A spaceship whose rest length is 350 m has a speed of 0.82c with respect to a certain reference frame. A micrometeorite, also with a speed of 0.82c in this frame, passes the spaceship on an antiparallel track. How long does it take this object to pass the ship as measured on the ship?
The time taken by the object to pass the ship is .
Suppose a particle is moving with speed u' in x' in an inertial frame S'. If the frame S' is moving with a velocity v with respect to another frame S, then the velocity of the particle with respect to frame S is given by,
Here, the speed of the light is c.
Rearrange the equation (1) for u'.
Substitute 0.82c for u, and -0.82c for v in equation (2).
The expression to calculate the time is given by,
Substitute 350m for data-custom-editor="chemistry" and 0.98c for u' in equation (3).
Therefore, the time taken by the object to pass the ship is data-custom-editor="chemistry" .
Superluminal jets. Figure 37-29a shows the path taken by a knot in a jet of ionized gas that has been expelled from a galaxy. The knot travels at constant velocity at angle from the direction of Earth. The knot occasionally emits a burst of light, which is eventually detected on Earth. Two bursts are indicated in Fig. 37-29a, separated by time as measured in a stationary frame near the bursts. The bursts are shown in Fig. 37-29b as if they were photographed on the same piece of film, first when light from burst 1 arrived on Earth and then later when light from burst 2 arrived. The apparent distance traveled by the knot between the two bursts is the distance across an Earth-observer’s view of the knot’s path. The apparent time between the bursts is the difference in the arrival times of the light from them. The apparent speed of the knot is then . In terms of , , and , what are (a) and (b) ? (c) Evaluate for and . When superluminal (faster than light) jets were first observed, they seemed to defy special relativity—at least until the correct geometry (Fig. 37-29a) was understood.
Question: Temporal separation between two events. Events and occur with the following spacetime coordinates in the reference frames of Fig. 37-25: according to the unprimed frame, and according to the primed frame, . In the unprimed frame and . (a) Find an expression for in terms of the speed parameter and the given data. Graph versus for the following two ranges of : (b) 0 to 0.01and 0.1 (c) 0.1 to 1. (d) At what value of is minimum and (e) what is that minimum? (f) Can one of these events cause the other? Explain.
In a high-energy collision between a cosmic-ray particle and a particle near the top of Earth’s atmosphere, 120 km above sea level, a pion is created. The pion has a total energy E of and is travelling vertically downward. In the pion’s rest frame, the pion decays 35.0 ns after its creation. At what altitude above sea level, as measured from Earth’s reference frame, does the decay occur? The rest energy of a pion is 139.6 MeV.
What is the speed parameter for the following speeds: (a) a typical rate of continental drift (1 in./y); (b) a typical drift speed for electrons in a current-carrying conductor (0.5 mm/s); (c) a highway speed limit of 55 mi/h; (d) the root-mean-square speed of a hydrogen molecule at room temperature; (e) a supersonic plane flying at Mach 2.5 (1200 km/h); (f) the escape speed of a projectile from the Earth’s surface; (g) the speed of Earth in its orbit around the Sun; (h) a typical recession of a distant quasar due to the cosmological expansion .
Question: (a) The energy released in the explosion of 1.00 mol of TNT is 340 mJ. The molar mass of TNT is . What weight of TNT is needed for an explosive release of ? (b) Can you carry that weight in a backpack, or is a truck or train required? (c) Suppose that in an explosion of a fission bomb, 0.080% of the fissionable mass is converted to released energy. What weight of fissionable material is needed for an explosive release of ? (d) Can you carry that weight in a backpack, or is a truck or train required?
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