Ball Rolls off of a circle :O PROBLEM

[Plutonium88]

Ball Rolls off of a circle :O! PROBLEM!

So the problem is, a ball at zero velocity begins to roll on a circle. At a certain point the ball and the circle "DISCONNECT". There is a height x from the roof to the point it disconnects.

Given Information. Height X, Diameter D of circle, Vi=0, r=1/2D Mo=Mass Of The ball

http://postimage.org/image/a91pl12ll/

Relative Equations:
Conservation Of Energy
-Maybe centripetal force formula (Fc=Fg,ffr,)
-

My attempt:

i believe that at the point the ball ejects from the surface of the big circle, that the FN = 0 because it isn't going to be connected anymore... (CORRECT ME IF I'M WRONG)

- I feel like i don't have enough information, (obviously i do) but maybe i do not have the skills... I was wondering if some one could lead me in the right direction...

Now ET1=energy of the system at the top at rest
ET2=energy of the system at the point it detaches...

Et1=Et2
mgD=mgD-mgX+1/2mov2^2 -simplify

X = V2^2/2g

Now obviously I'm left with a problem with two unknowns... I've been drawing triangles all over this circle and trying to figure out how i can get an angle.. I figured out it makes an isosceles triangle if you connect the radius twice to the the point at which it detaches... But still i don't know how to get an angle.. I think i need to learn radiants(Or would that even help me)?

Anyways I'm stuck just need a little hint, please don't answer the whole problem

 

[PeterO]

So the problem is, a ball at zero velocity begins to roll on a circle. At a certain point the ball and the circle "DISCONNECT". There is a height x from the roof to the point it disconnects.

Given Information. Height X, Diameter D of circle, Vi=0, r=1/2D Mo=Mass Of The ball

http://postimage.org/image/a91pl12ll/

Relative Equations:
Conservation Of Energy
-Maybe centripetal force formula (Fc=Fg,ffr,)
-

My attempt:

i believe that at the point the ball ejects from the surface of the big circle, that the FN = 0 because it isn't going to be connected anymore... (CORRECT ME IF I'M WRONG)

- I feel like i don't have enough information, (obviously i do) but maybe i do not have the skills... I was wondering if some one could lead me in the right direction...

Now ET1=energy of the system at the top at rest
ET2=energy of the system at the point it detaches...

Et1=Et2
mgD=mgD-mgX+1/2mov2^2 -simplify

X = V2^2/2g

Now obviously I'm left with a problem with two unknowns... I've been drawing triangles all over this circle and trying to figure out how i can get an angle.. I figured out it makes an isosceles triangle if you connect the radius twice to the the point at which it detaches... But still i don't know how to get an angle.. I think i need to learn radiants(Or would that even help me)?

Anyways I'm stuck just need a little hint, please don't answer the whole problem

Something to contemplate..

If at any point the circle could magically disappear, the ball would become a projectile - following a parabolic path.

At the point where it leaves the circle, the potential parabolic path is presumably parallel to the circle at the time.

 

[netgypsy]

So the question is to find out where it disconnects I assume??

Thinking about it, the point where it will leave the circle is going to be the point where the velocity exceeds the velocity needed to keep the object in the at circle (and you have a formula that allows you to calculate that) so why not calculate the velocity needed to keep the object in that circle and find out at what point, using energy, it will equal that value because at the point where it exceeds that value , it will leave the circle. Of course you may need Newton's laws and kinemeatics to get this info.

 

[ehild]

Hi Plutonium,

You made a very nice picture (with the ball changing shape as moving downward, it must have some deeper meaning... )

Draw the forces acting on the ball, and ask yourself the questions:

What force ensures motion along a circle of radius R with velocity v? What is the magnitude and direction of this force? Can the forces exerted on the ball result in the appropriate force that keeps the ball on track?

ehild

 

[asteriatic]

as it is important for me to figure it out on my own..Your approach is correct so far. To solve for the angle, you can use the fact that the ball rolls off the circle at the point where the normal force becomes zero. This means that the centripetal force (Fc) must equal the force of gravity (Fg) at that point. So you can set up the equation Fc=Fg and solve for the angle.

Fc=Fg can also be written as mv^2/r=mgcosθ, where θ is the angle you are trying to find. You already have values for m, v, and r, so you can solve for cosθ and then use inverse cosine to find the angle.

Another approach is to use conservation of angular momentum. At the top of the circle, the ball has zero angular momentum, but at the point where it rolls off, it has some angular momentum due to its rotational motion. You can set the initial angular momentum equal to the final angular momentum and solve for the angle. This approach would require you to use the moment of inertia of a rolling ball, which you can look up or calculate using the parallel axis theorem.

I hope this helps guide you in the right direction. Keep in mind that there may be multiple ways to solve this problem and it's important to understand the concepts behind the equations you are using. Good luck!