# Math Help - circular motion

1. ## 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 .

2. Originally Posted by thereddevils
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.

3. Originally Posted by malaygoel
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 ?

4. 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