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.

Solutions

Expert Solution

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

A commuter train passes a passenger platform at a constant speed of 38.1 m/s. The train...

A commuter train passes a passenger platform at a constant speed of 38.1 m/s. The train horn is sounded at its characteristic frequency of 340 Hz. (a) What overall change in frequency is detected by a person on the platform as the train moves from approaching to receding? (Indicate whether the frequency increases of decreases with the sign of your answer.) Hz (b) What wavelength is detected by a person on the platform as the train approaches? m

1. A commuter train passes a passenger platform at a constant speed of 41.7 m/s. The...

1. A commuter train passes a passenger platform at a constant speed of 41.7 m/s. The train horn is sounded at its characteristic frequency of 350 Hz. (a) What overall change in frequency is detected by a person on the platform as the train moves from approaching to receding? (Indicate whether the frequency increases of decreases with the sign of your answer.) (b) What wavelength is detected by a person on the platform as the train approaches? 2. Two small...

1. A train moving at a constant speed of 52.0 km/h moves east for 38.0 min,...

1. A train moving at a constant speed of 52.0 km/h moves east for 38.0 min, then in a direction 45.0° east of due north for 21.0 min, and then west for 65.0 min. What is the average velocity of the train during this run? a) magnitude- km/h b) ° (counterclockwise from east) 2. A golf ball is struck at ground level. The speed of the golf ball as a function of time is shown in the figure below, where...

A train at a constant 48.0 km/h moves east for 42.0 min, then in a direction...

A train at a constant 48.0 km/h moves east for 42.0 min, then in a direction 47.0° east of due north for 27.0 min, and then west for 52.0 min. What are the (a) magnitude and (b) angle (relative to east) of its average velocity during this trip?

Ball 1 with mass 1 kg moves at constant velocity to the right at 3.0 m/s,...

Ball 1 with mass 1 kg moves at constant velocity to the right at 3.0 m/s, towards Ball 2 with mass 2 kg moving to the right at 1.5 m/s. 1 and 2 collide elastically. What is the final velocity of 1 and 2?

1) An electron passes through a point 3.15 cm from a long straight wire as it...

1) An electron passes through a point 3.15 cm from a long straight wire as it moves at 33.9% of the speed of light perpendicularly toward the wire. The wire carries a current of 18.9 A. Find the magnitude of the electron's acceleration at that point. acceleration:____________ m/s2 2) A beam of protons is directed in a straight line along the positive ?‑direction through a region of space in which there are crossed electric and magnetic fields. If the electric...

You are 50m away from a train and running at a constant velocity of 26m/s. The...

You are 50m away from a train and running at a constant velocity of 26m/s. The train has a constant acceleration of 39m/s2. If it takes the train 4.92 seconds to reach a distance of 150m, and it takes you 5.78 seconds to reach a distance of 150m, then at what distance will the two meet? Please show what equations to use, THEN input the values. Thanks! Please let me know if there are any missing variables you need. I'm...

1. A freight car carrying sand moves along a frictionless level railroad track at constant speed....

1. A freight car carrying sand moves along a frictionless level railroad track at constant speed. An additional amount of sand is thrown straight down onto the car as it passes by a storage building. What happens to the velocity of the car? A) It decreases. B) It remains the same. C) It increases. D) cannot be determined from the information given 2. A 27g tennis ball heads straight toward a racket at 21 m/s. A player swings the racket,...

1. A metal loop moves at constant velocity toward a long wire carrying a steady current...

1. A metal loop moves at constant velocity toward a long wire carrying a steady current I = 2.0 A. The current induced in the loop is: A. Directed clockwise. B. directed counterclockwise. C. Zero. D. Cannot tell, more information is needed. 2. Loop A in the figure shown is part of a simple circuit with switch open. Loop B is another one that lies below Loop A. to A When the switch is closed, there is an induced current generated...

Compared to normal blood flow velocity, v0, what is the velocity of blood as it passes through this blockage?

Arteriosclerotic plaques forming on the inner walls of arteries can decrease the effective cross-sectional area of an artery. Even small changes in the effective area of an artery can lead to very large changes in the blood pressure in the artery and possibly to the collapse of the blood vessel. Imagine a healthy artery, with blood flow velocity of v0=0.14m/s and mass per unit volume of ρ=1050kg/m3. The kinetic energy per unit volume of blood is given by K0=12ρv20. Imagine that plaque...

Subjects