Shoutbox

doesn't move

quote:

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Originally posted by krissy-afc
The gravity will effect the right hand side more though

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no it wont...

there is more mass* on the left, hence, left-side.

The angles are irrelevant in a _frictionless_ environment**...

And since you don't have friction, you also do not need to know the exact figures like mass, angles, length, etc. All you need to know is that one end is longer than the other and that they are both slopes. So, the question isn't actual 'vague' at all.

** Unless the angle would be 0° (flat), in that case the gravitational pull on the left is cancelled out by the counterforce of the flat bed. And since there is nothing to 'hold' the chain on the right (it isn't flat; thus no counterforce), it would move right... very very slowly at first of course, but it will move...

*assuming the total mass of the chain is evenly distributed across its length of course.

PS: A chain isn't going to fall slower if you hold it in a 45° angle than when you hold it in a 90° angle! It would fall just as quick in a frictionless environment.

Or put in another way, if there is no friction, the angle of the slopes don't matter and could also be both 90° for all it matters. Looking it that way I think there would be no doubt that the chain would fall to the left.

This is exactly the same question as what would fall faster in a vacuum: 10Kg feathers or 10Kg lead. The answer is, because there is no friction (air resistance) to take in account: they fall at the same speed. In the real world 10Kg feathers would fall slower because of the air resistance/friction.




*at least I think, no?*

EDIT: no

Frictionless just means there's no counterforce along (i.e. preventing it from sliding across the surface), both Chancer and blessedguy already incorporated that into their models.

Regardless of friction, a component of the gravitational force on the object is into the sloping surface and similarly the ground is exerting an equal force onto the object at an angle perpendicular to the surface (see Wcos(A) in Chancer's model) which acts to cancel out a part of the gravitational force.


Probably a bit more intuitive to think of a practical example:
A man who is skating across ice which is angled ever so slightly downwards will not be accelerating at anywhere even remotely near the same rate at which a man who fell through the ice (or jumped out of a plane) would be.


The only difference friction would make is that there would be an additional force acting in the same direction as T (the tension on the rope in Chancer's model) i.e. across the surface, preventing it from sliding -- which as you can see has been omitted in his model :)

PS: I know im terrible at explaining stuff :P

One last go: a portion of the gravitational force is into the surface which is completely counteracted by equal+opposite force (stopping it from falling through the object). Therefore the only remaining net force is that portion of the gravitational force which remains.
The lesser the slope, the greater the component of the gravitational force which is counteracted (as there is a greater portion being applied into the surface).

quote:

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Originally posted by CookieRevised
This is exactly the same question as what would fall faster in a vacuum: 10Kg feathers or 10Kg lead. The answer is, because there is no friction (air resistance) to take in account: they fall at the same speed. In the real world 10Kg feathers would fall slower because of the air resistance/friction.

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What has mass got to do with acceleration due to gravity? In a vacuum, even 1g of feather would fall in the same time as 10kg of lead, if dropped from the same height.

I think what Volv is trying to explain here is that the force of gravity has been restricted to that of the motion of the plane due to the slope being an immovable plane.

So when we measure Force along (parallel to) the plane, it becomes a component of the downwards force.

This is described in blessedguy's post as proportional to (cos A)*(mass of chain above BC) or Chancer's post as W sin ( a ).
(On the left hand side)
Both being the same thing really.

My previous post was showing the proportions of mass on either side as being proportional to the inverse of these values.
This shows no movement in the chain.


Been a while since I've done maths. Good brain exercise.

quote:

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Originally posted by Felu

quote:

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Originally posted by CookieRevised
This is exactly the same question as what would fall faster in a vacuum: 10Kg feathers or 10Kg lead. The answer is, because there is no friction (air resistance) to take in account: they fall at the same speed. In the real world 10Kg feathers would fall slower because of the air resistance/friction.

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What has mass got to do with acceleration due to gravity? In a vacuum, even 1g of feather would fall in the same time as 10kg of lead, if dropped from the same height.

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yes, but they are made the same weight exactly to rule out the difference in weight; to keep things simple when you do the 'experiment' in a non-vacuum environment.

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Volv, reading your example made me see the error, thanks. (wasn't such a crappy example as you thought afterall ). So I stand corrected...

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But I now think, and even convinced, that the chain wouldn't move at all actually, no matter what the angles are (so even no math or equations needed) The whole thing is like a static block.

Think about it, what if you have something hanging from below connecting both ends of the chain. It would mean that there would be a 'force' pulling on each side eaqually from below no (so it doesn't matter if it is there or not)? So, if the top piece of the chain would move to some direction, it means the bottom part would move too (in the opposite direction). If that would happen, you would have something like a perpetual machine! Which isn't possible becaue there is no force to maintain it... hence, it would never move, no matter the angles and the lengths of the slopes, as long as both the 'bottom' parts are on a horizontal plane. Or am I missing something again (quite possible though, I'm not that awake anymore)?...

EDIT: wait... ermmm.

EDIT2: yeah, no movement...

EDIT3: ermm... hang on ... blah.... I give up... and now I can't sleep thinking about this all morning (8am already)
* CookieRevised shoots SonicSam for asking such questions...

quote:

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Originally posted by CookieRevised
If that would happen, you would have a perpetual machine! Which isn't possible

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how would it be a perpetual machine

quote:

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Originally posted by toddy

quote:

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Originally posted by CookieRevised
If that would happen, you would have a perpetual machine! Which isn't possible

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how would it be a perpetual machine

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because if it would move, it would keep on moving forever because nothing has changed in the system compared to the previous move because one end was connected to the other end. So, let's say it moves to the left (counterclockwise) on top, then a piece of the bottom chain would move a bit up to the right and a new piece from the once on top chain would become now the bottom chain. Again having equally amount of 'chain' on the top. Because it is the same length, mass, whatever as before. So the system is still the same. And hence, if it would have moved the first time it should be moving again now, (EDIT) like a perpetual machine. But that isn't possible.

EDIT: I meant: it is _like_ a perpetual motion machine _if_ the first inital movement made sense and if there is something to maintain it (aka if there was some unbalance in forces).

I really should not post when I'm tired, sorry

quote:

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Originally posted by CookieRevised

quote:

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Originally posted by Felu

quote:

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Originally posted by CookieRevised
This is exactly the same question as what would fall faster in a vacuum: 10Kg feathers or 10Kg lead. The answer is, because there is no friction (air resistance) to take in account: they fall at the same speed. In the real world 10Kg feathers would fall slower because of the air resistance/friction.

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What has mass got to do with acceleration due to gravity? In a vacuum, even 1g of feather would fall in the same time as 10kg of lead, if dropped from the same height.

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yes, but they are made the same weight exactly to rule out the difference in weight; to keep things simple when you do the 'experiment' in a non-vacuum environment.

--------------


Volv, reading your example made me see the error, thanks. (wasn't such a crappy example as you thought afterall ). So I stand corrected...

-

But I now think, and even convinced, that the chain wouldn't move at all actually, no matter what the angles are (so even no math needed) The whole thing is like a static block.

Think about it, what if you have something hanging from below connecting both ends of the chain. It would mean that there would be a 'force' pulling on each side eaqually from below no (so it doesn't matter if it is there or not)? So, if the top piece of the chain would move to some direction, it means the bottom part would move too (in the opposite direction). If that would happen, you would have a perpetual machine! Which isn't possible... hence, it would never move, no matter the angles and the lengths of the slopes, as long as both the 'bottom' parts are on a horizontal plane. Or am I missing something again (quite possible though, I'm not that awake anymore)?...

EDIT: wait... ermmm.

EDIT2: yeah, no movement...

EDIT3: ermm... hang on ... blah.... I give up... and now I can't sleep thinking about this all morning (8am already)
* CookieRevised shoots SonicSam for asking such questions...

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hahaha why are you connecting the chain at the bottom?

Get some sleep cookie. You really need it.

quote:

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Originally posted by gif83
hahaha why are you connecting the chain at the bottom?

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dunno, why not.... does that matter that you connect it? it doesn't add or substract any more 'force' on one side compared to the other side, does it?

As long as both the 'ends' in SonicSam's drawing are meant to be at equal height (on the same horizontal plane) though...

quote:

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Originally posted by gif83
Get some sleep cookie. You really need it.

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will do ... or at least try...