Planetarion Forums

MrL_JaKiri · 9 Jun 2003, 02:37

If you happen to meet two of the Jones sisters (assuming it's a random selection from the set of all the Jones sisters), it is exactly even money that they will both be blue eyed.

What's your best guess as to the total number of blue eyed Jones sisters?

poshphil · 9 Jun 2003, 02:41

42, thats the answer to everything.

I'll go now.

queball · 9 Jun 2003, 02:45

MrL_JaKiri · 9 Jun 2003, 02:52

Rather easy, isn't it.

queball · 9 Jun 2003, 03:28

A company has a very low opinion of its customers and decides that there should be at least an even chance that there are no consecutive numbers drawn in its lottery since the proles get suspicious when there's too many consecutive numbers. It is decided to use the least number of balls possible under this restraint. 6 balls are drawn without replacement. How many balls does the company decide to use?

MrL_JaKiri · 9 Jun 2003, 03:30

Is this consecutive balls after all 6 have been drawn and ordered?

queball · 9 Jun 2003, 03:57

yes

MrL_JaKiri · 9 Jun 2003, 04:02

I'll do it when I get some paper, but it looks simple enough.

queball · 17 Jun 2003, 16:26

A mechanics puzzle.

Preliminaries: if you have a tyre rolling along the road then the surface of the tyre touching the road at any point is stationary with respect to the ground, it has zero velocity.

Consider a rough tyre with the centre of mass at the edge, on horizontal ground (this can be accomplished using a pair of parallel rails or something, but consider an ideal cylinder). At the start the centre of mass is at the top and the tyre is set in motion forwards with a large velocity.

Now as the tyre rotates so does the position of its centre of mass. But if the centre of mass reaches the ground it will have zero velocity (as I explained), and zero gravitational potentional energy (since it's on the ground). Where does the energy go?

ELeeming · 17 Jun 2003, 17:10

Quote:

Originally posted by queball
A mechanics puzzle.

Preliminaries: if you have a tyre rolling along the road then the surface of the tyre touching the road at any point is stationary with respect to the ground, it has zero velocity.

Consider a rough tyre with the centre of mass at the edge, on horizontal ground (this can be accomplished using a pair of parallel rails or something, but consider an ideal cylinder). At the start the centre of mass is at the top and the tyre is set in motion forwards with a large velocity.

Now as the tyre rotates so does the position of its centre of mass. But if the centre of mass reaches the ground it will have zero velocity (as I explained), and zero gravitational potentional energy (since it's on the ground). Where does the energy go?

the cylinder moves along the grond. v != 0

Freakozoid · 17 Jun 2003, 17:12

32 balls

but I'm not too sure.

don't do mech but from my basic basic knowledge of forces the potential energy bleeds off into the ground until it stops through friction..

right GCSE science loses there methinks.

queball · 17 Jun 2003, 17:17

Quote:

Originally posted by ELeeming
the cylinder moves along the grond. v != 0

Which part didn't you understand? The (momentary) velocity of a point at the bottom is zero.

Quote:

Originally posted by Freakozoid
32 balls

but I'm not too sure.

No. How did you get 32?

Quote:

don't do mech but from my basic basic knowledge of forces the potential energy bleeds off into the ground until it stops through friction..

The tyre is so rough that it can't slide at all.

Freakozoid · 17 Jun 2003, 17:34

Type being the tread of the tyre right?

rough tread means more friction..

the gravitational energy downards is equal to the force that the ground exerts upon the tyre.

the energy given by the push is lost through friction between the tyre and the ground and air resistance and stuff.

so the forces affecting the tyre gradually become equal.

queball · 17 Jun 2003, 17:44

Quote:

Originally posted by Freakozoid
Type being the tread of the tyre right?

rough tread means more friction..

the gravitational energy downards is equal to the force that the ground exerts upon the tyre.

the energy given by the push is lost through friction between the tyre and the ground and air resistance and stuff.

so the forces affecting the tyre gradually become equal.

Yeah, typo. You only get friction when something slides. If it doesn't slide you don't get friction. There's no air resistance but it would hardly make a difference. Are you suggesting that all the energy of the tyre is lost to air resistance and friction and the tyre stops moving? Or does it retain some energy somehow?

Nodrog · 17 Jun 2003, 17:46

Quote:

Originally posted by queball
A mechanics puzzle.

Preliminaries: if you have a tyre rolling along the road then the surface of the tyre touching the road at any point is stationary with respect to the ground, it has zero velocity.

Consider a rough tyre with the centre of mass at the edge, on horizontal ground (this can be accomplished using a pair of parallel rails or something, but consider an ideal cylinder). At the start the centre of mass is at the top and the tyre is set in motion forwards with a large velocity.

Now as the tyre rotates so does the position of its centre of mass. But if the centre of mass reaches the ground it will have zero velocity (as I explained), and zero gravitational potentional energy (since it's on the ground). Where does the energy go?

Isnt this just Zeno's archery paradox?

queball · 17 Jun 2003, 17:48

Quote:

Originally posted by Nodrog
Isnt this just Zeno's archery paradox?

No. There are no infinities or philosophical aspects. It's purely a mechanics question.

Freakozoid · 17 Jun 2003, 17:49

no you do get friction from anything, without friction cars would not be able to move etc.

there are forces acting upon everything.

if you lean against a wall, then the force you are applying to the wall (your weight) is applied back at you, I never really understood how, but this explains how things do not move.

when the tyre looses its velocity through friction then it comes to a stand still with all the forces in equilibrium.

Freakozoid · 17 Jun 2003, 17:51

Zeno's archery paradox is the half time / speed thing right?

what philisophical issues are raised by that?

queball · 17 Jun 2003, 17:52

Quote:

Originally posted by Freakozoid
no you do get friction from anything, without friction cars would not be able to move etc.

there are forces acting upon everything.

if you lean against a wall, then the force you are applying to the wall (your weight) is applied back at you, I never really understood how, but this explains how things do not move.

when the tyre looses its velocity through friction then it comes to a stand still with all the forces in equilibrium.

OK, to be pedantic... you only get energy lost as heat through friction when something slides. Otherwise friction is a mechanical force like any other and does not generate heat.

Nodrog · 17 Jun 2003, 17:54

Quote:

Originally posted by Freakozoid
Zeno's archery paradox is the half time / speed thing right?

no

Quote:

Paradox of the Arrow. Consider the path of an arrow in flight: at each instant of its path the arrow occupies some position in space - this is what it means to say that space is discrete. But to occupy some position in space is to be at rest. So throughout the entire path of the arrow through space it is in fact at rest. In other words, an arrow in flight has an instantaneous position at a given instant of time. At that instant, however, it is indistinguishable from a motionless arrow in the same position, so how is the motion of the arrow perceived?

plasmas_arms · 17 Jun 2003, 17:57

See, this is why I was afraid to come back, you people scare me

queball · 17 Jun 2003, 18:07

Quote:

Originally posted by Nodrog
no

I don't see how you think it applies - velocity is a fairly concrete abstraction in mechanics. Would you conceed that a piston is momentarily at rest at a point in its stroke or that a ball thrown in the air is momentarily at rest at the height of its trajectory?

Nodrog · 17 Jun 2003, 18:18

Quote:

Originally posted by queball
I don't see how you think it applies - velocity is a fairly concrete abstraction in mechanics. Would you conceed that a piston is momentarily at rest at a point in its stroke or that a ball thrown in the air is momentarily at rest at the height of its trajectory?

Of course, but I dont get how the surface of a tire has 0 velocity when in contact with the ground, other than in an abstract Zeno-esque sense.

Sarina_Joy · 17 Jun 2003, 18:23

Quote:

Originally posted by plasmas_arms
See, this is why I was afraid to come back, you people scare me

I'm not scary! (Don't listen to a word Kura says)

queball · 17 Jun 2003, 18:25

Quote:

Originally posted by Nodrog
Of course, but I dont get how the surface of a tire has 0 velocity when in contact with the ground.

What velocity do you think it has? You could get a baked bean can or something and mark a spot on it if you want to be convinced. Or if you're into calculus, differentiate x=t+sin t, y=1+cos t, to find dx/dt and dy/dt at t=pi.

Nodrog · 17 Jun 2003, 19:23

Quote:

Originally posted by queball
What velocity do you think it has? You could get a baked bean can or something and mark a spot on it if you want to be convinced. Or if you're into calculus, differentiate x=t+sin t, y=1+cos t, to find dx/dt and dy/dt at t=pi.

I was talking about angular velocity...

queball · 17 Jun 2003, 19:34

Quote:

Originally posted by Nodrog
I was talking about angular velocity...

Are you saying you think that the centre of mass has no velocity but the wheel has angular velocity which is where the energy goes? So does momentum turn into angular momentum? Then back again?

BTW in the ideal situation I describe the tyre has no moment of inertia since its mass is at a point (how else could the centre of gravity be on the edge?). But even if it wasn't ideal, I don't see how this angular velocity business can explain anything.

W · 17 Jun 2003, 20:52

Quote:

Originally posted by queball
A mechanics puzzle.

Preliminaries: if you have a tyre rolling along the road then the surface of the tyre touching the road at any point is stationary with respect to the ground, it has zero velocity.

Consider a rough tyre with the centre of mass at the edge, on horizontal ground (this can be accomplished using a pair of parallel rails or something, but consider an ideal cylinder). At the start the centre of mass is at the top and the tyre is set in motion forwards with a large velocity.

Now as the tyre rotates so does the position of its centre of mass. But if the centre of mass reaches the ground it will have zero velocity (as I explained), and zero gravitational potentional energy (since it's on the ground). Where does the energy go?

Assuming perfect friction, and no air resistance or currents, then the energy is for the most part turned into angular kinetic energy of the earth-tyre system. Some is sure to go to heat of course.

queball · 17 Jun 2003, 21:12

Quote:

Originally posted by W
Assuming perfect friction, and no air resistance or currents, then the energy is for the most part turned into angular kinetic energy of the earth-tyre system. Some is sure to go to heat of course.

Are you saying the tyre will stop?

BTW, I've tried this out in the real world and it's quite fun.