At , a firecracker explodes at in reference frame S. Four seconds later, a second firecracker explodes at . Reference frame S′ moves in the x-direction at a speed of . What are the positions and times of these two events in frame S′?
Position of the events are
Times of the events are
We have given,
First firecracker positon =
Second firecracker positon =
Velocity of frame =
We have to find the positon and time of the events in the S' frame.
Using Galilean transformation,
where x' is coordinate in S' frame.
For first event in the S' frame
For second event in the S' frame
A firecracker explodes in reference frame S at . A second firecracker explodes at the same position at . In reference frame S′, which moves in the x-direction at speed v, the first explosion is detected at and the second at .
a. What is the speed of frame S′ relative to frame S?
b. What is the position of the two explosions in frame S?
A ball of mass m traveling at a speed of 0.80c has a perfectly inelastic collision with an identical ball at rest. If Newtonian physics were correct for these speeds, momentum conservation would tell us that a ball of mass 2m departs the collision with a speed of 0.40c. Let’s do a relativistic collision analysis to determine the mass and speed of the ball after the collision.
a. What is gp, written as a fraction like a/b?
b. What is the initial total momentum? Give your answer as a fraction times mc. c. What is the initial total energy? Give your answer as a fraction times mc2 . Don’t forget that there are two balls.
d. Because energy can be transformed into mass, and vice versa, you cannot assume that the final mass is 2m. Instead, let the final state of the system be an unknown mass M traveling at the unknown speed uf. You have two conservation laws. Find M and uf.
Your friend flies from Los Angeles to New York. She carries an accurate stopwatch with her to measure the flight time. You and your assistants on the ground also measure the flight time.
a. Identify the two events associated with this measurement.
b. Who, if anyone, measures the proper time?
c. Who, if anyone, measures the shorter flight time?
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