How Do You Calculate Maximum Height on an Inclined Plane with Friction?

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Homework Help Overview

The discussion revolves around calculating the maximum height a block reaches on an inclined plane after sliding down a frictionless track, with a focus on the effects of kinetic friction. The subject area includes concepts from mechanics and energy conservation.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss using energy methods to relate kinetic and potential energy, while considering the work done by friction. Questions arise about the definitions of variables, such as "theta," and the specific points where participants encounter difficulties.

Discussion Status

The conversation is ongoing, with participants providing insights into energy conservation principles and the role of friction. Some guidance has been offered regarding the relationship between kinetic energy, potential energy, and work done by friction, but no consensus has been reached on the specific calculations or interpretations.

Contextual Notes

There is a mention of the coefficient of kinetic friction and its impact on the energy calculations, as well as the need for clarity on the angle "theta." The discussion reflects the complexities of applying energy methods in the presence of friction.

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Prooving crazy formula

If anyone could help me with this that would be great. I keep getting stuck. Thanks.

A block slides down a curved frictionless track and then up an inclined plane. the coefficient of kinetic friction between the block and the incline is Uk. Use energy methods to show that the maximum height reached by the block is:

Ymax=

h
-----------------
1 + Uk cot(theta)
 
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The initial kinetic energy is equal to final potential energy minus the work done by the frictional force. Where exactly are you "getting stuck?"
 
Since the track is frictionless, it's path independent, so potential energy just before the block starts to slide is mgh (from gravity). Also you know that the change in thermal energy of the block due to friction is Uk * distance block travels up ramp. Hopefully that will help you some.
 
It might help us to know what "theta" means.
 

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