What is the velocity of the ice cube when it loses contact with the sphere?

[faidros]

Hello,

I've encountered some problems while doing a mechanics project, and was hoping for some help here.
The problem is what follows:

An icecube starts to move at the top of a half spherical building (start velocity 0, no friction, and can be regarded as a particle). What's the icecube's velocity at the time it looses contact with the sphere and begins to fall?

Any ideas?

 

[faidros]

The centripetal force for the particle is F=(mv^2)/R
Could this force be expressed as F = ma, where a is the acceleration in a cylindrical coordinate system?
i.e:
r=R(cosa, sina)
v=Ra'(-sina, cosa)
a=Ra''(-cosa,-sina) <----

Am I way off here?
Does anybody have an approach on this problem? Any ideas how to express the angle between the vertical and the particle in terms of time and gravity?

thanks for any help

 

[m2003]

I would approach this problem by first identifying the relevant physical principles involved. In this case, we are dealing with concepts of mechanics, specifically the laws of motion and forces acting on the ice cube. The sphere and ice also play important roles in this scenario.

To solve this problem, we can apply the laws of motion, specifically Newton's Second Law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. In this case, the net force on the ice cube would be the force of gravity pulling it down and the normal force exerted by the sphere pushing it up.

Since the ice cube is starting at rest and there is no friction, the initial net force would be zero. As the ice cube starts to slide down the sphere, the normal force will decrease while the force of gravity remains constant. At the point where the normal force becomes zero, the ice cube will lose contact with the sphere and begin to fall. At this point, the net force will be equal to the force of gravity, and we can use Newton's Second Law to calculate the acceleration of the ice cube. From there, we can use kinematic equations to determine the velocity of the ice cube at this point.

In summary, by applying the laws of motion and understanding the forces at play, we can determine the velocity of the ice cube when it loses contact with the sphere. It is important to always consider the physical principles involved when approaching a problem in science. I hope this helps with your project. Best of luck!