What angle does it separate from the bowl?

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An ice cube placed on an overturned spherical bowl is analyzed to determine the angle at which it separates from the bowl as it slides down. The problem involves applying conservation of energy and Newton's second law to understand the forces acting on the cube. The key point is that the cube will fall off when the normal force becomes zero, indicating that the net force equals the weight of the cube. The discussion emphasizes the importance of considering the radial direction and the components of weight in this context. Participants are encouraged to explore the implications of circular motion and the changing speed of the cube as it descends.
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Homework Statement


an ice cube is placed on top of an overturned spherical bowl of radious r. if the cube slides downward from rest at the top of the bowl, at what angle does it separate from the bowl?


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The Attempt at a Solution


i'm stuck with this problem. i have thought about it for a loong time and i am deperate for a huge hint. i know the answer but i need to know how they got it. the question came from the energy chapter and i simply don't know how to approach it. please help.
 
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Hint: In additional to using conservation of energy, you'll need to analyze forces and apply Newton's 2nd law.
 
yeah, I've thought about that. it will fall off when the normal force goes to zero. or when the net force is just the weight. but that still gets me no where. i am not noticing somehting very obvious apparently. please say more.
 
Take advantage of the fact that the bowl is spherical. What kind of motion does that imply for the ice cube?
 
yeah, circular motion. i know the cube follows a circle. i thought about using a=(v^2)/r but that equation is only valid for constant speed. the cube's speed increases as it falls. i have thought of everything, i think. what am i missing?
 
student24 said:
i thought about using a=(v^2)/r but that equation is only valid for constant speed.
Why do you think that? :wink:
 
hmm, my book says that "when an object moves in a circle of radius r with constant speed v, its cent accel is." i guess not then. let me play around with that then, i will return tomorrow if i am still stuck. ty for helping me so far. now i will attack some more.
 
ok, I've thought about it and i cannot get any closer. i need the answer. this problem is driving me crazy. the net force acting on it before it falls off is -W+N=(mv^2)/r that's all i see. need help.
 
Another hint: Consider forces in the radial direction (normal to the surface). What's the component of the weight in the radial direction?
 

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