An astronaut wishes to visit the Andromeda galaxy, making a one-way trip that will take 30.0 years in the spaceship’s frame of reference. Assume the galaxy is 2.00 million light-years away and his speed is constant. (a) How fast must he travel relative to Earth? (b) What will be the kinetic energy of his spacecraft, which has mass of 1.00 × 106 kg? (c) What is the cost of this energy if it is purchased at a typical consumer price for electric energy, 13.0¢ per kWh? The following approximation will prove useful:
(a)
Answer to Problem 39.71AP
Explanation of Solution
Given info: The time for one way trip is
Formula to calculate the speed that an astronaut travel relative to Earth is,
Here,
Formula to calculate the relativistic time for trip in frame of Earth reference is,
Here,
Substitute
Substitute
Simplify the equation further,
Use the following approximation
The ratio
`
Substitute
Conclusion:
Therefore, the speed that an astronaut travel relative to Earth is
(b)
Answer to Problem 39.71AP
Explanation of Solution
Given info: The time for one way trip is
Formula to calculate the kinetic energy of the spacecraft is,
Here,
Write the expression for the relativistic factor.
From equation (1), the ratio of
Substitute
Substitute
Substitute
Conclusion:
Therefore, the kinetic energy of the spacecraft is
(c)
Answer to Problem 39.71AP
Explanation of Solution
Given info: The time for one way trip is
Write the expression for the total cost of the energy consume by the spacecraft.
Substitute
Conclusion:
Therefore, the cost of the energy consume by the spacecraft is
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Chapter 39 Solutions
Physics For Scientists And Engineers, Technology Update, Loose-leaf Version
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