Target: 10 Questions in 10 minutes

An IB Physics data booklet is helpful

1-4: A space ship passes the Earth at a speed of ¾ c. (75% of the speed of light).

On board the space ship are a 1m ruler aligned in the direction of motion, and a clock.

cartoon rocket and Earth, Mohamed Hussain - Pixabay

1. What is the Lorentz factor γ for the space ship as it passes the Earth?

  • A. 0.5
  • B. 0.7
  • C. 1.5
  • D. 2

2. if the speed of the ship increases to 0.8c, how long is the ruler when measured from Earth?

  • A. 0.36 m
  • B. 0.60 m
  • C. 1.67 m
  • D. 2.78 m

3. The speed increases again to 0.9c. As viewed from Earth, how long does it take for the clock to show a duration on the space ship of 1 minute?

  • A. 11 seconds
  • B. 26 seconds
  • C. 138 seconds
  • D. 316 seconds

4. A student is discussing how the length of a space ship might change for observers on the ship and on Earth. Three statements are discussed:

I. On the ship, the length is seen to contract.
II. From Earth, the length is seen to contract, but the width remains constant.
III. From Earth, the space ship seems to shrink, and the ratio of length to width remain constant.

Which of these statements are true?

  • A. I and III
  • B. I and II
  • C. II only
  • D. III only

5. A particle accelerator produces two beams of protons travelling in opposite directions that collide with high kinetic energies.

Fermilab particle accelerator

Fermilab Particle accelerator, with two accelerating rings: Public domain image

  
If two protons are travelling at 0.9c in opposite directions, what is their relative velocity?
  • A. 0.90c
  • B. 0.99c
  • C. 1.80c
  • D. 9.47c

6+7: A spaceship passes a planet, and clocks on both planet and ship are matched as it passes, such that t=t'=0.

Mining is taking place on a moon a distance x = 2 x 108 m away, and an explosion takes place at a time t = 0.5 s in the planet's reference frame.

relativity graphic with space ship, planet and moon

The ship is travelling at a speed v = 2 x 108 ms-1, such that the Lorentz factor γ is 1.34, and the speed of light c = 3 x 108 ms-1.

 

6. At what position x' does the explosion event occur, in the reference frame of the space ship?

  • A. 2.0 x 108 m
  • B. 1.5 x 108 m
  • C. 1.3 x 108 m
  • D. 1.1 x 108 m
7. At what time t' does the explosion event occur, in the reference frame of the space ship?
  • A. At a time t'=0.5 s
  • B. At a time t' between 0.0 s and 0.5 s
  • C. At a time t' greater than 0.5 s
  • D. At a time t' less than 0.0s, so before the space ship arrives at the planet.

8. In the formula (Δs)2 = (cΔt)2 - (Δx)2, Δs is known as the spacetime interval. What are the units for Δs, and how does it change between reference frames?

units change between reference frames
A
 m invariant
B
 m2 invariant
C
 m different value in different frames
D
 m2 different value in different frames
9+10: These questions are about spacetime diagrams:

9. Which of the following spacetime diagrams shows the worldline of an accelerating space ship?

worldline of accelerating spaceship x4
 


10. A fast moving particle has the worldline shown in the diagram below. Using information from the graph, what is the velocity of the particle?

worldline of constant velocity particle

  • A. 0.50c
  • B. 0.58c
  • C. 0.87c
  • D. 1.73c