Question

In: Physics

PART 1: A train moves with constant velocity down a straight track that passes through a...

PART 1: A train moves with constant velocity down a straight track that passes through a tunnel. When the train is at rest with respect to the tunnel, the train is exactly the same length as the tunnel. However, the train in this case is moving relative to the tunnel at nearly the speed of light.

The engineer on the train says: “The tunnel is Lorentz-contracted and is shorter than the train;
therefore at no time can the train be wholly within the tunnel.”

The keeper of the tunnel says: “The train is Lorentz-contracted and is shorter than the tunnel;
therefore, there will be a time at which the train is wholly within the tunnel.”

The engineer decides to settle the issue by placing high-powered lasers on the front and rear of the train, on the roof pointing upward. The engineer sets timers so that the lasers will fire at the moment the midpoint of the train reaches the midpoint of the tunnel, in the train's reference frame.

For the scenario above, select all the statements below that are true:

A) The front laser will strike the inside of the tunnel

B) The rear laser will miss the tunnel

C) In the tunnel keeper's frame the rear laser fires before the midpoint of the train reaches the midpoint of the tunnel.

D) The tunnel keeper will not be convinced by the engineer's demonstration.

PART B: The tunnel keeper then tries to settle the issue (permanently) by erecting high-speed gates at the front and rear of the tunnel, equipped with timing devices such that the gates will close simultaneously when the midpoint of the train passes the midpoint of the tunnel. (The tunnel keeper knows that this will damage the train and perhaps the front gate when the front end of the train plows into it, but is so infuriated as to not care.)

For the scenario described above, select all the statements that are true:

A) The front of the train will make it out of the tunnel.

B) In the engineer's frame, the front gate will close at the moment the front of the train reaches it.

C) In the engineer's frame, the front gate will close before the end of the train enters the tunnel

D) The front of the train and the front gate are both damaged.

Expert Solution

genius_generous answered 2 years ago

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