Phys Sample Question: escape velocity

[sicboy188]

The fact that the Earth is rotating about its polar axis affects the escape velocity from the surface of the planet. Taking into account the Earth's rotation, the escape velocity at the North Pole is:

a) greater than the escape velocity at the South Pole.
b) less than the escape velocity at the South Pole.
c) greater than the escape velocity at the equator.
d) less than the escape velocity at the equator.

highlight below for the ans and my trubbles with it:
c) greater than the escape velocity at the equator.
wouldn't the centrpital force on the equator be greater on the equator thus requiring a greater escape velocity on the equator than on the polar axis (north or south pole)?

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[tncekm]

So, what's the difference between the north pole, south pole, and equator with respect to its rotation? I'd guess that relative to the north or south poles the equator gives you more kinetic energy since you're rotating at about 900mi/hr (KE = ½mv&#178. If you've got more KE to begin with, you'll need less energy to get you out of orbit. So, at the equators you need a lower escape velocity.

(C)

And, no, I didn't read the answer first!

edit: to further clarify, in order to get out of the atmosphere the rocket has to do work on the shuttle (force applied over some distance). That is, it has to impart energy to the shuttle. So, if it starts out with more energy in the first place (because of its higher relative KE) then it will need less energy input for the same amount of work. Its like, to push a car from stand-still is difficult, but, if you push a car that's already moving and already has some momentum behind it, its much easier.

Not sure if that's totally accurate, but its the best I can do!

 

[sicboy188]

So, what's the difference between the north pole, south pole, and equator with respect to its rotation? I'd guess that relative to the north or south poles the equator gives you more kinetic energy since you're rotating at about 900mi/hr (KE = ½mv²). If you've got more KE to begin with, you'll need less energy to get you out of orbit. So, at the equators you need a lower escape velocity.

(C)

And, no, I didn't read the answer first!

edit: to further clarify, in order to get out of the atmosphere the rocket has to do work on the shuttle (force applied over some distance). That is, it has to impart energy to the shuttle. So, if it starts out with more energy in the first place (because of its higher relative KE) then it will need less energy input for the same amount of work. Its like, to push a car from stand-still is difficult, but, if you push a car that's already moving and already has some momentum behind it, its much easier.

Not sure if that's totally accurate, but its the best I can do!

no this makes sense. i just realized where i made the mistake too. there centrip force on the equator works in the same direction of the as the escape velocity (ie an object on a rotating ball located furthest away from the axis of rotation feels a force pulling it away from the center of the ball). for some reason i guess i just had my vectors messed up.

the energy explanation really does simplify things. Thanks...

 

[tncekm]

no this makes sense. i just realized where i made the mistake too. there centrip force on the equator works in the same direction of the as the escape velocity (ie an object on a rotating ball located furthest away from the axis of rotation feels a force pulling it away from the center of the ball). for some reason i guess i just had my vectors messed up.

the energy explanation really does simplify things. Thanks...

Yeah, the centripital "force" is the force required to keep the object from changing its position from the center of rotation. So, if more force is required to keep it there, then obviously less force is needed to move it away from the earth.

E.g. if you swing a ball around on a string slowly it doesn't take very much force to keep the ball on a string, but as you continually increase the speed of rotation it is harder for the string to hold on and eventually it breaks!

So, just to clarify, the centripetal force doesn't work in the same direction as the escape velocity.

 

[sicboy188]

Yeah, the centripital "force" is the force required to keep the object from changing its position from the center of rotation. So, if more force is required to keep it there, then obviously less force is needed to move it away from the earth.

E.g. if you swing a ball around on a string slowly it doesn't take very much force to keep the ball on a string, but as you continually increase the speed of rotation it is harder for the string to hold on and eventually it breaks!

So, just to clarify, the centripetal force doesn't work in the same direction as the escape velocity.

Oops.. thanks for the clarification.

 

[tncekm]

No problem!