Suppose that due to a gravitational torque exerted by the Moon on the Earth, our
ID: 1468271 • Letter: S
Question
Suppose that due to a gravitational torque exerted by the Moon on the Earth, our planet's rotation slows at a rate of 1.40 ms/century. Calculate the Earth's angular acceleration due to this effect. Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully, rad/s^2 Calculate the torque exerted by the Moon on the Earth. Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. Calculate the length of the wrench an ordinary person would need to exert such a torque, as in Figure P10.67. Assume the person can brace his feet against a solid firmament and exert a 700 N force. Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully.Explanation / Answer
A:-
The angular velocity of the earth is V = 2pi/24 hours.
where, 24 hours is the period of rotation.
In radians/sec,it will be:- V = 2pi/(24*60*60) = 2pi/86400= 7.27/10^5
Now,Due to the moon, the period lengthens by 1.4 milli seconds per century.
Convert this to seconds/seconds: 1.4/(1000*100*365.25*24*60*60) = 4.436*10^-13
So after 1 second, the angular velocity is V1 = 2pi/(86400+ 4.436*10^-13)
Angular acceleration is A = V1-V = 2pi/(86400+ 4.436*10^-13) - 2pi/86400
= -3.73*10^-22 radians/second^2
B:- Torque = IA, I is the moment of inertia and A is the angular acceleration.
I = (2/5) mr^2
where
m is the mass of the earth = 5.9742 × 10^24kg
r is the radius of the earth = 6.38*10^6 meters
Torque=(2/5) * 5.9742 * 10^24 * (6.38*10^6)^2 *3.73*10^-22= 362.82*10^14
= 3.62 * 10^17 Newton meters.
C:- 700 * L = 3.62* 10^17 where, L is required length.
L = 3.62 * 10^17/700=5.17* 10^14 meters.
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