Galilean & Special Relativity (DP IB Physics: HL): Exam Questions

Describe the difference between Galilean relativity and special relativity.

Car A travels at a constant velocity of 25 m s^-1 relative to the road. Car B travels on the same road behind Car A at a constant velocity of 20 m s^-1 relative to the road. Car C travels in the opposite direction to Cars A & B on the same road at a constant velocity of 30 m s^-1 relative to the road.

Using ideas from Galilean relativity, explain why there is no such thing as 'true' velocity. You should include the velocity of Car A as an example in your answer.

As Car A passes a stationary observer on the side of the road, a child in the back seat of Car A throws a teddy bear at the windscreen. The teddy bear moves at a constant velocity of 2 m s⁻¹ relative to the passengers in Car A. 

Calculate the velocity of the teddy bear as measured by the stationary observer on the side of the road.

Determine the velocity of the teddy bear from the reference frame of Car C.

An observer on Earth sees a flashing light located at a distance $6.5\times {10}^{15}\mathrm{m}$ from Earth. The light source is stationary in the Earth frame.

A spacecraft travelling at $0.8c$ towards the light passes Earth at $t=t\text{'}=0$. A flash occurs as the spacecraft passes the Earth, and a second flash occurs at $t=3.2\mathrm{s}$, according to the observer on Earth.

Calculate

(i) $\gamma$ for a speed of $0.8c$

[1]

(ii) the distance $x\text{'}$ of the flash from the spacecraft as measured in the spacecraft frame.

[2]

Calculate, for the reference frame of the spacecraft, the time between flashes.

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

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.

Predict the number of muons per hour detected by the detector on the ground.

A distant quasar is found to be moving away from Earth at a speed of 0.754c. Between Earth and the quasar lies a galaxy named ASG4-RD. The quasar is moving away from ASG4-RD at a speed of 0.629c. 

Determine the recessional speed of the galaxy ASG4-RD relative to Earth.

The spacecraft Lyra, in orbit around Earth, is sent by Mission Control to collect data on the galaxy ASG4-RD. 

The Lyra travels at 0.555c relative to Earth in the x direction toward ASG4-RD. Part-way into it's mission, the Lyra sends the following message to Mission Control. 

Collision of two asteroids detected at location (x = 4.163 × 10¹⁰ m, t = 332 s)

Determine the coordinates of the asteroid collision relative to Earth.

The Lyra continues on its mission to ASG4-RD.

Determine the speed with which the Lyra would need to travel for the crew of the Lyra to age 10 years on the journey whilst 100 years passes for Mission Control. 

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:

(i) The time measured by the Centaurus for the Auriga to completely fly past it.

[2]

(ii) The amount of time that passes for the the crew of the Auriga.

[2]

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:

(i) Using Galilean relativity.

[1]

(ii) Using special relativity.

[2]

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.