Hi, this is my first post here. I was just wondering if anyone could validate my work done on this problem. (I have a feeling I missed something) Here is the problem: A box of mass m is released from rest at Point A, the top of a long, frictionless slide. Point A is at height H above the level of Points B and C. Although the slide is frictionless, the horizontal surface from Point B to C is not. The coeffiecent of kinetic friction between the box and this surface is [mu] sub k, and the horizontal distance between Points B and C is x. A) Find the speed of the box when its height above Point B is 1/2H . B) Find the speed of the box when it reaches Point B. [Edit in:] C) Determine the value of [mu]k so that the box comes to rest at Point C. [/Edit] D) Now assume that Points B and C were not on the same horizontal level. In particular, assume that the surface from B to C had a uniform upward slope so that Point C was still at a horizontal distance of x from B but not at a vertical height of y above B. Answer the question posed in part (c). E) If the slide were not frictionless, determine the work done by friction as the box moved from Point A to Point B if the speed of the box as it reached Point B was half the speed calculated in part (b). My answers in variable form (I'm guessing that's how my teacher wanted them answered): A) PE sub a + KE sub a + W = PE sub b + KE sub b mg1/2h sub a = 1/2mv^2 [squ] = square root, not check [squ] 2(g1/2h sub a) = v B) gh sub a = 1/2v^2 [squ]2(gh sub a) = v I'll just post my answer for the last two here because posting all of the work in order would take too long... C) [mu] sub k = -(v sub c ^2 - v sub b^2 / N) D) [mu] sub k = -(gh + 1/2v sub c ^2 - 1/2v sub b^2 / N) [Edit in:] E) fk = -(mvb^2 / 4mgha) [/Edit] I believe my problem is I'm not counting the force w sin [the] in the conservation of energy stuff but I'm not sure. I'd appreciate any help. Thanks in advance.