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Exercise 2 Conservation of Linear Momentum Is Covariant Under the Galilean Transformation. Assume that two masses
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Modern Physics
- Imagine a space vessel traveling at a constant velocity toward a star that is 6.05 ly from the Earth. A passenger aboard the moving space vessel measures the Earth-star distance to be 2.60 ly. What is the space vessel's speed with respect to the Earth? Express your answer as a fraction of the speed of light. Varrow_forwardR5B.5 An event occurs at t = 6.0 s and x = 4.0 s in the Home Frame. The Other Frame is moving in the +x direc- tion with x-velocity 3 = 0.5 relative to the Home Frame. (a) Use a two-observer spacetime diagram to determine when and where this event occurs in the Other Frame. (b) Check your work by applying the appropriate Lorentz transformation equation. R5B.6 An event occurs at tarrow_forwardProblem A new particle, the aarnion, has just been discovered! Careful measurements show that the aarnion has an average lifetime (at rest) of 64 ns. In one experiment, an aarnion traveled 14 m (as viewed from the lab frame) before it decayed. A.) Determine the proper velocity of the aarnion. Assume it had an average lifetime in its own frame. W = XC B.) Determine the velocity of the aarnion. Assume it had an average lifetime in its own frame. XCarrow_forward
- A particle of mass m and energy E falls from the Earth's zenith along the Z axis in the rest reference frame of a certain observer K. Another observer, K', moves with speed v along the positive X axis of K and observes the particle approaching him with an angle 0 with respect to the Z' axis. a) Calculate the angle 0 expressed in terms of the velocity u of the particle and the velocity v of K' b) Based on the result obtained in part a), give a description of what the starry sky would look like for a space cruiser moving at high speeds in our galaxy.arrow_forward▾ Part A A subatomic particle moves through the laboratory at 0.90 c. Laboratory experimenters measure its lifetime, from creation to annihilation, to be 2.1 ps. (1 ps 10-12s). = According to the particle, how long did it live? Express your answer using two significant figures. tp = ΜΕ ΑΣΦ Submit Request Answer Provide Feedback ? psarrow_forwardApply the special theory of relativity to prove that the time interval t in the moving reference frame S' appears to be longer by a factor 1//1– z to the observer in the stationary frame S. [CO3]arrow_forward
- Make a spacetime diagram on which the time axis is marked in years and the space axis is marked in light-years. Assume you are floating weightlessly and therefore consider yourself at rest. Assume the direction to the right of you as the positive direction, and that time is measured from the moment when you meet the person. ▼ Part A Draw a worldline for Sebastian, who is moving to your right at 0.5c. +* E₂ No elements selected Time (yr) -10 -8 -6 -4 -2 10 8 6 4 2 -2 L ■ I 02 4 6 Review 8 10 Space (ly)arrow_forwardA spacecraft is moving at a speed of 0.530 c relative to the earth. Part A What is the ratio of the length of the spacecraft, as viewed through a telescope on earth, to its length when measured after landing on earth? (Assume that the spacecraft is moving at a right angle to the line of observation.) ? Submit Request Answerarrow_forwardD, E AND F PLEASE (c) An electron is moving at a velocity 0.9c in a direction which is 30° from the x- axis in the direction of the y-axis. Write down the 4-velocity vector for the electron. (d) Write down the momenergy vector of the electron described in the previous section. (e) A spaceship travels towards the centre of a black hole. It sends regular light pulses at a single frequency to an observer located far away from the black hole. Describe what the observer will see. (f) An isotropically emitting source of light is moving towards an observer at high speed. Describe the source as seen by the observer.arrow_forward
- Exercise 6: An object with m and velocity v collides elastically with a stationary object and continues in the same direction with speed 0.25v. What is the mass of the object that was initially stationary?arrow_forwardthat the axes get closer to one another. 2. Prove that the "interval", defined as x² +v² + =² – c²¢ is a conserved quantity across reference frame transformations. 3. Consider two events. Give an example of coordinates x,y,z,t and x',y',z',t and relativearrow_forwardA new particle, the aarnion, has just been discovered! Careful measurements show that the aarnion has an average lifetime (at rest) of 14 ns. In one experiment, an aarnion traveled 24 m (as viewed from the lab frame) before it decayed. A.) Determine the proper velocity of the aarnion. Assume it had an average lifetime in its own frame. W = B.) Determine the velocity of the aarnion. Assume it had an average lifetime in its own frame. V = XCarrow_forward
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