Energy conservation law problem?

Question

I have got a physics problem which is described below.

There is a ring which radius is R. A little ball moves inside this ring. Ring's flat is normal to the surface of ground. When a ball is moving inside a ring (ring is in quiet), the ball reaches a height which is equal to R/2.
The ring starts to move plumb with a fixed acceleration. What is the value of the fixed ring acceleration, if the ball inside the ring reaches the top of the ring?

(I know the answer of this problem - acceleration is equal to 4g/5 and a ring moves down with this acceleration. How to achieve this answer?)

Thanks in advance.

Sorry for my bad English :(.

"Ring's flat" is Ring's plane. So "Ring's plane is perpendicular to the surface of ground"

"The ring starts to move plumb" means that the ring starts to move upright.

Hope this will help to understand my question.

Answer 1

Under these conditions, the acceleration w/r/t the ring is g/5 downward.

What's not clear from the question is where is the ball when the ring acceleration starts?

It makes a big difference.
For example, if the ball is at R/2, it has no kinetic energy w/r/t the ring. Since acclereation of the ring creates a relative gravit of g/5, it would still osccilate within the ring at R/2.
If the ball is at the bottom of the ring, then there is kinetic energy when it starts of m*g*R/2 (I am using this versus .5*m*v^2). This will get converted to potential energy at a rate of m*(g-a)*h, or m*g/5*h. Since the translational distance within the frame is 2*R, then
m*g*R/2=m*(g-a)*2*R
simplify
g/2=2*g-2*a
I get a= 3*g/4

If the problem is also to keep the ball in the ring so it doesn't fall, then it has to have kinetic energy at the top to counter act the force of gravity relative to the ring.

j

Answer 2

I think that one of the reasons that folks haven't been answering your problem is that the English does not make sense. I have no idea what the setup is. For example what does this mean:
Ring's flat is normal to the surface of the ground? What is "Ring's flat"?

What does it mean: "The ring starts to move plumb... "?

Answer 3

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