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23 Feb 2007 20:59:40 IST
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Q.Two Identical trains are moving on rails along the equator on the Earth in opposite directions with same speed.They will exert the same pressure on the rails . True/False
A.false because the angular speed and hence the required centripetal force fo both the trains will be different..
Why? Cant get the logic....
tibu
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Rajat Barve
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23 Feb 2007 21:03:42 IST
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why would they have different angular speeds.u said they have same speed and radius is same.therefore angular speed should also be the same.hence, the answer should be -true
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23 Feb 2007 21:09:38 IST
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It should be false as the angular speeds would be different.
What u ppl are taking is angulas speer wrt earth but here we will have to consider angular speed as observed from outside the earth.
Now, one train is moving in the direction of rotatuon of th earth while the other train is moving opp to the direction of sipn of the earth. So, the one moving in the direction of spin of the earth will have a greater angular speed to the train moving opp to the direction of spin on the earth.
23 Feb 2007 21:13:35 IST
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because the earth is also revolving !! the train moving with the direction of the earth has to apply less force and hence less pressure since it's angular velocity w.r.t earth is less.so less centripetal force
whereas, the train moving against the direction of angular velocity of the earth has to applya negative torque to move forward.hence, greater force or greater pressure as it has greater relative angular velocity!!
hope u understood ! do reply if u don't understand !
23 Feb 2007 21:16:07 IST
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Hi tibu,
Look,
The velocity of the trains according to the formula v = r
would be the same. But you have to add the velocity of earth's rotation also. Let velcity of the trains according to v = r be v1. Andlet speed of earth be v2. So, net velocities of the trains are v1+ v2 , v1 - v2.
would be the same. But you have to add the velocity of earth's rotation also. Let velcity of the trains according to v = r be v1. Andlet speed of earth be v2. So, net velocities of the trains are v1+ v2 , v1 - v2. Hope you got it !!!
Do inform in case of problems.
26 Feb 2007 11:53:21 IST
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If the case is observed from the earth then their velocoties are equal.
But from outside the earth one train would be having angular velocity in the direction of earth's angular velocity and the angular velocity for the other would be in opposite direction.
Hence the pressure exerted would be different.
Best Wishes
But from outside the earth one train would be having angular velocity in the direction of earth's angular velocity and the angular velocity for the other would be in opposite direction.
Hence the pressure exerted would be different.
Best Wishes
26 Feb 2007 12:10:27 IST
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I agree with bipin, and lemme explain a little bit more...
Although earth can be considered an inertial frame of reference, it is not perfectly an inertial frame of reference as it has centripetal acceleration, (and maybe some other accelerations if the solar system is accelerating)
So, we must consider pseudo forces while working from earth frame, or we should work from space frame as Aditya has explained, both cases giving the same result...
But one more point to tell is that there are two more pseudo forces when the frame of reference is rotating, (corriolis force, and the 'third force') but these are not in your syllabus... so if you get stuck in some problem of rotating frame... you may well leave it.. (actually here also, corriolis force is acting on the train, downwards in one case and upwards in another, hence changing the pressure on the ground)
Although earth can be considered an inertial frame of reference, it is not perfectly an inertial frame of reference as it has centripetal acceleration, (and maybe some other accelerations if the solar system is accelerating)
So, we must consider pseudo forces while working from earth frame, or we should work from space frame as Aditya has explained, both cases giving the same result...
But one more point to tell is that there are two more pseudo forces when the frame of reference is rotating, (corriolis force, and the 'third force') but these are not in your syllabus... so if you get stuck in some problem of rotating frame... you may well leave it.. (actually here also, corriolis force is acting on the train, downwards in one case and upwards in another, hence changing the pressure on the ground)
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