Kaplan FL 5 PS Q42

[upchurch]

The fact that the earth is rotating about its polar axis affects the surface escape velocity from the surface of the planet. Taking into account earth's rotation, the escape velocity at the North Pole is:
a) greater than the escape velocity on the south pole.
b) less than the escape velocity on the south pole.
c) greater than the escape velocity on the equator.
d) less than the escape velocity on the equation.

The answer is c, but I don't really understand Kaplan's explanation as to why.

Can anyone explain why? Thanks!

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[Wakesc]

Honestly not sure but I would assume since it's rotating around it's polar points that there is little ummm centripetal force (for lack of a better word) holding in compared to around the equator.

 

[TwoPaddles]

The fact that the earth is rotating about its polar axis affects the surface escape velocity from the surface of the planet. Taking into account earth's rotation, the escape velocity at the North Pole is:
a) greater than the escape velocity on the south pole.
b) less than the escape velocity on the south pole.
c) greater than the escape velocity on the equator.
d) less than the escape velocity on the equation.

The answer is c, but I don't really understand Kaplan's explanation as to why.

Can anyone explain why? Thanks!

You can use the escape velocity formula
v = sqrt(2GM/r)

Considering that the north pole has a smaller radius than the equator, a smaller number in the denominator will give you a large velocity; whereas in the case of equator, r value is larger and therefore the velocity is smaller.

 

[ilovemcat]

You can use the escape velocity formula
v = sqrt(2GM/r)

Considering that the north pole has a smaller radius than the equator, a smaller number in the denominator will give you a large velocity; whereas in the case of equator, r value is larger and therefore the velocity is smaller.

Did you mean v = sqrt(GM/r)?

 

[TwoPaddles]

Did you mean v = sqrt(GM/r)?

No there's a 2 in there; here's some more info on escape velocity if you need: http://en.wikipedia.org/wiki/Escape_velocity

The formula is in there as well.

 

[ilovemcat]

No there's a 2 in there; here's some more info on escape velocity if you need: http://en.wikipedia.org/wiki/Escape_velocity

The formula is in there as well.

Ah okay. I thought you derived the other formula by equating the Gravitational Force (GMm/R^2) to the Centripetal Force (mv^2/r) and then solving for V. The way they solved it was by doing something weird lol. Are we suppose to know remember that equation for the MCAT?

 

[TwoPaddles]

Ah okay. I thought you derived the other formula by equating the Gravitational Force (GMm/R^2) to the Centripetal Force (mv^2/r) and then solving for V. The way they solved it was by doing something weird lol. Are we suppose to know remember that equation for the MCAT?

I don't think so, since it's not even in the AAMC content outline list. They would probably give it in a passage if we were to use it.