6. A cloaked Borg ship enters the solar system on a mission to destroy the Earth

Question

6. A cloaked Borg ship enters the solar system on a mission to destroy the Earth. Their plot is to stop the Earth from rotating by firing their "earth de-roton beam" tangent to the surface and opposite its direction of rotation. Assume the earth rotates counter-clockwise as viewed frotm the north pole. By de-spinning the earth, half of the surface will experience continuous daylight for half the year the dramatie temperature change will kill crops and destroy humanity. Do not assume that the needed numbers are provided for you in this problem.] (a) If the Borg want to de-spin the earth in one-week, what angular acceleration must their de-roton beam achieve? (b) Three days after the Borg have begun their evil plan, Captain Riker and the crew of the Er discover the cloaked Borg ship and destroy it. How long is the lemgth of the Earth's day (in hours)? (c) Relative to a nou-rotating observer orbiting the sun along the Earth's orbit, what is the traanslational speed of somcone standing on the Earth's rotating surface (in m/s and before the Borg attack)?

Explanation / Answer

a) Present angular speed of earth = 2 pi /T, where T is length of a day. = 86400 seconds
so wo = 2 pi / 86400 = 7.3x10-5 rad/sec.
Final angular speed = 0, time to achive this = 7 days = 6.05x105 seconds
angular acceleration = change in angular speed / time = 1.2x10-10 rad/sec2

b)Angular speed after three days ( 259200 sec.) w = wo - alpha * t = 7.3x10-5 - 1.2x10-10 *( 259200)
= 4.2x10-5 rad/sec
length of day = 2 pi / w = 149523 = 41.5 Hrs

c) Speed of earth's surface = wR , where R is radius of earth = 6.4x106 m

= 7.3x10-5 * 6.4x106 = 467.2 m/s

  

Related Questions

Navigate

• Browse (All)
• Browse 6
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.