A cylindrical bucket filled with water is whirled around
in a vertical circle of radius r. What can be the minimum
speed at the top of the path if water does not fall out
from the bucket ? If it continues with this speed, what
normal contact force the bucket exerts on water at the
lowest point of the path ?

Question

A cylindrical bucket filled with water is whirled around
in a vertical circle of radius r. What can be the minimum
speed at the top of the path if water does not fall out
from the bucket ? If it continues with this speed, what
normal contact force the bucket exerts on water at the
lowest point of the path ?

maheshmeghwal9 · Answer

@mahmit2012 @ganeshie8 Please help:D

maheshmeghwal9 · Answer

@vishweshshrimali5 :)

ghazi · Answer

here potential energy at bottom gets converted to the kinetic energy whilst in motion at the top so 1/2*m*V^2= m*g*2r (height from base=2r) therefore v= 2 * $$\sqrt{gr} $$

maheshmeghwal9 · Answer

yeah but it is $$V_{\min.}$$not v  :/

maheshmeghwal9 · Answer

well plz make me understand that why the solution has chosen N as $$N \ge 0.$$
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maheshmeghwal9 · Answer

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anonymous · Answer

i think N>=0 is only stating that, in the top most position, N and Mg will always be in the same direction. which is obvious from looking at the figure. at the top, N can't be opposite to Mg, ie, in upward direction, right?

maheshmeghwal9 · Answer

isn't there any other good reason?

maheshmeghwal9 · Answer

@Vaidehi09 :)

anonymous · Answer

i don't know....this is the best i could come up with.
see, its given that N>=0....
1) N=0 -----> yup, possible.
2) N>0-----> so the LHS of eq becomes Mg + N ----->Mg and N in same direction -----> definitely the case.
3) N<0 -------> LHS becomes Mg - N -----> compare this to the second last eq in the given sol. so this would imply that Mg and N are opposite to each other ------> which, at the top, cannot happen ------> so, not possible.

hence N>=0.

this is what i infer from that.

dominusscholae · Answer

N is considered the contact force. The contact force in general is what holds the water in the bucket. It will always act normal to gravity. In the case of the top, the normal (contact force) is along gravity's direction.  When the contact force is zero, the water will leave the pail. That is why the solution has N (or rather, the magnitude of N) to be >=0.  This is the case at the minimum speed mentioned (i.e, when there's no contact force, or when mg = mv^2/r). Does that clear up some things?