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A futuristic rocket ship of mass mahip- 6.0 x 10° kg is sent into space carrying one person with the goal of traveling to nearby stars. The ship uses a newly discovered matter-antimatter drive that converts matter into energy at 100% efficiency. We will take Earth as the rest frame. For parts (a) through (d) you are interested in the portion of the spaceship's travel where it is using its drive to convert matter into the kinetic energy of the ship. (a) What is the speed of the ship when the work done by the ship's drive is equal to 150,000 TWh (the total energy used by humanity in 2014)? (b) How much work must the drive do for the rocket to reach a final speed of 0.95c? (c) How much matter would the drive need to annihilate in order for the ship to reach the final speed of 0.95c? Assume that the matter used in the antimatter drive is collected from the interstellar medium and that the mass of the ship remains constant.

A futuristic rocket ship of mass mahip- 6.0 x 10° kg is sent into space carrying one person with the goal of traveling to nearby stars. The ship uses a newly discovered matter-antimatter drive that converts matter into energy at 100% efficiency. We will take Earth as the rest frame. For parts (a) through (d) you are interested in the portion of the spaceship's travel where it is using its drive to convert matter into the kinetic energy of the ship. (a) What is the speed of the ship when the work done by the ship's drive is equal to 150,000 TWh (the total energy used by humanity in 2014)? (b) How much work must the drive do for the rocket to reach a final speed of 0.95c? (c) How much matter would the drive need to annihilate in order for the ship to reach the final speed of 0.95c? Assume that the matter used in the antimatter drive is collected from the interstellar medium and that the mass of the ship remains constant.

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A futuristic rocket ship of mass m,hip = 6.0 × 10° kg is sent into space carrying one person with the goal of traveling to nearby stars. The ship uses a newly discovered matter-antimatter drive that converts matter into energy at 100% efficiency. We will take Earth as the rest frame. For parts (a) through (d) you are interested in the portion of the spaceship's travel where it is using its drive to convert matter into the kinetic energy of the ship. (a) What is the speed of the ship when the work done by the ship's drive is equal to 150,000 TWh (the total energy used by humanity in 2014)? (b) How much work must the drive do for the rocket to reach a final speed of 0.95c? (c) How much matter would the drive need to annihilate in order for the ship to reach the final speed of 0.95c? Assume that the matter used in the antimatter drive is collected from the interstellar medium and that the mass of the ship remains constant. (d) When at the final speed of 0.95c, by what factor is the ship's momentum greater than its classical momentum at that same speed. For parts (e) and () you are interested in the portion of the spaceship's travel once it has reached a constant speed of v, = 0.95c. (e) If eight years pass for the person inside the ship, then how much distance in the rest frame does the ship cover? How much distance does the person inside the ship measure? (f) How many years would pass for the person on the ship by the time that the ship covered 100 light years in the rest frame? How much distance does person inside the ship measure in this time? (g) If once the ship was 100 light years from Earth as measured in the rest frame, and then launched a very small rocket with a speed of v' = .56c relative to the ship, then what distance would that small rocket travel as measured by the person in the ship by the time a signal sent back to Earth arrived? Assume the signal was sent by the ship at the moment that the small rocket was launched.
Transcribed Image Text:A futuristic rocket ship of mass m,hip = 6.0 × 10° kg is sent into space carrying one person with the goal of traveling to nearby stars. The ship uses a newly discovered matter-antimatter drive that converts matter into energy at 100% efficiency. We will take Earth as the rest frame. For parts (a) through (d) you are interested in the portion of the spaceship's travel where it is using its drive to convert matter into the kinetic energy of the ship. (a) What is the speed of the ship when the work done by the ship's drive is equal to 150,000 TWh (the total energy used by humanity in 2014)? (b) How much work must the drive do for the rocket to reach a final speed of 0.95c? (c) How much matter would the drive need to annihilate in order for the ship to reach the final speed of 0.95c? Assume that the matter used in the antimatter drive is collected from the interstellar medium and that the mass of the ship remains constant. (d) When at the final speed of 0.95c, by what factor is the ship's momentum greater than its classical momentum at that same speed. For parts (e) and () you are interested in the portion of the spaceship's travel once it has reached a constant speed of v, = 0.95c. (e) If eight years pass for the person inside the ship, then how much distance in the rest frame does the ship cover? How much distance does the person inside the ship measure? (f) How many years would pass for the person on the ship by the time that the ship covered 100 light years in the rest frame? How much distance does person inside the ship measure in this time? (g) If once the ship was 100 light years from Earth as measured in the rest frame, and then launched a very small rocket with a speed of v' = .56c relative to the ship, then what distance would that small rocket travel as measured by the person in the ship by the time a signal sent back to Earth arrived? Assume the signal was sent by the ship at the moment that the small rocket was launched.
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