Print

Please login or register.
1 Hour 1 Day 1 Week 1 Month Forever
Login with username, password and session length

[ashersky]

Okay, can someone help me out with this physics problem:

You have a marble moving in a hemispherical (frictionless) "bowl".  The vertical distance from the marble to the bottom of the bowl is y, and the radius of the hemisphere is R.  What is the minimum angular velocity, in terms of R, y, and g (acceleration of gravity), at which the marble will continue to move in a circle (rather than sliding down to the bottom of the bowl)?

For context, this is the second part of a three-part problem.  The first part asked for an expression for the angular velocity, and I got sqrt(g/(R-y)), which was correct.

I want to set the y-component of the Normal force greater than or equal to mg, because that would make the net acceleration vector point downward (and toward the center of the circle).  But whenever I do that, I just end up with the same thing that I got for the first part (sqrt(g/(R-y))), which is wrong.

Pretty sure the answer is: Moat     

[scott_pilgrim]

Are you supposed to know the formula of the centrifugal force for a circular motion?

EDIT: or equivalently, basic non Galilean frame transformations?

I'm not sure exactly what you're asking.  Centrifugal force is not a real thing, right?  I don't know what a non Galilean frame transformation is, that sounds too fancy for a high school physics class (I'm not in high school, but I'm working with someone who is).  Centripetal force should be mv^2/r (where lowercase r is the radius of the circle the ball is moving in; you could use Pythageorean theorem to get little r in terms of big R and y), which should be equal to the x-component of the Normal force.  (I assume that part is right, because I used that in my solution to the first part, which was correct.)  My intuition says that in order for the ball to not slide into the bottom of the bowl, the y-component of the Normal force must be greater than or equal to the weight.

In a somewhat related problem, I had a bunch of people in an amusement park ride that spun in a vertical circle (like a ferris wheel, but with the people inside the circle), and I needed to find the minimum angular velocity to keep the people from falling down at the top of the circle.  For this one, I just set the normal force greater than or equal to the weight and solved for v (and then converted linear velocity to angular velocity), and that worked.

So I thought something similar should work for the original problem.  The difference is that now the Normal force points at an angle (instead of completely vertically), so I thought now we should be looking at just the y-component of the Normal force in comparison to weight.  But that doesn't seem to work.

[pacovf]

Are you supposed to know the formula of the centrifugal force for a circular motion?

EDIT: or equivalently, basic non Galilean frame transformations?

I'm not sure exactly what you're asking.  Centrifugal force is not a real thing, right?  I don't know what a non Galilean frame transformation is, that sounds too fancy for a high school physics class (I'm not in high school, but I'm working with someone who is).  Centripetal force should be mv^2/r (where lowercase r is the radius of the circle the ball is moving in; you could use Pythageorean theorem to get little r in terms of big R and y), which should be equal to the x-component of the Normal force.  (I assume that part is right, because I used that in my solution to the first part, which was correct.)  My intuition says that in order for the ball to not slide into the bottom of the bowl, the y-component of the Normal force must be greater than or equal to the weight.

In a somewhat related problem, I had a bunch of people in an amusement park ride that spun in a vertical circle (like a ferris wheel, but with the people inside the circle), and I needed to find the minimum angular velocity to keep the people from falling down at the top of the circle.  For this one, I just set the normal force greater than or equal to the weight and solved for v (and then converted linear velocity to angular velocity), and that worked.

So I thought something similar should work for the original problem.  The difference is that now the Normal force points at an angle (instead of completely vertically), so I thought now we should be looking at just the y-component of the Normal force in comparison to weight.  But that doesn't seem to work.

You can work it out with what you call the centripetal force too.

You got the right intuition, but you are trying to compensate the wrong component of the weight. You have to compensate the projection of the weight on the (local) surface of the bowl.

Aside: To the best of my knowledge, centrifugal and centripetal forces are names applied to any number of forces in circular motions. When people say that "centrifugal force is not a real thing", what they really mean (if they know what they are talking about) is that it does not exist when studying circular motions in Galilean frames. However, if you place yourself in a non-Galilean frame, independently of your motion in the new frame, a series of inertial forces appear (among them, the "centrifugal force"), which you have to take into account in your analysis.

[ConMan]

Are you supposed to know the formula of the centrifugal force for a circular motion?

EDIT: or equivalently, basic non Galilean frame transformations?

I'm not sure exactly what you're asking.  Centrifugal force is not a real thing, right?  I don't know what a non Galilean frame transformation is, that sounds too fancy for a high school physics class (I'm not in high school, but I'm working with someone who is).  Centripetal force should be mv^2/r (where lowercase r is the radius of the circle the ball is moving in; you could use Pythageorean theorem to get little r in terms of big R and y), which should be equal to the x-component of the Normal force.  (I assume that part is right, because I used that in my solution to the first part, which was correct.)  My intuition says that in order for the ball to not slide into the bottom of the bowl, the y-component of the Normal force must be greater than or equal to the weight.

If you use co-ordinates that are rotating, then there is an additional acceleration that appears, which is the centrifugal force. It doesn't behave quite like normal forces because it's an artifact of the co-ordinate system, and so it's called a virtual force. This is one of those things where you get told something, then get told it's a lie and told something else, then get told that that too is a lie and the original lie is not quite so untrue from a certain perspective.

[scott_pilgrim]

You got the right intuition, but you are trying to compensate the wrong component of the weight. You have to compensate the projection of the weight on the (local) surface of the bowl.

Okay, I think I see what you're saying.  Just to make sure, here's a picture I drew in paint.net:



So I wanted to set N_y (which is just Nsin(theta)) equal to mg, but you're saying it should be N=mgsin(theta).  And that makes sense, because the other component of the weight isn't doing anything to the Normal force.  I can also see how that's analogous to the other problem with the vertical circle.  Then I should be able to get the rest of it from there.

Thanks for your help!

[Seprix]

I'm pretty sure centrifugal force is a real thing.

[sudgy]

Ah, θ.  So hard to type.

[Seprix]

Ah, θ.  So hard to type.

Theta?

[pacovf]

So I wanted to set N_y (which is just Nsin(theta)) equal to mg, but you're saying it should be N=mgsin(theta).  And that makes sense, because the other component of the weight isn't doing anything to the Normal force.  I can also see how that's analogous to the other problem with the vertical circle.  Then I should be able to get the rest of it from there.

Thanks for your help!

No problem. It took me more than I would care to say to find out which component of the weight you wanted to compensate...

Note that if you use the "centripetal force" analysis, you aren't actually compensating anything. You are finding the value of y for which the weight plus the normal reaction of the surface equate the required centripetal force to sustain the circular motion.

The reason why, when you look at it backwards (or using centrifugal force analysis instead), you are trying to compensate the projection of the weight on the local surface of the bowl is because the projection of the weight on the normal of the surface of the bowl is always compensated by the reaction of the surface, so you don't care about it.

... I don't know if that makes anything clearer, or quite the opposite.

EDIT: I've reread your analysis. Yes, you want N_y = mg to force the sum of the weight and the normal reaction to be horizontal. You were forgetting the principal characteristic of the normal reaction, which is to compensate all forces in the direction of the normal to the surface. Since here the only other force is the weight, this is what gives the relation |N| = mg*sin(theta).

I'm pretty sure centrifugal force is a real thing.

One thing I've learnt during my short existence on this Earth is how irredeemably subjective the word "real" is.

[eHalcyon]

[Titandrake]

I've watched Meet the Soldier around 10 times, and only noticed one of the jokes after somebody pointed it out to me.

At the end of the video, when the Soldier says "And that's why whenever there's a bunch of animals in one place it's called a ZOO!", he's actually saying, "And that's why whenever there's a bunch of animals in one place it's called a TZU!" His speech is about Sun Tzu building an ark, getting two of every animal and beating the crap out of all of them, and that's where he thinks the name comes from.

This whole time I thought it was just a non-sequitur.

[Archetype]

[Ozle]

Mate came to the pub the other day
'Get Ozle, you like games, I've got a great new one you should try. It's called Dominion!"

[Witherweaver]

Mate came to the pub the other day
'Get Ozle, you like games, I've got a great new one you should try. It's called Dominion!"

Take him up on the offer.  Propose playing for money to make things more interesting.

[Polk5440]

Mate came to the pub the other day
'Get Ozle, you like games, I've got a great new one you should try. It's called Dominion!"

I don't even care if you just made this up. I could totally see this happening to me, too.

[Kirian]

Aside: To the best of my knowledge, centrifugal and centripetal forces are names applied to any number of forces in circular motions. When people say that "centrifugal force is not a real thing", what they really mean (if they know what they are talking about) is that it does not exist when studying circular motions in Galilean frames. However, if you place yourself in a non-Galilean frame, independently of your motion in the new frame, a series of inertial forces appear (among them, the "centrifugal force"), which you have to take into account in your analysis.

XKCD:  A relevant comic for almost any scientific subject.

[Seprix]

Mate came to the pub the other day
'Get Ozle, you like games, I've got a great new one you should try. It's called Dominion!"

Do you hear that sound? That is the sound of free money.

[Kuildeous]

Mate came to the pub the other day
'Get Ozle, you like games, I've got a great new one you should try. It's called Dominion!"

Do you hear that sound? That is the sound of free money.

The con may be up when he buys a Chapel despite having no Witch on the board.

[pacovf]

So, I just finished watching Evangelion just to see what all the fuss was about (spoiler alert: naked 14 year old kids).

Well, it was something, that much I can say. I wasn't particularly offended by the final two chapters, knowing that the studio was basically bankrupt by then, although they definitely could have dedicated a bit more than two frames and five sentences to the actual plot, and the congratulations were uncalled for.

Then I watched the End of Evangelion. It was hard to follow the plot even before it got mythological, then it got even harder as huh well shit goes down, and then there's the choking thing and my brain just BSoD'd.

So of course I went to the interwebs to seek answers. And in the end I kinda understood the mythos; in hindsight there are hints here and there in the series, even though a lot of them are of the blink-and-miss variety (and bad subs don't help). I'm still completely at a loss about the choking thing though, so huh any fellow geek wants to try to explain it to this troper?

[Awaclus]

I thought the choking was one of the more straightforward parts of EoE. I've only seen it twice, though.

[Ichimaru Gin]

I saw it for the first time a few months ago. I don't pretend to be an expert on it. However, the explanation I normally here is Shinji was the first one to emerge from the LCL and had been by himself for awhile. He was already pretty emotionally unstable for a lot of the show and had some conflicted feelings about Asuka--and was also confused about sex and relationships and in general. So being in isolation just made him even more insane. He might have seen Asuka as trying to kill him (sometimes sexual attraction is viewed as an attack) and responded in "self-defense". Also, there's the whole thing with Instrumentality making the world perfect--something, something that means everything he did was permissible. I don't know. I just enjoyed the whole thing for what it was. Definitely one of the better animes I've watched, though it is very polarizing in terms of whether people love the show or hate it. I fall into the category of preferring the movie ending, which I'm fairly certain is the minority.

Edit: added a few more details

[pacovf]

I thought the choking was one of the more straightforward parts of EoE. I've only seen it twice, though.

There's two choking scenes. The first one, Shinji is the focus of the End of the World, and dreaming some sort of nightmare. The choking is just whatever.

The second one, however, Shinji has just reached the conclusion that he needs other people if he ever wants to be happy; I read that, if not necessarily as the end of his depression, at least as a will to improve. So he stops the Human Complementation, and is deposited back on Earth, together with his "it's complicated" partner, Asuka, apparently sleeping. For all he knows, it might be the only human he is going to see in a long, long time.

His first reaction is to choke her.

That would have been surprising at certain points of his character development, and outright impossible at others. By the end of the movie, I just don't see how that makes sense.

tl;dr: your definition of straightforward is different from mine.

PPE: Shinji wasn't violent during the whole Instrumentality thing. He went from afraid and disgusted with himself to accepting himself and others, both in the anime and in the movie. I mean, the whole purpose of the Instrumentality plan was to heal humanity. I just don't see the rape-violence right after he wakes up.

[Ichimaru Gin]

The other major answer I hear is that reasons behind Shinji's reaction are unknowable or unexplained (2deep4me). I'm betting there was a difference between being part of Instrumentality and then returning to a human body--I don't think you keep the same connection with others once you separate. I don't think the humans had perfect knowledge about exactly what Instrumentality would mean either.

[pacovf]

The other major answer I hear is that reasons behind Shinji's reaction are unknowable or unexplained (2deep4me).

That seems like a lazy answer to me. Shinji's reaction cannot be unknowable, since someone wrote that scene. It is unexplained, sure, but because of the placement of the scene, I understand that we are expected to glean some meaning from it, even if that meaning is not unique.

I'm betting there was a difference between being part of Instrumentality and then returning to a human body--I don't think you keep the same connection with others once you separate. I don't think the humans had perfect knowledge about exactly what Instrumentality would mean either.

Eh, I guess you could say that scene can be explained by the shock of Shinji coming back, assuming that it was the oneness with others which let him get over his depression, and not something coming from himself. So suddenly he is back to Earth, and so is the despair, and he is momentarily overwhelmed from being back to square one... I guess... Not the most uplifting of endings, then.


Also, don't you like big chunks of black, Ichi? I sure do.

[Ozle]

I think it turned out to be all a dream