Question

In: Physics

An observer (O) is standing on a long tunnel that has a rest length of 12...

An observer (O) is standing on a long tunnel that has a rest length of 12 c^.µs. O sees a long train that he measures to be 12c^.µstravel through the tunnel at a speed of 0.600c. The front and back of the tunnel are mounted with strobe lights so that when the front or end of the train reaches the end of the tunnel the light flashes. So we have 4 events (flashes).

Event 1: Front of train enters tunnel.

Event 2: Front of train exits tunnel.

Event 3: End of train enters tunnel.

Event 4: End of train exits tunnel.

With the first event being (x=0, t=0) list the xand tcoordinates of each event in O’s IRF.
For an observer moving with the train (),what is the length of the train and what is the length of the tunnel?
With the first event being (x’=0, t’=0) use the Lorentz transformation to list the x’and t’ coordinates of each event in ’s IRF.
Are there two events in the tunnel’s IRF that are simultaneous? Are these events simultaneous in the train’s IRF? If not, what is the time elapsed between these two events?
Does the train fit in the tunnel?
Make a graph of the motion of both ends of the train and both ends of the tunnel in (x,t) and in (x’,t’). (Put t on the vertical axis and x on the horizontal axis.

Expert Solution

a.

Event 1: (0,0)

Event 2: Time taken by train to exit the tunnel will be

so, coordinates will be(12 c µs,20µs)

Event 3

Since the length of the train and tunnel is same in O's IRF. so, these two event occur at the same time but different x.

coordinates(0,20µs)

Event 4

It will take additional 20µs for back of the train to exit the tunnel. so, coordinates are (12 c^.µs, 40µs).

b) Original length of the train:

length in O's frame =Original length/gamma

Now, in train's frame the track is moving so length of track

c) Lorentz transfornations are

Event 1: (0,0)

Event 2 (x,t)=(12 c µs,20µs)

Event 3: (x,t)= (0,20µs)

Event 4 (x,t) (12 c^.µs, 40µs)

d) Two events simultaneous in tunnel's frame are event 2 and event 3 but these events are not simultaneous in train's frame. time elapsed=6µs

e) It depends upon the frame, for tunnel's frame it fits. For, trains frame it does not when everything is in rest train does not fit inside the tunnel.

genius_generous answered 2 years ago

A 425-m long spaceship passes by an observer at the speed of 2.60×108 m/s. What length...

A 425-m long spaceship passes by an observer at the speed of 2.60×108 m/s. What length does the observer measure for the spaceship? .... m What is the rest energy of 37 g of shelled peanuts? .... J Find the energy in joules of a single photon of microwave radiation with the wavelength of 0.76 cm..... J Using the Bohr model, find the wavelength in nanometers of the radiation emitted by a hydrogen atom, when it makes a transition from...

Tunnel Problem You are going to build a tunnel 10 miles long with a shaft at...

Tunnel Problem You are going to build a tunnel 10 miles long with a shaft at one end and a portal at the other. It is part of the first phase of the gateway tunnel to New York. * The shaft is 185 ft. deep to the invert of the tunnel and 22 ft. excavated diameter. * The tunnel is 26 ft. excavated diameter in competent sandstone and limestone. * The profile of the shaft is as follows: From the...

A train, travelling with velocity v = 0.8c, enters a tunnel. The train has proper length...

A train, travelling with velocity v = 0.8c, enters a tunnel. The train has proper length 100m and the tunnel has proper length 80m. When the center of the train coincides with the center of the tunnel, two gates located at either end of the tunnel come crashing down. The three events (the center of the train reaching the center of the tunnel, the front gate closing and the rear gate closing) occur simultaneously in the stationary reference frame. a)...

A spacecraft with a proper length of 350 m passes by an observer on the Earth....

A spacecraft with a proper length of 350 m passes by an observer on the Earth. According to this observer, it takes 0.780 µs for the spacecraft to pass a fixed point. Determine the speed of the spacecraft as measured by the Earth-based observer. Please show how you arrive at your answer!

Atoms at rest emit photons isotropically. For an observer watching a beam of atoms moving at...

Atoms at rest emit photons isotropically. For an observer watching a beam of atoms moving at speed 0.9 c relative to the lab, does the emission appear isotropic to an observer in the lab? For photons emitted at angles 0,30,60,90,120,150,180 in the reference frame of the atoms, what angles of emission does the observer see? Describe qualitatively and draw the distribution of emission. Will atoms appear brighter as they approach or recede from the observer?

Jack and Zack are standing on a crate at rest on a frictionless horizontal surface. Jack...

Jack and Zack are standing on a crate at rest on a frictionless horizontal surface. Jack has a mass of 70 kg, Zack has a mass of 45 kg, and the crate has a mass of 15 kg. In what follows, we will see that both jump of the crate. You may assume that they push themselves off with a speed of 4 m/s relative to the crate and in a direction that is essentially horizontal. 1) what is the...

The tax burden and fairness issue has been a long standing debate at all levels of...

The tax burden and fairness issue has been a long standing debate at all levels of government. As an individuals circumstances change, how much should a taxpayer's burden change? Three possibilities exist: regressive distribution, progressive distribution, and proportional distribution. Discuss which option you feel is the most equitable and why? Not counting the question, your post should be 350 words

The client has been on bed rest for the last 12 days and has consistently been...

The client has been on bed rest for the last 12 days and has consistently been placed in the Semi Fowler’s position. The nurse assesses the client for tissue breakdown escpecially on the a) greater trochanter b) ankles c) occipital area d) sacrum 2) additional teaching is indicated when a family member visiting a patient in Droplet Isolation says I must. a) pinch the metal band on the mask around the bridge of my nose b) put on new mask...

Standing for a long time will decrease COP ? T or F

You are called to the ER to evaluate b Mr. Collins who has a long standing history...

You are called to the ER to evaluate b Mr. Collins who has a long standing history of COPD. He was brought to the ER by ambulance and is complaining of increasing shortness of breath and productive high laugh with thick, green sputum. During an examination the his chest you notice hyperesonant percussion with decreased fremitus over the lung except the lower right lope that has a dull percussion note and increased fremitus. What are the reasons for the differences in...