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## #1 2012-10-12 23:45:05

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
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### Pseudo-Force

Can any one explain the concept of Pseudo-Force to me in simple words?
Please also show how it is different from the real force

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #2 2012-10-13 00:42:42

bob bundy
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Registered: 2010-06-20
Posts: 7,925

### Re: Pseudo-Force

hi Agnishom,

Wiki gives three examples at

http://en.wikipedia.org/wiki/Fictitious_force

Of these,  the ones I have spent most time arguing against is centrifugal force, so I'll use that one here.

Everyone knows that as you go round a bend in a car you feel as though you are being thrown outwards.

You may also have tied a conker to a string and spun it around in a circle.  You can 'feel' the string tugging you.

But to call this centrifugal force, is to stand the mechanics on its head.

Any object that is travelling in a circular path must have a force acting on it to cause this to happen

Newton's first and second laws at http://en.wikipedia.org/wiki/Newton%27s_laws_of_motion

There's no string here; the satellite is being pulled towards the Earth by gravity.

To travel in a circle requires a centrally acting force and gravity provides this.  The satellite is said to be in 'free fall' as it is constantly falling towards the centre of the Earth.  Imagine it travelling along a tangental line plus falling inwards a small amount;  the amount it falls in exactly  cancels with the curvature of the circle, meaning it stays at the same distance from the Earth.

For the conker the tension in the string provides the force, and for the car it is friction between the tyres and the road.  That makes the car go in a circle (unless the friction is insufficient in which case the car continues in a straight line) .  Inside the car something has got to make you go in a circle too.  If you're a passenger in the back with no seat belt, you feel as though you are being flung sideways, but actually you are just continuing to go straight while the car bends round.  When the side of the car hits you it makes you go in a circle too.

Because of what it feels like, some people have invented a fictious force called centrifugal force that seems to be throwing you outwards.  There's an easy test to show this isn't really what happens. When a car loses traction which way does it travel.

Michael Schumacher seems to be constantly demonstrating Newton's laws. No centrifugal force here!

When I was your age I had many happy arguments with friends whom I called 'centrifugalists'.  We tried to devise an experiment in which someone spun round in a circle holding on to a rope with a weight at the end.  At a key moment someone would cut the string.  Now what would happen?  Would the weight travel out radially (centrifugalist argument) or along a tangent (Newtonian argument).  We never actually tried it; just argued about it!

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #3 2012-10-13 02:56:43

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,722
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### Re: Pseudo-Force

Hmm..
How is it different from the non-pseudo forces?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #4 2012-10-13 05:51:57

bob bundy
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Registered: 2010-06-20
Posts: 7,925

### Re: Pseudo-Force

Well I'd say they are non-existent forces.  Some people find it helps to do certain questions by making up such a force.

eg.  a conker is spun around in a circle.

in 'equilibrium'

tension in string = centrifugal force acting out from the centre.

eg2.

When an object is rotating around the Earth, an observer sees it move in a frame of reference which is itself rotating.  As I understand it you can get an equation that accounts for this apparent extra motion by inventing a coriolis force on the object.  Sorry that is a bit 'woffly' but I'm not good on coriolis forces.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #5 2012-10-13 23:35:42

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,722
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### Re: Pseudo-Force

When I was your age I had many happy arguments with friends whom I called 'centrifugalists'.  We tried to devise an experiment in which someone spun round in a circle holding on to a rope with a weight at the end.  At a key moment someone would cut the string.  Now what would happen?  Would the weight travel out radially (centrifugalist argument) or along a tangent (Newtonian argument).  We never actually tried it; just argued about it!

What should happen in reality?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #6 2012-10-14 00:33:08

bob bundy
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Registered: 2010-06-20
Posts: 7,925

### Re: Pseudo-Force

Well the rope has a real force; the tension; and that is what pulls the weight into a circular orbit.

By Newton's first law, an object will continue with uniform motion (ie. go in a straight line) unless acted upon by an external force (that's the tension).

If you cut the rope there's suddenly no tension.  So the weight should carry on in a straight line ie. along a tangent to the circle.

[My centrifugalist friends argued that there is an outward acting force on the weight that balances the tension.  If you take away the tension the weight should fly out on a radial line.  Because that force isn't really there it is called a pseudo force.  Time and time again I would tell them that there is no equilibrium because the weight is always accelerating towards the centre;  so no 'balancing force' is necessary.]

The trouble is you can invent centrifugal force and get all the right answers.  So it may seem not to matter.  It's a bit like the proving argument; is it Ok to do something back to front, if you get the right answer.  The Ptolemaic system of epi-cycles was used to predict the position of planets in the 'fixed star background'.  Then Copernicus suggested a Sun centred system and it has been used ever since.

Is it a better way to do things?  ... Discuss.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #7 2012-10-14 01:09:20

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,722
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### Re: Pseudo-Force

Because that force isn't really there it is called a pseudo force.

That force doesn't exist??!!
Then, what makes it feel so???

Is it a better way to do things?  ... Discuss.

Excuse me, Which way are you talking about?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #8 2012-10-14 06:33:51

bob bundy
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Registered: 2010-06-20
Posts: 7,925

### Re: Pseudo-Force

hi Agnishom,

That force doesn't exist??!!
Then, what makes it feel so???

Our perception often plays tricks on us.  You have probably met lots of visual tricks where lines look longer than they are or bent when they are straight, etc.

So when have you experienced a force that isn't really there.

Picture a situation where you are in a car, or a roller coaster or similar, experiencing a high acceleration.

There must be a force acting here.  Something is driving your seat forwards with mounting speed.  But what do you feel?  You seem to be being pushed back in your seat as if an unseen force is pressing against you.  Think about it.  There cannot be such a force but try telling your brain that.

What is happening is the seat is trying to overtake you but clearly it cannot.  So it is pressing against you, trying to speed you up.  But your brain interprets what is happening from your personal perspective.  Your brain doesn't 'see' the world from the position of the seat; it tells you that you are being forced into the seat.  'Forced';  by what?  It's another pseudo force.

Analysis of the maths helps us to understand what is really happening, independent from our personal world of perception.  That's why I've tried to give you some experimental evidence that centrifugal force isn't really there.

Is it a better way to do things?  ... Discuss.

Excuse me, Which way are you talking about?

I believe in the scientific method.  Observe; try to find a theory that fits the facts;  and then test it.  That's my 'better way'.  But I was only joking in suggesting that you discuss this.  You can if you want; but it is optional.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #9 2012-10-14 16:17:53

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,722
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### Re: Pseudo-Force

There must be a force acting here.  Something is driving your seat forwards with mounting speed.  But what do you feel?  You seem to be being pushed back in your seat as if an unseen force is pressing against you.  Think about it.  There cannot be such a force but try telling your brain that.

Ofcourse, there is a force of Inertia acting.

And.... If the centrifugal force is unreal then where does the tension on the string come from?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #10 2012-10-14 19:10:28

bob bundy
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Registered: 2010-06-20
Posts: 7,925

### Re: Pseudo-Force

Inertia is not a force.

If you are holding the string then you pull it.  So your muscles provide the force.

Bob

ps.  When I've woken up properly I'll show you how to derive the formula for central acceleration.

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #11 2012-10-14 22:19:51

bob bundy
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Registered: 2010-06-20
Posts: 7,925

### Re: Pseudo-Force

Proof that any object rotating in a circle must be continuously accelerating towards the centre.

Preliminary:  By Newton's first law, an object will continue with uniform motion (ie. fixed speed and direction) unless acted upon by an externally impressed force.

This means that to make an object go in a circle there must be a force to cause the change.

I need to establish some formulas before the main proof.

Look first at my table of values for small angles, the cosine and sine of the angle.  I am working in radians not degrees.

You can see that as the angle gets smaller the cosine of the angle approaches 1 and the sine of the angle approaches the same value as the angle itself.

screen shot 2 shows the diagram to prove this.

As the angle gets smaller,  AC gets closer and closer in length to arcAB so

Now for the main proof.  See the third screen shot.  This shows an object rotating in a circle.  It has speed v.  Consider the position after it has moved around through a small angle.

The change in velocity along the line of the tangent is

and along the line of the radius is

This change takes place in a small period of time.

So the time for one revolution is

Now to calculate the two accelerations.  I'll do the tangential one first.

The part in brackets tends to 1 so the whole tends to zero as the angle tends to zero.

So there is no tangential acceleration.

The minus sign means it acts towards the centre of the circle and is equal to v^2/r in size.

So, if an object has to accelerate towards the centre for circular motion, there has to be a centrally acting force to provide it (Newton's second law).

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #12 2012-10-16 00:56:47

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,722
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### Re: Pseudo-Force

Er, I am not yet so well versed at Trig but I will try to read this

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #13 2012-10-16 05:12:58

bob bundy
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Registered: 2010-06-20
Posts: 7,925

### Re: Pseudo-Force

OK.  Ask if anything needs more clarification.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #14 2012-10-18 02:36:40

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,722
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### Re: Pseudo-Force

Sorry for the delay
You said:

cos2x = 1 - 2sin^2x

How?

I am going through the rest of the proof and I am not done yet

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #15 2012-10-18 06:09:23

bob bundy
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Registered: 2010-06-20
Posts: 7,925

### Re: Pseudo-Force

It comes from the compound angle formula:

Put A = B = x and this becomes

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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