Max Speed of Cart: Determine Without Losing Contact

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SUMMARY

The discussion focuses on determining the maximum speed of a cart at the top of a hill shaped like an arc of a circle with radius r, without losing contact with the surface. Participants emphasize the necessity of creating a free body diagram and selecting an appropriate coordinate system, such as cylindrical coordinates, to analyze the forces acting on the cart. The equations of motion must be derived and solved to find the critical speed at which the cart maintains contact with the hill's surface. Logical reasoning alone is insufficient; a systematic approach using physics principles is essential.

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  • Understanding of free body diagrams in physics
  • Knowledge of cylindrical coordinate systems
  • Familiarity with equations of motion
  • Basic concepts of centripetal force and gravitational force
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  • Study the derivation of equations of motion for circular motion
  • Learn how to construct and interpret free body diagrams
  • Research centripetal force calculations in physics
  • Explore examples of maximum speed problems in circular motion scenarios
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Students studying physics, educators teaching mechanics, and anyone interested in understanding dynamics related to circular motion and forces.

Pearce_09
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max speed of cart...

A persone rides in a cart moving at a speed v at the top of a hill that is in the shape of an arc of a circle with radius r.
determine the maximum speed that the cart may travel at the top of the hill without losing contact with the surface.

How do i know that the cart leaves the surface at values of v.
what i mean, i don't know the steps or process on solving this. I am trying to think about this logically and I am getting no where..
 
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Some problems can be solved just by looking at them and using some logic. This isn't one of them. You need to create your free body diagram, choose a coordinate system (cylindrical would seem appropriate), write the equations of motion, and go from there.

You'd be surprised how many physics problems can be solved by just plug-n-chug write the equations of motion and see what you get.
 

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