Hi Friend, I have found many questions relating to gravity and UCM. I'm posting one of the typical but confusing problem. Plz have a look.
Q. A car is driven eastward and then westward and finally in the north-south direction and always with a constant speed. Explain how the rate of fuel consumption will vary - if any.
Ans.
We know,
gl = gs - w2Rcos2l [where l= latitude
w = angular velocity of earth]
The angular velocity of earth is in west-east direction and in west to east sense.
Now,
[MOST IMP. READ THOROUGHLY]
When the car moves in west-east direction with a constant linear speed, if its angular velocity due to its own motion be wo , then a due to the additive effect of the angular velocity of earth and that of the car a resultant angular velocity (w+wo) occurs.
Hence the effective acc. due to gravity experienced by the car is
gr = gs - (w+wo)2Rcos2l
Evidently, when the car moves in west to east sense taking the sense of the earth's rotation +ve the value of wo is +ve and for the reverse sense taking the same convention it is -ve.
Therefore for west to east sense,
grw = gs - (w+wo)2Rcos2l
Therefore for east to west sense,
gre = gs - (w-wo)2Rcos2l
Clearly,
(w+wo)2 > (w-wo)2
Hence, grw < gre
We know,
Fk = ukN
as N is proportional to g therefore Fk is also proportional to g.
Hence,
Fkw < Fke
Thus we may conclude that,
The fuel consumption will be low in west to east direction and it will be high in east to west direction.
Now when the car is driven in north-south direction then there is no component of the linear velocity of the car along the west-east direction.
Thus, the frictional force will remain constant.
Hence there will be no variation is fuel consumption.
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