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

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To calculate the maximum height on an inclined plane with friction, the initial kinetic energy of the block is equated to the final potential energy minus the work done by friction. The formula for maximum height is derived as Ymax = h / (1 + Uk cot(theta)). The frictional force's work is determined by the coefficient of kinetic friction (Uk) and the distance traveled up the ramp. The discussion emphasizes the importance of understanding the relationship between gravitational potential energy and thermal energy changes due to friction. Clarification on the angle theta is suggested for a more precise calculation.
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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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