What angle does it separate from the bowl?

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Homework Help Overview

The problem involves an ice cube placed on top of an overturned spherical bowl, with the question focusing on determining the angle at which the cube separates from the bowl as it slides down. The context is rooted in concepts from energy and circular motion.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the use of conservation of energy and the analysis of forces, particularly Newton's second law. There is consideration of when the normal force becomes zero as a condition for separation. Some participants express confusion about the implications of circular motion and the application of acceleration equations.

Discussion Status

The discussion is ongoing, with participants offering hints and exploring various interpretations of the problem. Some guidance has been provided regarding the analysis of forces and the nature of motion, but no consensus or resolution has been reached.

Contextual Notes

Participants mention the challenge of applying concepts from their textbook and express frustration over the lack of clarity in their understanding of the problem. There is an acknowledgment of the complexity involved in analyzing the forces acting on the ice cube.

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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?


Homework Equations





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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