Unit 4 Topic 1: Special relativity

Which of the following is an inertial frame of reference?

Which statement correctly gives one of the two postulates of special relativity?

A spacecraft travels directly towards Earth at 0.50c and fires a laser pulse forwards, towards Earth. At what speed does an observer on Earth measure the pulse to travel?

A bus on Ipswich Road brakes sharply. A passenger sees a tennis ball on the smooth floor start to roll forwards, although nothing in the bus pushes it forwards. Which explanation is correct?

A student is inside a sealed, windowless carriage of a train that moves with constant velocity along a straight track. She does experiments with pendulums, springs and a laser. Which result is expected?

A passenger on a train moving at constant velocity along a straight, level track drops a coin from rest in her hand. Ignore air resistance. Which describes the coin's path as seen by the passenger and by a person standing on the platform?

A torch fixed at the exact centre of a train carriage sends out one flash of light towards the front and back doors. The train moves forwards at a constant, very high speed past a platform. Which statement is correct?

Two lightning bolts strike the front and back ends of a fast train, leaving scorch marks on the train and the track. A passenger seated at the exact midpoint of the train sees both flashes at the same instant. The train moves forwards at constant speed. According to an observer standing beside the track, which statement is correct?

Cosmic rays make muons about 10 km above the ground. The muons travel at 0.98c and their mean lifetime, measured at rest, is 2.2 μs. Using classical physics, about how far does a typical muon travel in one mean lifetime? (c = 3 × 10⁸ m s⁻¹)

In an accelerator, the momentum of electrons is measured at four speeds and compared with the classical value m₀v. The table shows the results. Which conclusion do the data support?

A cyclist rides north at 8 m s⁻¹ beside a train travelling north at 20 m s⁻¹ along a straight track. What is the cyclist's velocity measured by a passenger on the train?

Which statement about simultaneity is correct in special relativity?

A spacecraft passes Earth at 0.70c. A lamp fixed inside the spacecraft blinks twice. Who measures the proper time interval between the two blinks?

Which statement describes the proper length of an object?

An astronaut on a spacecraft travelling at 0.80c relative to Earth times her exercise routine as 3.0 minutes on her own clock. How long does the routine last according to an observer on Earth?

A spacecraft is 120 m long when measured by its crew. It flies past a space station at 0.60c, parallel to its length. What length does an observer on the station measure for the spacecraft?

A proton (rest mass 1.67 × 10⁻²⁷ kg) moves at 0.80c in a particle accelerator. What is its relativistic momentum? (c = 3 × 10⁸ m s⁻¹)

A muon has a mean lifetime of 2.2 μs when at rest. It moves at 0.99c relative to Earth. According to an observer on Earth, how far does a muon travel in one mean lifetime? (c = 3 × 10⁸ m s⁻¹)

A pion has a mean lifetime of 26 ns in its own rest frame. In a laboratory, a beam of pions is measured to have a mean lifetime of 65 ns. At what speed do the pions move relative to the laboratory?

Muons made 10 km above sea level, as measured from the ground, travel straight down at 0.995c. In the muons' own frame of reference, what is the distance from where they are made to sea level?

The fission of one uranium-235 nucleus releases 200 MeV of energy. By how much does the total rest mass decrease in this fission? (1 eV = 1.60 × 10⁻¹⁹ J, c = 3 × 10⁸ m s⁻¹)

The Sun radiates energy at a rate of 3.8 × 10²⁶ W. By how much does the Sun's mass decrease each second because of this radiation? (c = 3 × 10⁸ m s⁻¹)

Why can a particle accelerator never bring a proton up to the speed of light?

Ari travels on a fast round trip to a distant star while his twin Jo stays on Earth. While Ari moves at constant velocity, each twin finds the other's clock running slow, yet Ari is younger when he returns. Which explains the difference?

A star is 6.0 light-years from Earth, measured in Earth's frame. An astronaut travels there and straight back at 0.80c while her twin stays on Earth. Ignoring the time taken to turn around, how much younger is the astronaut than her twin when she returns?

A ladder runs at high speed through a barn that is shorter than the ladder's proper length. In the barn's frame, the ladder is contracted enough that both barn doors can be closed for an instant with the whole ladder inside. In the ladder's frame, the barn is contracted and is much shorter than the ladder. Which statement resolves the paradox?

The graph shows the Lorentz factor γ = 1/√(1 − v²/c²) against speed. A spacecraft passes Earth at 0.80c. A light on the spacecraft flashes every 6.0 s according to the crew. Reading from the graph, what is the time between flashes measured by an observer on Earth?

Which observation is direct experimental evidence for time dilation?

An observer on Earth finds that a clock on a passing spacecraft, moving at constant velocity, runs slow. What does an astronaut on the spacecraft find when she compares Earth's clocks with her own?

In a fusion experiment two deuterium nuclei join to make one helium-4 nucleus. The table gives the rest masses. How much energy is released in one fusion? (1 u = 1.66 × 10⁻²⁷ kg, c = 3 × 10⁸ m s⁻¹, 1 eV = 1.60 × 10⁻¹⁹ J)

A star is 4.2 light-years from Earth, measured in Earth's frame. A spacecraft travels from Earth to the star at a constant 0.90c. How long does the journey take according to the crew?

Observers on a space station measure a passing spacecraft to be 75% of its proper length. A clock on the spacecraft records 1.00 h. How much time passes on the station's clocks during that hour?

An electron and a positron, each of rest mass 9.11 × 10⁻³¹ kg, meet at rest and annihilate, making two photons of equal energy. What is the energy of each photon? (c = 3 × 10⁸ m s⁻¹, 1 eV = 1.60 × 10⁻¹⁹ J)

Muons moving straight down at 0.99c pass a detector on a mountain top, 2000 m above a second detector at sea level. At rest, the muons have a half-life of 1.5 μs. Taking time dilation into account, about what percentage of the muons passing the top detector reach the bottom one? (c = 3 × 10⁸ m s⁻¹)

A spacecraft is 150 m long as measured by its crew. As it passes a space station at constant velocity, observers on the station measure its length as 90 m. It keeps the same velocity until it reaches a relay beacon, which is at rest relative to the station and 1.8 × 10¹⁰ m from it, measured in the station's frame. How much time passes on the spacecraft's own clock between passing the station and reaching the beacon? (c = 3 × 10⁸ m s⁻¹)

A muon has a mean lifetime of 2.2 μs in its own rest frame. Observers on the ground measure that a muon moving straight down at constant speed travels 1.32 km during one of its mean lifetimes (on ground clocks, this lifetime is dilated). In the muon's own frame, how far does the ground move past the muon during its 2.2 μs lifetime? (c = 3 × 10⁸ m s⁻¹)

A straight particle detector in a laboratory is 5.0 m long, measured in the laboratory. A proton (rest mass 1.67 × 10⁻²⁷ kg) moves along it at constant velocity, and in the proton's own frame the detector is 2.2 m long. What is the proton's relativistic momentum in the laboratory frame? (c = 3 × 10⁸ m s⁻¹)

A deep-space probe is powered by plutonium-238, which decays by alpha emission into uranium-234. The rest masses of the atoms are: plutonium-238, 238.049560 u; uranium-234, 234.040952 u; helium-4, 4.002603 u. The source undergoes 2.0 × 10¹⁵ decays each second, and the probe's generator turns 6.0% of the released energy into electrical energy. What electrical power does the generator supply? (1 u = 1.66 × 10⁻²⁷ kg, c = 3 × 10⁸ m s⁻¹)

A traveller flies from Earth to a star at constant speed and straight back at the same speed; ignore the time taken to turn around. In the traveller's own frame, the distance between Earth and the star is 3.0 light-years, and the traveller's clock records 10.0 years for the whole round trip. When they meet again, how much older is the traveller's twin, who stayed on Earth, than the traveller?