A light bulb at point x in the frame of reference of O blinks on and off at intervals Δt = t2 − t1. Observer O′, moving relative to O at speed u, measures the interval to be Δt′ = t′2 − t′1. Use the Lorentz transformation expressions to derive the time dilation expression relating Δt and Δt′.

Q: A particle with mass m has speed 0.335c relative to inertial frame S. The particle collides with an…

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Q: What is the speed of an electron having the same momentum with a proton having speed 0.005c? (Just…

A: Given data: Speed of proton is, v=0.005c.

Q: You are an observer in a 100-m long spacecraft traveling from the earth to the moon at 0.8c. (a)…

A: Given: Length of the spacecraft as per observer (you) is 100 m Speed 'v' = 0.8 c

Q: A cube has a volume of 1.2 cm and a mass of 7.3g when at rest on the Earth. If this cube is now…

A: Volume of cube V=1.2 cm3 and mass of cube m=7.3 g. Now the cube is given a velocity u=0.75c say in…

Q: The elementary particle called a muon is unstable and decays in about 2.20μs, as observed in its…

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Q: alculate the interval Δs2 between two events with coordinates (x1 = 55m, y1 = 0m, z1 = 0m, t1 = 1…

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Q: If a spaceship, approaching the Earth at 0.190c, sends a message capsule toward the Earth at 0.390c…

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Q: Recall, from this chapter, that the factor gamma (γ) governs both time dilation and length…

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Q: Two spaceships, each 100 m long when measured at rest, travel toward each other with speeds of 0.85c…

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Q: A supertrain of proper length 94 m travels at a speed of 0.93c as it passes through a tunnel having…

A: The Lorentz transformation is the contraction of length l of any object with respect to the moving…

Q: The Galilean transformation as compared to the Lorentz transformation has no symmetry for the…

A: Galilean transformations and lorentz transformation are same at low speed

Q: A space traveler takes off from Earth and moves at speed 0.9900c toward the star Vega, which is…

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Q: Show that the following form of Newton's second law satisfies the Lorentz transformation. Assume the…

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Q: The origins of two frames coincide at t = t' 0 and the relative speed is 0.991c. Two micrometeorites…

A: t=277μS x=83500 m

Q: Calculate the interval ∆s2 between two events with coordinates (x1 = 50 m, y1 = 0, z1 = 0, t1 = 1…

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Q: A space traveler takes off from Earth and moves at speed 0.9700c toward the star Vega, which is…

A: in this question  we use simple space motion equation  and get answer.

Q: ay from Earth? (b)To what frequency must Earth receivers be tuned to receive the report when the…

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Q: Starting from the Lorentz transformation, derive time dilation ?t = ? ?t0. Sketch the situation,…

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Q: The origins of two frames coincide at t = t' 0 and the relative speed is 0.991c. Two micrometeorites…

A: We have two inertial frames of references as S and S' with coordinates (x, y, z, t) and (x', y', z',…

Q: Inertial frame S' moves at a speed of 0.60c with respect toframe S. Further, x = x' = 0 at t = t' =…

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Q: Frame S' has a speed v = 0.6c relative to S in x direction which is parallel to x'. The clocks on S…

A: Given : Speed of S' with respect to S, v = 0.6c The clocks on S and S' are adjusted so that t= t'= 0…

Q: What situation does relativistic formula for length contraction, time dilation, and relativistic…

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Q: As an example, consider a spaceship moving away from you at a velocity of 0.5c. Suppose that the…

A: Given: The speed (v) of the spaceship is 0.5c. Introduction: According to the relativistic velocity…

Q: The average lifetime of a pi meson in its own frame of reference (i.e., the proper lifetime) is 2.6…

A: Given, The average lifetime of a pi meson t = 2.6 x 10-8 s.   (a) If the meson moves with a speed of…

Q: The origins of two frames coincide at t = t' 0 and the relative speed is 0.993c. Two micrometeorites…

A:

Q: The formula for length contraction gives the length of an interval on a ruler moving with velocity v…

A: Given: The formula for length contraction gives the length of an interval on a ruler moving with…

Q: The positive muon (µ), an unstable particle, lives on average 2.20 x 10 reference) before decaying.…

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Q: Recall, from this chapter, that the factor gamma (γ) governs both time dilation and length…

A:

Q: A space traveler takes off from Earth and moves at speed 0.9900c toward the star Vega, which is…

A:

Q: A spaceship whose rest length is 378 m has a speed of 0.91c with respect to a certain reference…

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Q: For a body moving along the x-axis at the speed of light, x = ct. Use the Lorentz transformation to…

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Q: You are an observer in a 100-m long spacecraft traveling from the earth to the moon at 0.8c.…

A: Observer measure the length of the spacecraft,   It is left measure by observer according to whom…

Q: The average lifetime of a pi meson in its own frame of reference (i.e., the proper lifetime) is 2.6…

A: Meson Particles Meson Particles are the hadronic subatomic particles that have an equal number of…

Q: Derive the Lorentz transformation connecting a frame S (the lab frame) to a frame S′ that moves with…

A: SOlution: To derive the  Lorentz transformation connecting a frame S (the lab frame) to a frame S'.

Q: A spaceship, 180 m long as seen on board, moved by the earth at 0.980c. What is it's length in m as…

A: Given data: Original Length (L0) = 180 m Speed (v) = 0.980 c Required: The length of spaceship…

Q: 2.2. A rod of mass m = 1 kg flies with constant velocity past a mark which is stationary in the K…

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Q: (a) A spaceship moves along the x' axis of frame S' with velocity 0.40c. Frame S' moves with…

A: Given: velocity of spaceship in frame S'  = 0.40 C velocity of frame S' with respect to S = 0.60 C

Q: Show that the following form of Newton's second law satisfies the Lorentz transformation. Assume the…

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Q: Suppose a spacecraft of mass 17000 kg is accelerated to 0.200 c. How much kinetic energy would it…

A: Given:- Mass(m)=17000 kg Velocity (V)=0.20 c Now, The relativistic kinetic energy of the particle.…

Q: The muon is an unstable particle that spontaneously decays into an electron and two neutrinos. In a…

A: a) The equation to determine the life time of the moving muon is,

Q: A rocket measures 100 m long in its own frame (S') and is travelling at 0.995c relative to a frame…

A: a) In the S' frame, the time taken by the light pulse to arrive back at the tail of the rocket is…

Q: An armada of spaceships that is 1.00 ly long (as measured in its rest frame) moves with speed 0.800c…

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Q: The control panel on a spaceship contains a light that blinks every 2.76 s as observed by an…

A: Given data: Speed of the spaceship, v=0.693c

Q: Calculate the interval ∆s2 between two events with coordinates ( x1 = 50 m, y1 = 0, z1 = 0, t1 = 1…

A: Einstein with his special theory of relativity brought in an entirely new understanding of the world…

Proper Length

The theory of special relativity explains the connection between space and time to objects that move in a straight line at a constant speed. The objects move at the speed of light. When an object approaches light speed, its mass is endless and cannot move faster than light. The most crucial postulate of Einstein's special relativity is that the laws of nature do not change in each frame of reference.