Box on a sphere is nudged- when does it fall off?

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SUMMARY

The discussion focuses on a physics problem involving a box of mass "m" placed on a sphere of radius "r" and determining the conditions under which the box will fall off after being nudged. The maximum speed before leaving the sphere is derived using energy conservation principles, specifically gravitational potential energy (Ugpe = mgh) and kinetic energy (KE = mv²/2). Additionally, the centripetal force equation (Fc = mv²/r) is crucial for understanding the forces acting on the box as it slides down the sphere. Newton's second law is also emphasized as a necessary tool for solving the problem.

PREREQUISITES
  • Understanding of gravitational potential energy (Ugpe = mgh)
  • Knowledge of kinetic energy (KE = mv²/2)
  • Familiarity with centripetal force (Fc = mv²/r)
  • Basic grasp of Newton's second law of motion
NEXT STEPS
  • Study energy conservation in mechanical systems
  • Learn about centripetal motion and its applications
  • Explore advanced topics in dynamics involving forces on inclined planes
  • Review problems involving Newton's laws in non-linear motion
USEFUL FOR

Students studying introductory physics, particularly those focusing on mechanics and dynamics, as well as educators looking for examples of energy conservation and force analysis in real-world scenarios.

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Box on a sphere is nudged-- when does it fall off?

Homework Statement



A box of mass "m" is placed on a sphere of radius "r". The box is given an extremely small nudge to get it moving.

(a) What is the maximum speed the ball may have without leaving the sphere?
(b) At what angle from the vertical does the ball last touch the sphere?

Homework Equations



I think this is a question requiring energy, so

Ugpe = mgh
KE = mv2/2

But knowing there is a circle involved,

Fc = mv2/r

The Attempt at a Solution



I'm not sure how to attack the problem... I do know that our physics class has not yet gone over anything beyond Newton's three laws and the concepts of gravitational potential and kinetic energy.
 
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ball on sphere?
you asked box on sphere
please rephrase question correctly
 


Aesops said:
I'm not sure how to attack the problem... I do know that our physics class has not yet gone over anything beyond Newton's three laws and the concepts of gravitational potential and kinetic energy.
That's all you need. Hint: In addition to energy conservation, make use of Newton's 2nd law. What forces act on the box as it slides down?
 

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