Question

Shooting a Block up an Incline

A block of massmis placed in a smooth-bored spring gun at the bottomof the inclineso that it compresses the spring by an amount x_c.The spring has spring constant k. The incline makes an angletheta with the horizontal and the coefficient ofkineticfriction between the block and the incline is mu. The blockis released, exits the muzzle of the gun, andslides up an incline a total distance L.5506.jpgFind L,the distance traveled along the incline by the block afterit exitsthe 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 movesa distance x_c while inside of the gun). Use gfor the magnitude of acceleration due to gravity.Express the distance L in terms of x_c, k,m,g,mu, and theta.
L =
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