Zorch, an archenemy of Superman, decides to slow the earth\'s rotation to once p
ID: 2259170 • Letter: Z
Question
Zorch, an archenemy of Superman, decides to slow the earth's rotation to once per 29.0 h by exerting an opposing force at the equator and parallel to it. Superman is not immediately concerned, because he knows Zorch can only exert a force of 5.00 ? 107 N (comparable to a Saturn V rocket's thrust). Assume the earth's initial rotation is exactly once per 24.0 h and use energy considerations to find how long Zorch must push with this force to accomplish his goal. (This gives Superman time to devote to other villains.)
Explanation / Answer
According to Source given below, the mean value of Earth Rotational Inertia is 8.023 x 10^37 kg.m^2
The equatorial radius of the earth 6378 km
So the braking Torque of Zorch = Force x radius = 3.50 x 10^7 x 6.378 x 10^6 = 2.2323 x 10^14 N.m
Torque = I ?
Angular deceleration = T / I = 2.2323 x 10^14 / 8.023 x 10^37
? = - 0.278 x 10^ -23 rad /sec^2
Initial angular vel , ?o = 1rev /24 hr = 2 ? / 24 x 3600 = 7.272 x 10^ -5 rad /s
Final angular vel, ?f = 1rev/29 hr = 2 ? / 29 x 3600 = 6.018 x 10^ -5 rad /s
Time = ?f - ?o / ?
= (6.018 x 10^ -5 - 7.272 x 10^ -5) / - 0.278 x 10^ -23
= 4.51 x10^18 sec
1Yr = 365.25 (days) x 24 (hrs) x 3600 (sec) = 3.156 x10^7 sec
Time = 4.51 x10^18 / 3.156 x10^7
= 1.429 x 10^11 years
= 142,900,000,000 Years
That is almost 143 Billion years
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.