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# Circular Motion on rough horizontal table. watch

1. I'm deep into studying for my 1st Year Finals now at University, they start 3rd May.

To prepare obviously I've been doing everything I can and beyond. I've finished studying for my Vectors and Linear Algebra course, Statistics course, Algebra and Combinatorics course and also my Real Analysis course which just leaves me with my final course in Mechanics.

Back when I was doing A-Levels I did all the offered Mechanics modules and got good scores on all my papers so I was pretty good. I've been completing all of the topic areas for the course and I'm on the 8th of 13 topics which is Circular Motion. The lecturers notes are terrible so I've collated his with mine from A-Level and proceeded. I decided to look back at A-Level and do some practice, however I came across a problem thats stumped me but I'm embarrased as to why. Its not from an exam paper, infact I cant find it in an exam paper in this context.

Say a particle of mass M kg is attached to an inextensible string (Just to ignore elasticity for the moment) with the other side of the string fixed at the origin on a rough horizontal plane so that the particle when in motion (Obviously with a taut string) moves in a circle. Now the tension in the string acts toward the centre of the 'circle' mapped out by the motion of the particle, and velocity is tangential to the 'circle'. Friction acts to oppose motion, so if a diagram was drawn (Sorry I havent uploaded a photo) the Friction would be in the opposite direction to the velocity, also tangential to the 'circle'.

If the particle was 'moving' with constant magnitude of velocity the tension in the string would remain the same as the force due to friction is perpendicular to the acceleration, but surely the friction (lets assume its a constant resistive force) would cause the particle to travel at a slower velocity and thus the tension in the string would be lower than the tension in the same string with the same mass moving at the same intial velocity on a smooth horizontal surface. Any help? If its unclear I'll upload a photo of what Im saying but I hope someone can fill in a few gaps for me.

I may be getting confused or just being stupid because I'm tired and havent stopped working for the last 5 weeks because until Wednesday i had severe left lung Pneumonia for 6 weeks and have been at home constantly, and apart from sleeping for 12 hours a day I've done nothing but study and my brains pretty rammed at the moment and I cannot sleep if I cant answer a question and this is really bugging me.

I've tried looking through the internet for anyone who has asked this before and cannot find anything, maybe its what im searching, but searching for friction in horizontal circular motion always results in objects placed on disks and sliding at certain velocities (or similar) and cars going through bends. I like to write and solve my own questions you see and this is one I wrote myself

Any help would be great, thanks!
2. (Original post by Jake011268)
I'm deep into studying for my 1st Year Finals now at University, they start 3rd May.

To prepare obviously I've been doing everything I can and beyond. I've finished studying for my Vectors and Linear Algebra course, Statistics course, Algebra and Combinatorics course and also my Real Analysis course which just leaves me with my final course in Mechanics.

Back when I was doing A-Levels I did all the offered Mechanics modules and got good scores on all my papers so I was pretty good. I've been completing all of the topic areas for the course and I'm on the 8th of 13 topics which is Circular Motion. The lecturers notes are terrible so I've collated his with mine from A-Level and proceeded. I decided to look back at A-Level and do some practice, however I came across a problem thats stumped me but I'm embarrased as to why. Its not from an exam paper, infact I cant find it in an exam paper in this context.

Say a particle of mass M kg is attached to an inextensible string (Just to ignore elasticity for the moment) with the other side of the string fixed at the origin on a rough horizontal plane so that the particle when in motion (Obviously with a taut string) moves in a circle. Now the tension in the string acts toward the centre of the 'circle' mapped out by the motion of the particle, and velocity is tangential to the 'circle'. Friction acts to oppose motion, so if a diagram was drawn (Sorry I havent uploaded a photo) the Friction would be in the opposite direction to the velocity, also tangential to the 'circle'.

If the particle was 'moving' with constant magnitude of velocity the tension in the string would remain the same as the force due to friction is perpendicular to the acceleration, but surely the friction (lets assume its a constant resistive force) would cause the particle to travel at a slower velocity and thus the tension in the string would be lower than the tension in the same string with the same mass moving at the same intial velocity on a smooth horizontal surface. Any help? If its unclear I'll upload a photo of what Im saying but I hope someone can fill in a few gaps for me.

I may be getting confused or just being stupid because I'm tired and havent stopped working for the last 5 weeks because until Wednesday i had severe left lung Pneumonia for 6 weeks and have been at home constantly, and apart from sleeping for 12 hours a day I've done nothing but study and my brains pretty rammed at the moment and I cannot sleep if I cant answer a question and this is really bugging me.

I've tried looking through the internet for anyone who has asked this before and cannot find anything, maybe its what im searching, but searching for friction in horizontal circular motion always results in objects placed on disks and sliding at certain velocities (or similar) and cars going through bends. I like to write and solve my own questions you see and this is one I wrote myself

Any help would be great, thanks!
It would be better if you posted a photo of the question(s) and any attempt you made
3. So here in the first photo its the simple horizontal circular motion of a particle on a smooth surface, how would this motion be affected if the horizontal surface was rough? I know friction acts to oppose motion so the Frictional force would be tangential to acceleration, therefore it wont affect the tension in the string...will it?

And the second photo has the same pretty much except for the string isnt hooked to a fixed point it feeds through a hole to another mass hanging, again how would this motion be affected if the horizontal surface was rough instead of smooth? The two questions here are done from a book called 'Introducing Mechanics' that I own, but i cannot find anywhere on the net how these would change if the surfaces were rough instead of smooth.

Like I said my initial thought is friction is tangential so shouldnt affect tension in the string, and of course doesnt affect centripetal acceleration and therefore the Centripetal Force acting toward the centre of the circle, but I just cant get past the thought that a frictional force that would be opposing motion would be slowing down the moving mass so surely it would have to be moving at a quicker 'speed' relative to the smooth plane problem to maintain the same results.

Does that make any more sense?
Attached Images

4. you are certainly getting confused!! The tangential velocity (if the surface is rough) will certainly be affected. This will mean that the radial acceleration will be affected (since the two are connected by a=-(v^2)/r). Hence the particle cannot remain moving in a circle. The fact that frictional force (and hence the radial velocity) is at right angles to the string does NOT mean that one does not affect the force in other!! The particle is supposed to be moving in a circle which means there is a connection.
5. (Original post by mikelbird)
you are certainly getting confused!! The tangential velocity (if the surface is rough) will certainly be affected. This will mean that the radial acceleration will be affected (since the two are connected by a=-(v^2)/r). Hence the particle cannot remain moving in a circle. The fact that frictional force (and hence the radial velocity) is at right angles to the string does NOT mean that one does not affect the force in other!! The particle is supposed to be moving in a circle which means there is a connection.
I just had a shower (TMI I know sorry) And just remembered this! Can't believe I let that slip my mind and to think such atrocities! But thank you anyway!
It crossed my mind because I started thinking of variable forces in circular motion and then i remembered if the tangential velocity is reduced the particle's motion can be visualised by a spiral type shape (Provided the string remains taut) and yeah I kinda facepalmed hard at that moment. Sorry everyone xD
6. (Original post by mikelbird)
you are certainly getting confused!! The tangential velocity (if the surface is rough) will certainly be affected. This will mean that the radial acceleration will be affected (since the two are connected by a=-(v^2)/r). Hence the particle cannot remain moving in a circle.
If I've understood the question correctly, then the particle will simply move in a circle with a constant tangential deceleration until it comes to rest. The tension in the string will decrease as the tangential velocity decreases. If we had a spring, then as the particle decelerates, then the spring extension would decrease, as it has to provide a smaller centripetal force over time, so in this case, the particle would spiral inwards.

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