Centripetal Force + Friction

[Izack]

Hello, it's me again.
I've just picked up the book Rendezvous with Rama by Arthur C. Clarke, and near the beginning (I don't think this counts as a spoiler unless you didn't read the back cover) the Endeavour lands on the end of a rotating cylinder (Rama.) The captain worries that Rama's centrifugal force will sling the ship off the side and into space.

My question is this: would that really happen? There was not yet any hard connexion between Endeavour and Rama other than the static friction between the landing struts and the surface. Is a soft contact like that enough to impart a centrifugal velocity?

 

[tori]

Upon contact any friction would apply some force to the Endeavour in the direction you're describing. The bounce of the contact would also give it some kind of backwards velocity, preventing it from further contact with the Rama (unless thrusters are fired). So it would slowly drift away.

I'm gonna admit that I haven't read the book, so I don't know what could hold that ship's struts on the cylinder (produce static friction), but if all it had was inertia, then yes, it would fly off, since it would "bounce" off shortly after contact (the static friction would be only temporary).

 

[Izack]

There were pillars of some sort nearby which they rested the ship against to prevent further outwards movement. But...wouldn't they bounce from those too? There was no method of attachment mentioned other than contact and a tiny force of gravity from Rama (it weighed "at least ten trillion tons".)

 

[tori]

If those pillars looked anything like those red things, then the apparent centrifugal force (green arrow) caused by the Rama spinning (orange arrows) would rest the ship (green box) on them just like gravity, so even if they bounced off a little, they would eventually come to a rest, just like when landing.

 

[Izack]

So Clarke did know his stuff.

I have one more question, which is pretty simple... If the ship were inside the cylinder, and there was no atmosphere inside it, there would be no outwards force on the vehicle, correct? So, by this line, if the ship were landed on the inside of the cylinder (which had 10m/s^2 centrifugal acceleration, similar to Earth's gravity) and made a tiny thrust away from the apparent nadir, would it no longer be affected by the centrifugal acceleration (assuming that the cylinder's real gravity had no effect on it, thanks to my previous question's answer :tiphat?

 

[tori]

It wouldn't be affected by the centrifuge anymore (the crew would feel zero gravity), but the ship would continue moving sideways, until it would hit the Rama and get accelerated by it again.

Now if you think about it, that's exactly what happens in a regular gravity field - you jump up and you stop feeling gravity until you hit the ground again. So it behaves just like gravity, again.

Clarke did indeed know his stuff :thumbup:

 

[mohammednasim]

Wait, centrifugal force in an inertial frame?

If those pillars looked anything like those red things, then the apparent centrifugal force (green arrow) caused by the Rama spinning (orange arrows) would rest the ship (green box) on them just like gravity, so even if they bounced off a little, they would eventually come to a rest, just like when landing.

Wait, how do you depict centrifugal force in an inertial frame? Centrifugal force is a pseudoforce which applies only when you're in a non-inertial frame. The green arrow would have made sense if you were inside that little cube (which is again, a non inertial frame of reference).
I can't call it centripetal force, only because it doesn't point to the center of that cylinder. In short, there's a problem with that little green arrow.

 

[River Crab]

The green arrow shows apparent centrifugal force. If it were centripetal force, it would lie on a tangent of the circle at the end of the cylinder, but there's nothing wrong with it as it is, I think.

 

[tori]

The green arrow would have made sense if you were inside that little cube

What makes you think that the observer isn't inside? Just because my camera was outside doesn't mean the observer (in this case the entire Endeavour spacecraft = the green cube) was too.

 

[Andy44]

Clarke did indeed know his stuff, but ironically Rama is one of the few stories he wrote where he got something completely wrong!

The trajectory that Rama follows through the Solar system doesn't jive with the time scales he gives in the book. About 2 years ago some guys here on the forum tested it in Orbiter and couldn't make things match up. So it appears that this would one of the few times that Clarke got lazy and didn't do his homework!

 

[dougkeenan]

Maybe Clarke got it right and Martins got it wrong.

Or not. :lol:

 

[Izack]

The green arrow shows apparent centrifugal force. If it were centripetal force, it would lie on a tangent of the circle at the end of the cylinder, but there's nothing wrong with it as it is, I think.

Wouldn't a centripetal force point directly to the middle of the circle?

If anything's on a tangent to the outside edge, it's inertia.

 

[Izack]

A quick search gave me a link to this thread about Rama's orbit. I assume this is what you meant, Andy? (I didn't read it because I'm still not done the book )

Just thought I'd add it in case someone stumbles across this thread in the future and finds it useful.

 

[mohammednasim]

The green arrow shows apparent centrifugal force. If it were centripetal force, it would lie on a tangent of the circle at the end of the cylinder, but there's nothing wrong with it as it is, I think.

I disagree centripetal force is never, never tangential. For instance, the sun's gravity on earth is centripetal if you're looking at the solar system from somewhere far beyond. Assuming our presence on earth, the Sun's gravitational influence is centrifugal.
And velocity is tangent to the circular path (as we plot it). http://en.wikipedia.org/wiki/File:Centripetal_force_diagram.svg

Here's a great tutorial on centripetal force. http://khanexercises.appspot.com/video?v=TNX-Z6XR3gA

Moreover, this article clearly states that centrifugal force is fictitious and is a direct consequence of any given non-inertial frame of reference. [ame="http://en.wikipedia.org/wiki/Centrifugal_force"]Centrifugal force - Wikipedia, the free encyclopedia[/ame]

Cheers.

---------- Post added at 06:41 PM ---------- Previous post was at 06:37 PM ----------

Wouldn't a centripetal force point directly to the middle of the circle?

If anything's on a tangent to the outside edge, it's inertia.

Izack got it perfect. Centripetal force points directly to the middle of the circle.
And velocity is indeed tangential at any point.

 

[tori]

Centripetal (lat. centrum, petere) force is by definition perpendicular to the tangent of the circle. It can never be anything else, and that includes it being tangential.

Sun's gravitational acceleration acting on Earth is always centripetal, no matter where the observer is.

 

[statickid]

<snip>

Moreover, this article clearly states that centrifugal force is fictitious and is a direct consequence of any given non-inertial frame of reference. Centrifugal force - Wikipedia, the free encyclopedia

Cheers.

---------- Post added at 06:41 PM ---------- Previous post was at 06:37 PM ----------



Izack got it perfect. Centripetal force points directly to the middle of the circle.
And velocity is indeed tangential at any point.

whereas the "centrifugal force" is "fictitious" it has not been eradicated. There is an observable phenomenon that appears (by illusion) that a force is acting when there is not. However, it is has been deemed correct to refer to this as the reactive or apparent centrifugal force that tori has illustrated. I don't see anything wrong with tori's illustration in this sense as they have indicated it is "apparent."

the other arguments are indeed correct as well, the centripetal force must point at the center and not tangential because it is the force that directly holds the body at a distance from the center whether it be a wall or what have you.

one main difference between landing in the area indicated and just by gravity is that while preparing to land, a ship with no tangential velocity would, to the pilots, seem to be travelling over the landing area at the velocity of the spinning cylinder. they would either have to match this or deal with its consequences. making contact with the surface would impart some movement to the ship and complicate the landing. It would definitely not be as "easy" as making a hovering vertical landing as though there were gravity. docking to a port would probably be much easier.

 

[tblaxland]

Sun's gravitational acceleration acting on Earth is always centripetal, no matter where the observer is.

A minor nit here. Since the Earth's orbit is elliptical, the gravitational acceleration of the Earth by the Sun has both centripetal and tangential components for all parts of its orbit except the apsides (and is a good way of visualising why the Earth speeds up as it approaches perihelion and slows down as it approaches aphelion).