Galilean & Special Relativity (HL IB Physics)

The Starship Phoenix travels 12 light years from Earth to the planet Okoye. The Phoenix travels at a constant velocity for the duration of the journey, and the crew stays on the planet Okoye for 2 years before returning at the same constant speed. 

28 years have passed on Earth by the time the crew of the Phoenix returns.

Assume any time accelerating is negligible and that the distance between Earth and Okoye remains constant for the two years.

Calculate the speed of the Phoenix in metres per second. 

Determine how much time had passed for the crew of the Phoenix between leaving Earth and returning to Earth.

Explain the difference in measured time between the crew of the Phoenix and the observers on Earth.

The spaceships Centaurus and Auriga approach Earth from opposite directions at a speed of 2.394×10⁸ m s⁻¹ relative to each other. The length of each spaceship as measured in its rest frame is 9680 m.

Determine the length of the Centaurus as measured from the Auriga.

The Centaurus and the Auriga fly past one another. As each crew sees the other ship approach, they measure the time it takes for the nose of their own vessel to pass the entire length of the other spacecraft.

Calculate:

An engineer and a junior engineer are fixing an electrical wire on the Centaurus.

The engineer explains how special relativity is responsible for the fact that from the inertial reference frame of a stationary observer, an externally moving negative charge is attracted to a current carrying wire due to the magnetic field induced by the current. However, from the moving reference frame of the external negative charge, the negative charge is attracted to the wire due to the electric field induced by the current.

Use the phenomenon of length contraction to explain why this is the case. 

A spaceship passes by Earth travelling at a speed of 0.679c. As it passes Earth, it launches a rocket out in front of the spaceship. The rocket travels at 0.967c relative to the spaceship.

Determine the speed of the rocket relative to Earth:

Sketch a spacetime diagram for the motion of the rocket for the S reference frame.

Add to your diagram form part (b) the axes for the S' reference frame and draw the world line for the rocket from the S' reference frame.

A scientist on Earth is observing a flashing light 6.5 ×10¹⁵ m away. The scientist observes that the time between flashes is 32 s. A spaceship travelling at 0.8c also observes the flashing light. The spaceship passes Earth at exactly the time of a flash. 

Calculate the distance from the spaceship to the flash at t = 32 s as measured by the crew on the spaceship.

Determine the time between flashes as measured from Earth.

The spaceship launches a probe toward the flashing light. The probe travels at 0.9c relative to the spaceship.

Calculate the speed of the probe as measured from Earth.

The probe sends a radio signal back to the spaceship transmitting data collected by the probe. 

The radio signal travels at a constant velocity of c as measured by the spaceship.

Suggest a value for the velocity of the radio signal as measured from Earth. Explain your answer.

Spaceships A and B pass each other at point C where an observer is watching them from Earth. Spaceships A and B are identical and both travel at 0.6c in opposing directions as measured by the observer on Earth. The observer on Earth measures the separation of the spaceships increasing at a rate of 1.2c. 

The observer claims they have disproved the law that nothing can travel faster than the speed of light. 

Explain how the observer is mistaken. 

Spaceship A fires a laser beam out ahead just as it passes Earth. 

Show that from the reference frame of an observer on Earth, the laser beam would be measured to travel at the speed of light, c.

Spaceship D also passes point C at time t = 0. Spaceship D is travelling at 0.85c in the same direction as Spaceship B.

The observer on Earth detects a flash of light from Spaceship A at t = 480 s at a distance of 5.40×10¹⁰ m from point C.

The observer on Earth detects a flash of light from Spaceship D at t = 555 s at a distance of 7.65×10¹⁰ m from point C.

Determine whether the flashes occurred simultaneously for the observer on Earth.

Explain whether Flash A is detected before, after, or at the same time as Flash D for Spaceship B.

State and explain one piece of experimental evidence that supports the theory of special relativity.

Muons are unstable particles that are created in the Earth's upper atmosphere. Muons have an average half-life of 1.49 µs as measured from the reference frame where the muon is at rest. Muons travel at a speed of 0.987c towards the surface of the Earth relative to Earth. 

A detector positioned at 5196 m above the surface of the Earth detects muons at a rate of 3.2 × 10⁴ per hour.

A second detector is positioned at ground level.

Calculate the half-life of the muons as measured by an observer on Earth.

Calculate the distance between the detectors as measured from the reference frame of the muon.

Suggest a prediction for the number of muons per hour detected by the detector on the ground.