Projectile motion - ball in circular motion

Homework Statement

Okey, so the problem started with a ball in circular motion on a table (xy-plane, seen from above). Eventually the rope that held the ball snapped and the ball continued on (no friction/air resistance) with constant velocity in x-direction. Gravity working in negative z-direction, just too clarify.

Mass: 0.01kg
Starting velocity x-dir. : 0.5m/s (constant, from when the rope snapped)
Starting velocity z-dir : 0
Distance from were the ball snapped too the edge: 0.5m

Suppose you now turn the table in such a way that there always is ("barely") contact
between the ball and the table, but there is no force between them.

So my problem:

How long does it take before the ball falls off the table?

The situation starts when the rope snapped (time=0)

The Attempt at a Solution

Well I have been really stuck on this. I have been trying to express the angle of the table, function of gravity. Also tried using pytagoras too express z-x in the motion equations. Since I know that the hypotenuse is 0.5m. Tried and failed alot really.

If anyone have any suggestions or how I can express this, that would be appreciated.

Thank you

PeterO
Homework Helper

Homework Statement

Okey, so the problem started with a ball in circular motion on a table (xy-plane, seen from above). Eventually the rope that held the ball snapped and the ball continued on (no friction/air resistance) with constant velocity in x-direction. Gravity working in negative z-direction, just too clarify.

Mass: 0.01kg
Starting velocity x-dir. : 0.5m/s (constant, from when the rope snapped)
Starting velocity z-dir : 0
Distance from were the ball snapped too the edge: 0.5m

Suppose you now turn the table in such a way that there always is ("barely") contact
between the ball and the table, but there is no force between them.

So my problem:

How long does it take before the ball falls off the table?

The situation starts when the rope snapped (time=0)

The Attempt at a Solution

Well I have been really stuck on this. I have been trying to express the angle of the table, function of gravity. Also tried using pytagoras too express z-x in the motion equations. Since I know that the hypotenuse is 0.5m. Tried and failed alot really.

If anyone have any suggestions or how I can express this, that would be appreciated.

Thank you

Suppose that at the point the string broke, the table magically disappeared. The ball would then travel as a projectile - following a parabolic path. That seems to indicate that unless the table surface is parabolic - there cannot be "such a way that there always is ("barely") contact between the ball and the table"

That is unless the table surface is vertical - in which case you need more than a string to have the ball travelling in a (now) vertical circle at constant speed.

The situation may be impossible - both to occur and also to analyse.

Yes well I have been trying too solve this without thinking about the table. But I was thinking of something, since I know that the hypotenuse is 0.5m. If you imagine a right-angled triangle, one side that illustrates the difference in height and the other traveled in x-direction.

But still I find this very hard to solve.

gneill
Mentor
Hmm. If the table is (actively) tilted in such a fashion as to always be barely in contact with the projectile without exerting force on it, what might one say about the plane of the surface of the table with respect to the velocity vector of the projectile?

I have solved it;)