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PHYSICS, M7 2016 HSC 10 MC

In a thought experiment, a train is moving at a constant speed of 0.8 `c`. A lamp is located at the midpoint of a carriage. There are doors `W` and `Z` at each end of the carriage which open automatically when light from the lamp reaches them.
 

The passenger standing at the midpoint of the carriage switches on the lamp.

Which statement best explains what the passenger observes about the doors?

  1. `Z` opens before `W` because the lamp is moving towards `Z`.
  2. `W` opens before `Z` because `W` is moving towards the lamp.
  3. `W` and `Z` open simultaneously because the lamp is placed at an equal distance from both.
  4. `W` and `Z` open simultaneously because the distance from the lamp to each door has contracted by the same amount.
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`C`

Show Worked Solution

→ The observer, the lamp and the doors are all in the same frame of reference. Observations are therefore not affected by length contraction.

→ The observer sees light travel an equal distance to each of the doors.

→ As the speed of light is constant the observer sees light reach the doors at the same time and thus sees the doors open simultaneously.

`=>C`

PHYSICS, M7 2018 HSC 16 MC

When a train is at rest in a tunnel, the train is slightly longer than the tunnel.
 

In a thought experiment, the train is travelling from left to right fast enough relative to the tunnel that its length contracts and it fits inside the tunnel.

An observer on the ground sets up two cameras, at `X` and `Y`, to take photos at exactly the same time. The photos show that both ends of the train are inside the tunnel.
 

A passenger travelling on the train at its centre can see both ends of the tunnel and is later shown the photos.

From the point of view of the passenger, what is observed and what can be deduced about the photos?

  1. The tunnel's length contracts so the train does not fit, and photo 2 is taken before photo 1.
  2. The tunnel's length contracts so the train does not fit, and photos 1 and 2 are taken at the same time.
  3. The tunnel appears to expand due to length contraction of the train, allowing it to fit in the tunnel, and photo 1 is taken before photo 2 .
  4. The tunnel appears to expand due to length contraction of the train, allowing it to fit in the tunnel, and photos 1 and 2 are taken at the same time.
Show Answers Only

`A`

Show Worked Solution

→ From the frame of reference of an observer on the train, the tunnel’s length will contract (all objects outside the train will appear length contracted).

→ Due to the relativity of simultaneity, the photo that the observer on the train sees as taken first is the photo taken at the end of the tunnel that the train was moving towards at that moment.

`=>A`


♦♦♦ Mean mark 36%.