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Math Help - circular motion

  1. #1
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    circular motion

    A pail filled with water of mass m is whirled in a vertical circle of radius , r . When the pail is at its highest point , its speed is v and the normal reaction of the pail on the water is R . Water does not fall out because ??

    i know i am supposed to this :

    R+mg=\frac{mv^2}{r} so R=\frac{mv^2}{r}-mg >0

     \frac{mv^2}{r}>mg

    It is because the centripetal force is greater than the gravitational acceleration ??If that's the case , water would spill up since F is downwards .

    Why R+mg ?? When i draw the diagram , my R is pointing upwards and mg is pointing downwards and if the acceleration is downwards , shouldn't it be mg-R=ma ??

    And why must R be greater than 0 and not other values ??

    I really appreciate ur effort to explain this to me .
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  2. #2
    Super Member malaygoel's Avatar
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    Quote Originally Posted by thereddevils View Post
    And why must R be greater than 0 and not other values ??
    R is defined as that force which arises between two surfaces in contact and is normal to the plane of contact and repulsive...hence the mathematical form R>0.

    if you see closely, at the top, R will be in downward direction.
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  3. #3
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    Quote Originally Posted by malaygoel View Post
    R is defined as that force which arises between two surfaces in contact and is normal to the plane of contact and repulsive...hence the mathematical form R>0.

    if you see closely, at the top, R will be in downward direction.

    If R is downwards , then the forces are not balanced .. there is no force to balance mg . ??

    From what i understand , if there is a book on the table , mg is acting on it downwards so there is also another force which is R acting on it upwards ..

    But if both forces are downwards , which is also my doubt , then is it against newton's 3rd law ?
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  4. #4
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    The force R is not balanced by mg.

    Force R is the force that exerted by the pail on the water. It will be balanced by the force on the pail by the water. R is directed downward, so the force on the pail by the water is upward
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