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Using the lorentz transformation for length

A surveyor measures a street to be L = 100 m long in Earth frame S. Use the Lorentz transformation to obtain an expression for its length measured from a spaceship S , moving by at speed 0.20 c , assuming the x coordinates of the two frames coincide at time t = 0 .


  1. Identify the known: L = 100 m ; v = 0.20 c ; Δ τ = 0 .
  2. Identify the unknown: L .
  3. Express the answer as an equation. The surveyor in frame S has measured the two ends of the stick simultaneously, and found them at rest at x 2 and x 1 a distance L = x 2 x 1 = 100 m apart. The spaceship crew measures the simultaneous location of the ends of the sticks in their frame. To relate the lengths recorded by observers in S and S, respectively, write the second of the four Lorentz transformation equations as:
    x 2 x 1 = x 2 v t 1 v 2 / c 2 x 1 v t 1 v 2 / c 2 = x 2 x 1 1 v 2 / c 2 = L 1 v 2 / c 2 .
  4. Do the calculation. Because x 2 x 1 = 100 m , the length of the moving stick is equal to:
    L = ( 100 m ) 1 v 2 / c 2 = ( 100 m ) 1 ( 0.20 ) 2 = 98.0 m.

    Note that the Lorentz transformation gave the length contraction equation for the street.
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Lorentz transformation and simultaneity

The observer shown in [link] standing by the railroad tracks sees the two bulbs flash simultaneously at both ends of the 26 m long passenger car when the middle of the car passes him at a speed of c /2. Find the separation in time between when the bulbs flashed as seen by the train passenger seated in the middle of the car.

An observer on the ground watches a train car that is moving to the right with velocity v. Inside, at each end of the train car are lamps, each emitting a signal that is propagating toward the center of the car, and in the center of the car sits a passenger.
An person watching a train go by observes two bulbs flash simultaneously at opposite ends of a passenger car. There is another passenger inside of the car observing the same flashes but from a different perspective.


  1. Identify the known: Δ t = 0 .
    Note that the spatial separation of the two events is between the two lamps, not the distance of the lamp to the passenger.
  2. Identify the unknown: Δ t = t 2 t 1 .
    Again, note that the time interval is between the flashes of the lamps, not between arrival times for reaching the passenger.
  3. Express the answer as an equation:
    Δ t = Δ t + v Δ x / c 2 1 v 2 / c 2 .
  4. Do the calculation:
    0 = Δ t + c 2 ( 26 m ) / c 2 1 v 2 / c 2 Δ t = 26 m/s 2 c = 26 m/s 2 ( 3.00 × 10 8 m/s ) Δ t = −4.33 × 10 −8 s.


The sign indicates that the event with the larger x 2 , namely, the flash from the right, is seen to occur first in the S frame, as found earlier for this example, so that t 2 < t 1 .

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Relativistic phenomena can be analyzed in terms of events in a four-dimensional space-time . When phenomena such as the twin paradox, time dilation, length contraction, and the dependence of simultaneity on relative motion are viewed in this way, they are seen to be characteristic of the nature of space and time, rather than specific aspects of electromagnetism.

In three-dimensional space, positions are specified by three coordinates on a set of Cartesian axes, and the displacement of one point from another is given by:

( Δ x , Δ y , Δ z ) = ( x 2 x 1 , y 2 y 1 , z 2 z 1 ) .

The distance Δ r between the points is

Δ r 2 = ( Δ x ) 2 + ( Δ y ) 2 + ( Δ z ) 2 .

The distance Δ r is invariant under a rotation of axes. If a new set of Cartesian axes rotated around the origin relative to the original axes are used, each point in space will have new coordinates in terms of the new axes, but the distance Δ r given by

Questions & Answers

عند قذف جسم إلى أعلى بسرعة إبتدائية فإنه سيصل إلى ارتفاع معين (أقصى ارتفاع) ثم يعود هابطاً نحو سطح الأرض .   إذا قُذِفَ جسم إلى أعلى ووجد أن سرعته 18 م / ث عندما قطع 1/4 المسافة التي تمثل أقصى ارتفاع سيصله فالمطلوب إيجاد السرعة التي قُذِف بها بالمتر / ث . إن هذه السرعة هي واحدة من الإجابات التالية
Aml Reply
what is light
Ayebanifesunday Reply
light is a kind of radiation That stimulates sight brightness a source of illumination.
Electromagnet radiation creates space 7th, 8th, and 9th dimensions at the rate of c.
That is the reason that the speed of light is constant.
This creation of new space is "Dark Energy".
The first two sets of three dimensions, 1 through 6, are "Dark Matter".
As matter decays into luminous matter, a proton, a neutron, and an electron creat deuterium.
There are three sets of three protons, 9.
There are three sets of three neutrons, 9.
A free neutron decays into a proton, an electron, and a neutrino.
There are three sets of five neutrinoes, 15.
Neutrinoes are two dimensional.
A positron is composed of the first three dimensions.
An electron is composed of the second three dimensions.
What is photoelectric
Hsssan Reply
light energy (photons) through semiconduction of N-P junction into electrical via excitation of silicon purified and cristalized into wafers with partially contaminated silicon to allow this N-P function to operate.
i.e. Solar pannel.
If you lie on a beach looking at the water with your head tipped slightly sideways, your polarized sunglasses do not work very well.Why not?
Rakhi Reply
it has everything to do with the angle the UV sunlight strikes your sunglasses.
this is known as optical physics. it describes how visible light, ultraviolet light and infrared light interact when they come into contact with physical matter. usually the photons or light upon interaction result in either reflection refraction diffraction or interference of the light.
I hope I'm clear if I'm not please tell me to clarify further or rephrase
what is bohrs model for hydrogen atom
Swagatika Reply
what is the value of speed of light
Propessor Reply
1.79×10_¹⁹ km per hour
what r dwarf planet
Sivalakshmi Reply
what is energy
Isiguzo Reply
কাজের একক কী
কাজের একক কী
Energy is ability so capacity to do work.
friction ka direction Kaise pata karte hai
Rahul Reply
friction is always in the opposite of the direction of moving object
A twin paradox in the special theory of relativity arises due to.....? a) asymmetric of time only b) symmetric of time only c) only time
Varia Reply
b) symmetric of time only
fundamental note of a vibrating string
fasoyin Reply
every matter made up of particles and particles are also subdivided which are themselves subdivided and so on ,and the basic and smallest smallest smallest division is energy which vibrates to become particles and thats why particles have wave nature
what are matter waves? Give some examples
mallam Reply
according to de Broglie any matter particles by attaining the higher velocity as compared to light'ill show the wave nature and equation of wave will applicable on it but in practical life people see it is impossible however it is practicaly true and possible while looking at the earth matter at far
a centeral part of theory of quantum mechanics example:just like a beam of light or a water wave
Mathematical expression of principle of relativity
Nasir Reply
given that the velocity v of wave depends on the tension f in the spring, it's length 'I' and it's mass 'm'. derive using dimension the equation of the wave
obia Reply
What is the importance of de-broglie's wavelength?
Mukulika Reply
he related wave to matter
at subatomic level wave and matter are associated. this refering to mass energy equivalence
it is key of quantum
Practice Key Terms 4

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Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
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