Suppose an astronaut travels to a distant star and returns to Earth. Except for brief intervals of time when he is accelerating or decelerating, his spaceship travels at the incredible speed of v = 0.995c relative to the Earth. The star is 46 light-years away. (A light-year is the distance light travels in 1 year.) a. Show that the factor γ for this velocity is approximately equal to 10.
a. How long does the trip to the star and back take as seen by an observer on Earth?
b. How long does the trip take as measured by the astronaut?
c. What is the distance traveled as measured by the astronaut?
d. If the astronaut left a twin brother at home on Earth while he made this trip, how much younger is the astronaut than his twin when he returns?
(a)
To show that the factor
Answer to Problem 3SP
It is shown that the factor
Explanation of Solution
Given info: The velocity of the spaceship is
Write the expression to find the
Here,
Substitute
Conclusion:
Therefore, it is shown that the factor
(b)
The time taken for the travel to the star and back to earth as seen by an observer on earth.
Answer to Problem 3SP
The time taken for the travel to the star and back to earth as seen by an observer on earth is
Explanation of Solution
Write the expression to find the distance travelled in meter.
Write the expression to find the time taken by the spaceship to travel back and forth.
Here,
Substitute
Conclusion:
Therefore, the time taken for the travel to the star and back to earth as seen by an observer on earth is
(c)
The time taken for the travel to the star and back to earth as seen by the astronaut.
Answer to Problem 3SP
The time taken for the travel to the star and back to earth as seen by the astronaut is
Explanation of Solution
Write the expression to find the distance travelled in meter.
Write the expression to find the time taken by the spaceship to travel back and forth as seen by the astronaut.
Here,
Substitute
Conclusion:
Therefore, the time taken for the travel to the star and back to earth as seen by the astronaut is
(d)
The distance travelled as measured by the astronaut.
Answer to Problem 3SP
The distance travelled as measured by the astronaut is
Explanation of Solution
Write the expression to find the distance as measured by the astronaut.
Here,
Substitute
Conclusion:
Therefore, the distance travelled as measured by the astronaut is
(e)
The age difference between the astronaut and his twin after he returns from his space journey.
Answer to Problem 3SP
The age difference between the astronaut and his twin after he returns from his space journey is
Explanation of Solution
Write the expression to find the age difference between the astronaut and his twin.
Here,
Substitute
Conclusion:
Therefore, the age difference between the astronaut and his twin after he returns from his space journey is
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Chapter 20 Solutions
EBK PHYSICS OF EVERYDAY PHENOMENA
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- The muon is an unstable particle that spontaneously decays into an electron and two neutrinos. If the number of muons at t = 0 is N0, the number at time t is given by , where τ is the mean lifetime, equal to 2.2 μs. Suppose the muons move at a speed of 0.95c and there are 5.0 × 104 muons at t = 0. (a) What is the observed lifetime of the muons? (b) How many muons remain after traveling a distance of 3.0 km?arrow_forward(a) Find the kinetic energy of a 78.0-kg spacecraft launched out of the solar system with speed 106 km/s by using the classical equation K=12mu2. (b) What If? Calculate its kinetic energy using the relativistic equation. (c) Explain the result of comparing the answers of parts (a) and (b).arrow_forward(a) How long would the muon in Example 28.1 have lived as observed on the Earth if its velocity was 0.0500c ? (b) How far would it have traveled as observed on the Earth? (c) What distance is this in the muon's frame?arrow_forward
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