h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

You can't do this with satellites (as far as I know), but maybe you can do it with buckets of water...

Tie a bucket of water to a short piece of rope (logically unnecessary, but it avoids the messy severing of limbs later in the experiment).

Swing the bucket around yourself so that it describes a perfect circle (this requires a surprising amount of strength, since the bucket pulls outwards/onwards, but then that's what we're talking about).

Get someone with a really, really, perfectly sharp knife to cut through the rope as you swing (even that's rather hard to achieve, but easier than causing the earth to disappear and watch what a satellite does).

Where does the bucket go when it is released from the rope?

Outwards (along a projection of the radius of the circle it was describing at the time the rope was cut, drawn from the point at which the rope intersected with the knife when it was cut)?

Onwards (along a tangent of the circle it was describing at the time the rope was cut, drawn from the point at which the rope intersected with the knif when it was cut, and at 90 degrees from the radius above)?

Somewhere between the two?

When you swing your bucket of water round your head, then tire of the game and slow it down, you are aware of the tendency of the bucket to move on round the circle (and then down to the ground). The outward pull ceases, so centrifugal force doesn't exist.

But before you stop, if there were two ropes on a square bucket handle, one in each of your hands, would you feel a stronger force-trying-to-escape-from-its-constraints from the leading rope or the trailing rope (relative to the movement of the bucket)?

Are your arms preventing the bucket moving onwards round the circle or outwards? At what angle to the movement of the bucket?

OK reply to the first and if it's a bit inarticulate it's because local time is 03:42.

Spin the bucket. Cut the rope. Assume ideal conditions. The bucket continues on a tangent. Not anything in between - a tangent, because the only thing preventing it moving in a straight line (the tangent) was the centripetal force. Take that away, instantly, and the tangential velocity vector is restored.

H.

Hoovooloo, I think I agree with you. What I'm trying to get at (it was about 3am when I sent my queries in, too) is what centripetal force is. I wish I could draw a diagram, but let's accept the challenge of words. If the force drawing the bucket away from you is a force "onwards" - at 90 degrees to the line of the rope at each different instant, then what is the direction of the compensating, "centripetal" force? The rope is the agent of this force (?) but do you draw the force along the line of the rope? Surely it's more complex than that?

No, it's not. In fact, it's *simpler* than that, because there is no "force" drawing the bucket away from you. The bucket "wants" to continue in a straight line because that's what bodies with mass and therefore inertia *do*. No force is required to make that body continue in a straight line. What is required is a force to *stop* it moving in a straight line. One force is enough.


Whirl that bucket in a circle, and the one and only force is the one directed inwards along the rope (i.e. radially). That is the centripetal force.

Draw a circle, then a radius, then a tangent at the point of intersection with that radius. That's your diagram. The force is inwards along the radius. So the acceleration (F=ma) is along that line. The velocity is along the tangent, at ninety degrees to the acceleration.

Hope that helps
Think it might not, but until GuideML allows scrawled diagrams (!) it'll have to do.



H.

Freeze frame.

I'm swinging a bucket round in the best circle I can manage. I'm leaning back, because there is a force pulling the bucket "away from the centre".

Draw a perfect circle, modelled on the less than perfect circle I am probably managing. Draw a tangent on that circle at the point currently represented by the position of the bucket. The bucket "wants" to fly off along that tangent in one direction.

Newton's first (?) law says that a body in motion will maintain that motion unless a force acts upon it to change the direction and/or speed of that motion.

Eric the rugby player, charging towards the goal, can be turned by swinging on his shirt. But if you're the person doing the pulling, at the centre of a newly described circle, is the only force you exert the one which pulls towards the centre of that circle?

There would be a line from you at the centre to Eric at the point on the circumference where the tangent is drawn. I suspect that Eric's momentum would be such that the line of his movement before you grabbed him would be significant.

You would be pulling across this line at something like 90 degrees, but you would have to exert force against the line of Eric's original movement as well as along the line of the radius of the circle which lies between you. The lines of force would probably result in you holding on desperately, attempting to hold Eric back from an angle of something like 45 degrees.

And, depending on how closely Eric resembles Jonah Lomu, you would be dragged along behind him at 45, 40, 35... degrees. So the case of the bucket and the case of Eric are not identical.

All I'm trying to understand is the diagram of forces in the idealised bucket case. There is a force which tends to move the bucket along a tangent of the circle. There is a force which prevents that. Is that force actually exerted at 90 degrees to the tangent? Is it exerted along a radius of the circle?

Never mind the (perhaps) composite factors which make up that force. Is the rope between me and the bucket at 90 degrees to the tangent (can it be anything else?). What is the relationship between the line drawn across the top of the bucket and that tangent?

You have to imagine the bucket as a point mass. You have to imagine the rope as a perfectly rigid one dimensional rod. You have to get AWAY from the idea that there is any force making the body move along the tangent. This is crucial...

Newton's first law: A body will remain in a state of rest or uniform motion unless acted on by a resultant external force.

So, without an external force, the body remains in uniform motion, i.e. a straight line and there's no need for any force. Think of the rather odd sport of curling. Once that stone is moving across the ice, no force is needed to *keep* it moving. It slows down only because of the very slight friction. But if there was no friction, it would continue moving in a straight line, forever (given a large enough ice rink...).

If you exert a force on that stone at 90 degrees to its direction of motion, it will change direction. But if you change the direction of the force, so that it stays at ninety degrees to the direction of the motion all the time, the body will continue moving in a circle around the centre of the circle to which it's motion at any given instant is a tangent.

It's very important to realise that there's only ONE force at work. Inertia is not a force as we currently understand it. Inertia is the tendency to obey Newton's first law. You sit still unless pushed, and if pushed you keep moving until something slows down, speeds you up or veers you off. All this is very frustrating to try to express verbally, and I'm obviously not doing a very good job of it. I can only suggest, therefore, that you find a physics or applied mathematics textbook with some really good diagrams, because I'm reaching the limits of my ability to express this stuff.

H.
Thanks for pushing me to the limit!

Hoovooloo,

Don't get mad if I say this fun! I'd like to draw diagrams too, but I also like a challenge to express things in words. (Sorry if you don't.) Let me play the sucker and analyse your argument line by line.

You have to imagine the bucket as a point mass (= something like 10kg assumed to act at the bucket's centre of gravity).

You have to imagine the rope as a perfectly rigid one dimensional rod (so that you can draw the diagrams we can't).

You have to get AWAY from the idea that there is any force making the body move along the tangent. This is crucial... (But the force which tends to move the body along the tangent is the one you're trying tell me is real.)

Newton's first law: A body will remain in a state of rest or uniform motion unless acted on by a resultant external force.

So, without an external force, the body remains in uniform motion, i.e. a straight line and there's no need for any force. Think of the rather odd sport of curling. Once that stone is moving across the ice, no force is needed to *keep* it moving. It slows down only because of the very slight friction. But if there was no friction, it would continue moving in a straight line, forever (given a large enough ice rink...). THIS IS ACTUALLY A GOOD EXAMPLE - GRAVITY IS THE ROPE, AND THE WHOLE CIRCUMFERENCE OF THE WORLD IS A CIRCULAR ICE RINK...

If you exert a force on that stone at 90 degrees to its direction of motion, it will change direction...

I was about to say that the force is not at 90 degrees to its direction of motion, but then I thought "parachute me in, put in my hand a rope attached to the stone, assume that I land at a point where I can pull at exactly ninety degrees, that my feet land somewhere with a good chance of gripping, and that I can exert exactly the right amount of force..."

The body has a velocity, presumably the result of force previously applied. The only other force is the one I'm applying, at 90 degrees to the path the body never takes. The diagram might actually be quite simple.

BUT!!!

This case never actually arises. The bucket is only moving around my head because I am swinging it. The forces involved are therefore...

Me pulling the rope so as to prevent the bucket flying off into space, and

Me pulling the rope to propel the bucket along its never achieved tangent - the rope is presumably not at 90 degrees to the tangent, or this force would have no effect.

Mund: I'm going to do this a line at a time because I'm drunk and I need to concentrate...

>Don't get mad if I say this fun!
Are you kidding? I love this stuff!

>I'd like to draw diagrams too, but I also like a challenge to express things in words. (Sorry if you don't.)

If a certain friend of mine (who knows who she is) is reading this, she's laughing out loud right now because she knows about me and how much I like expressing things in words...

>Let me play the sucker

She's laughing again now, probably harder than before...

>and analyse your argument line by line.

Okey dokey.

>You have to get AWAY from the idea that there is any force making the body move along the tangent. This is crucial... (But the force which tends to move the body along the tangent is the one you're trying tell me is real.)

NOOOOOO!!! There is NO tangential *force*. There is ONLY radial force. NO TANGENTIAL FORCE, tattoo it on the inside of your eyelids... The velocity vector is tangential, but there's no force acting in that direction.

>So, without an external force, the body remains in uniform motion, i.e. a straight line and there's no need for any force. Think of the rather odd sport of curling. Once that stone is moving across the ice, no force is needed to *keep* it moving. It slows down only because of the very slight friction. But if there was no friction, it would continue moving in a straight line, forever (given a large enough ice rink...). THIS IS ACTUALLY A GOOD EXAMPLE - GRAVITY IS THE ROPE, AND THE WHOLE CIRCUMFERENCE OF THE WORLD IS A CIRCULAR ICE RINK...

Yes! Now do exactly the same thing, only set the curling stone moving at a speed of about 17,000 mph at an altitude of about 22,500 miles (I think). Same result, no rink, no force *at all* on the satellite except gravity, and round and round and round and round and round it goes...

>The body has a velocity, presumably the result of force previously applied.

YES! and the only reason in the real world why it loses that velocity is inconvenient things like friction and air resistance. In space, no resistance, no friction, no problem, satellites stay up.

>The only other force is the one I'm applying, at 90 degrees to the path the body never takes. The diagram might actually be quite simple.

Yes!!!!


>BUT!!!

>This case never actually arises. The bucket is only moving around my head because I am swinging it. The forces involved are therefore...

>Me pulling the rope so as to prevent the bucket flying off into space, and

>Me pulling the rope to propel the bucket along its never achieved tangent - the rope is presumably not at 90 degrees to the tangent, or this force would have no effect.

Ask yourself this question: you're at the centre of the circle. The rope is a radius. By virtue of the fact that you're spinning the bucket around, it's *always* a radius of a circle with you at the centre. How can you apply a force in any direction except radially? Obviously you do, to get things going, but where is that force, actually *applied*? At your feet. You rotate your body by pushing with your feet. You maintain the rotation by pushing with your feet. But when the bucket is at speed, the only force acting on it is radial, right along the rope. You pull the rope inwards, and that is the direction of the force - in towards you in the centre.

I'm rambling, but that's the scotch. I'm probably going to have to try this again sober another day.

You're right, it's fun.

H.

OK, I'm nearly there...

There is no actual force along the tangent, just velocity, and therefore momentum. The velocity has been achieved by the previous application of force. That's the idealised picture.

Now, what was this previous application of force? The bucket started off on the ground (continuing at rest until...). Somebody had to do some work to get it flying. And since it's me keeping this argument going, I'll try to swing it round my head while otherwise standing still (to avoid dizziness).

I apply force by lifting the bucket and swinging it in a series of curved paths. The speed of rotation increases until the rope is horizontal and the path taken by the bucket is pretty well a perfect circle. While I am applying the force, accelerating the bucket, the rope cannot be a radius of the circle, but must be pulling "ahead" of the bucket, because it isn't a rigid rod.

For a short time, the speed of the bucket is maintained and the idealised state is achieved - the bucket describes a circle touched by the tangents that it would "like" to fly off along. But in the real world it will slow down and dip, and therefore more force will have to be applied pretty constantly to keep it up.

If I tie my end of the rope to a spring balance and hold that when I swing into action, the balance will indicate "weight" while I'm applying force. Will it return to its neutral position when the idealised state is reached?

What about a steam governor? When it rotates faster, the weights rise and move further from the centre, opening the valve, slowing the rotation and allowing the weights to drop and move closer to the centre. What's happening there?

I quote from an article on Newton's third law...

"There are no isolated forces; for every external force that acts on an object there is a force of equal magnitude but opposite direction which acts back on the object which exerted that external force."

Our object, which is constrained to travel in a circle, is acted upon at every instant by a force which prevents it hurtling off along the tangent of the circle that it "desires" to move along and shifts its velocity to the "next" tangential direction. This force is the force along my arms (it's a bucket of water, after all).

So what is the equal and opposite force that acts back on my arms?

To put it another way...

The artificial satellite Dark Star 5.7 is in orbit around the earth.

In fact, the earth and this satellite are in orbit around a point a few nanometres away from the earth's centre.

In fact, the earth and a few hundred artificial satellites are all in orbit around a point somewhere near the centre of the earth. This point is defined by the relative masses of the earth, the artifical satellites and any other bodies involved (the moon, for example), and the distances between the centres of these objects.

(Shall we ignore the sun and anything else beyond the orbit of the moon, just for now? And don't even think about various small masses ejected from early manned space probes.)

All of the objects we are considering "want" to move off in a straight line, every instant of time. But they are constrained by forces from all the other objects (gravity, basically).

So (Newton's third law) each of these objects "feels" a force equal and opposite to the gravitational force of each of the others at every instant of time.

Why aren't more moons travel sick?

Forces always exist in pairs, like Newton said. When you swing a bucket of water in a circle, from a rope, there are two forces involved, as Newton's third law states. The first force is a force along the rope, pulling the bucket inwards towards your body. The second force is a force also along the rope, pulling your arms outward towards the bucket. No force is pulling the *bucket* outward. The bucket is being pulled inward. Your arms are being pulled outward.

In the case of a satellite, here are the two forces. The first force is a force from the earth that is pulling the satellite inwards towards the earth. The other is a force from the satellite pulling the earth outwards towards the satellite. This is why the moon, mainly, shifts the point the earth/moon system revolves around slightly away from the centre-of-gravity of the earth itself. In practice, the two objects revolve around their common centre-of-gravity.

You are therefore making a mistake when you say "each of these objects "feels" a force equal and opposite to the gravitational force of each of the others at every instant of time." That is not the way it is meant. Each of these objects only feels the sum-total of the gravitational forces from the other objects. The opposite force is the force that the OTHER OBJECTS feel from THIS OBJECT.

Suppose the object is you, and the other object is the earth. Suppose you weigh 150 pounds.

The earth attracts you with a force equivalent to 150 pounds. You also attract the earth with a force equivalent to 150 pounds.

There you can see the two involved forces. Get it?

Thanks. That was a different way of looking at it. I'll consider it and get back to you.

"When you swing a bucket of water... the first force is a force along the rope, pulling the bucket inwards towards your body. The second force is a force also along the rope, pulling your arms outward towards the bucket. No force is pulling the *bucket* outward. The bucket is being pulled inward. Your arms are being pulled outward." What exerts the force to pull my arms outward? The rope?

(Incidentally, let's skip the stuff about the bucket wanting to hurtle off into space along the line of the rope. I'm quite happy that it wants to toddle off into the universe along the line which is its current tangent to the circle defined by the rope I'm holding.)

"In the case of a satellite... the first force is a force from the earth that is pulling the satellite inwards towards the earth. The other is a force from the satellite pulling the earth outwards towards the satellite."

No. The satellite and the earth can be said to revolve around a point slightly to the satellite side of the centre of the earth, but this second force is not the same as the pull on my arms when I'm swinging a bucket of water round my head (weight of bucket plus water? 12kg? Weight of me? 80kg. Gravity does not define this effect.)

An object continues in a state of rest or continuous movement until acted on by a force. That's Newton, right? So the bucket would continue off in a straight line if it wasn't for the rope, which exerts a force to change its direction to a new tangent, and then another, and another, so that it describes a circle. I said that the rope exerts a force, but actually it only transmits forces. My hands exert the inward force. The momentum of the bucket, at right angles to the rope and my hands (I approximate) contributes the outward force.

A moon also "wants" to move off in a straight line, at a tangent to the circle it is describing. If the planet it is moving round suddenly ceased to exist, then it would do exactly that. But a force prevents it doing so. That force is the gravitational pull of the planet.

The planet too would change its direction if the moon suddenly ceased to exist, and rather more so if the sun around which it moves suddenly ceased to exist.

There's more than gravity here (in the simple diagrams we're discussing, anyway). There is the energy invested in a body by history, which is now its tendency to move in a straight line, but for the constantly exerted force of gravity (or my arms) which changes its direction again and again, moment by moment. And if forces go in pairs, then there's an outward pull, however you describe it. And it ain't just gravity.

If it was just gravity, then the moon would fly off at 90 degrees to the current tangent if the earth suddenly ceased to exist.

Holy mackerel..

I've seen this conversation before...

Bye,

HELL

The moon is constantly trying to move in a straight line. (Hence, the tangent) The Earth's gravity prevents it from doing so. But the moon isn't exerting any force due to its orbit. The only force that the moon is exerting is it's own gravitational field.

Imagine that you're standing in a rather large ring of people. Place a smallish object at the center of said circle. Now run at an angle at any one person as if trying to break free of the circle. When you reach the boundary that person will give you a slight push and direct your energy to the side and into the next person who will do exactly the same thing (the process continues indefinately) though you're still running in a straight line. The people constantly adjusting your course represent the effect gravity has on the moon. You have not effected the smallish object in the center of the circle by your circular path.

This may not be helpful to you but it seemed to make sense when I wrote it. In short, the moon has no momentum along its orbit but along each of those tangents. It won't move in a 90 degree angle to the tangent but exactly along the tangent because centrifugal force does not exist. I think that I may be rambling so I'm going to post it and do my best to clarify if you have questions.