How Far Will the Block Travel Up the Incline?

[cj3]

Homework Statement

A block of mass m is placed in a smooth-bored spring gun at the bottom of the incline so that it compresses the spring by an amount x_c. The spring has spring constant k. The incline makes an angle \vartheta with the horizontal and the coefficient of kinetic friction between the block and the incline is \mu. The block is released, exits the muzzle of the gun, and slides up an incline a total distance L.
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Find L, the distance traveled along the incline by the block after it exits the gun. Ignore friction when the block is inside the gun. Also, assume that the uncompressed spring is just at the top of the gun (i.e., the block moves a distance x_c while inside of the gun). Use g for the magnitude of acceleration due to gravity.
Express the distance in terms of g, \vartheta, \mu, m, k, x_c
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Homework Equations

W_f+KE_i+PE_i+W_s=KE_f+PE_f+W_s

The Attempt at a Solution

i ahve no idea...

 

[physics girl phd]

Generallly with energy problems, it is best to calculate all the pieces of potential energy and kinetic at initial and final positions, as well as look at any work that was done on the object in between -- causing it to either gain energy (perhaps by an external force) or lose energy (perhaps by an external opposing force like fricion). Start finding these terms. If one of the terms involves the distance (what you are looking for, just leave that in as "d." once you have expersions for these terms, you can use them in a work-energy theorem calculation.