What are the energy equations for solving a crate sliding on an inclined plane?

AI Thread Summary
To solve for the maximum height ymax reached by a crate sliding down a frictionless lunar crater and up an inclined plane, one must apply energy conservation principles. The relevant equations include potential energy (PE = mgh), kinetic energy (KE = 1/2 mv^2), and the expression for frictional force (F_friction = k * N), where N is the normal force. The components of weight acting on the incline must also be considered, particularly the gravitational force parallel to the incline. By equating the initial potential energy at the top of the crater to the kinetic energy at the bottom and the potential energy at the maximum height, one can derive the necessary equations to find ymax. Understanding these energy relationships is crucial for solving the problem effectively.
Leesh09
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Homework Statement


A crate with scientific equipment slides down a curved frictionless side of lunar crater of the depth h, and then up along the other side which is an inclined plane. The coefficient of kinetic friction between crate and incline is k, and the inclined side makes an angle θ with the horizontal. Use energy methods to find the maximum height ymax reached by the crate.


Homework Equations





The Attempt at a Solution


I have no idea where to begin this. Any input would be very helpful.
 
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Write down the relevant equations of potential energy, kinetic energy, components of weight on the inclined plane and the expression for frictional force and its direction.
 

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