted from the left wall of the box towards the right wall. The box has proper length L. Consider the event E = light arrives at the right wall of the box.
Using Galilean relativity,
explain why the time coordinate of E in frame S is t = L/c.
hence show that the space coordinate of E in frame S is x = L + vL/c.