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edison's Avatar
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4 May 2008 15:32:50 IST
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Mechanics of a conical cylinder
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We know that due to gravity, if free to move, everything falls downward.  Explain why a conical cylinder placed on a small inclined ramp, can roll up the incline.  (No magnets or tricks of any kind were used).

 


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Aatish Pandit's Avatar

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Joined: 3 Feb 2007
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4 May 2008 16:31:09 IST
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Well sir.......I think this diagram by me is sufficient explanation to ur question.......

edison's Avatar

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4 May 2008 16:54:37 IST
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Hi aatish thanks a lot for this wonderful figure that gives good insight to the problem.


 


Have a salute from me.


 


I have tried the following explanation


 


When a conical cylinder is placed on a small inclined ramp, it roll up the incline. It happens to be so because the conical ramp has got different area of cross section at two ends and thus it can not roll down the inclined plane due to the fact that if it tries to do so the angular displacement of the two ends has to be same. This implies that end with greater cross section area or diameter will travel a large distance and another will travel smaller. This is possible only if the end with larger diameter moves in a circle with greater radius and the one with smaller diameter will describe a circle with smaller radius but inside the larger circle.


 


Now when the conical cylinder is placed on a small inclined ramp, the cylinder can not come down even though the gravity is acting downwards. This is because the frictional force between the ramp and cylinder surfaces is preventing it from being sliding (it can slide down the inclined plane only if inclination is such that gravitational force exceeds the frictional force).


 


Withstanding this fact the conical cylinder moves up as the circular end which acquires velocity has sufficient inertia to overcome the gravitational force and will stop somewhere above the inclined plane

animal's Avatar

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Joined: 5 May 2008
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5 May 2008 12:11:58 IST
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sir nice approach but can we conserve the energy to get the angular velocity of the cone or we cant as there is friction . Is it is a case of pure rolling with translational vel. =0.


Cool goIITian

Joined: 13 Nov 2008
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6 Dec 2008 15:05:47 IST
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Listen edison i think u r confused with sum thing else here i dont think a cone could move by an inclined plane its impossibe by itself if u mean a restricted double cone yes it can climb up the incline the reason behin it is simple since center of mass and cone roll in opposite directions u can see this phenomenon on many objects but sumthing as large and heavy as cone its difficult and defies common sense.



and ps it is more complicated than that actually it reqiures the rails dont run parellel and all the logic simple cone want to at place where there is more width it at higher end than lower thatz how this is made(i made one for my project so iknow).







Learn to see simplicity of thing rather than complicating it.....HEHEHEHEHEEEEE

snail's Avatar

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7 Dec 2008 15:41:31 IST
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Does it really roll up?


I don't think. In Aatish's figure we can see that the conical cylinder goes up beyond its initial position which is not possible I think. In the inclined plane,due to eccentricity of the baseline and the CG of the cone it will rotate as shown in the figure and when it reaches to the diametrically opposite side it stops and rotates back . This oscillations will continue and finally it will rest at a perpendicular orientation like a simple pendulam.


What Rizking1000 has described is a mechanism we can see in science museums.It is a different case.


I agree with him but not the tone of his language.


Cool goIITian

Joined: 13 Nov 2008
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9 Dec 2008 19:40:53 IST
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Totally sorry man i just get carried away with some questions u know.sorry no offence.... ok  




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