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)(adsbygoogle = window.adsbygoogle || []).push({});

Here is the problem: A box of massmis released from rest at Point A, the top of a long, frictionless slide. Point A is at heightHabove 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 isx.

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 ofxfrom B but not at a vertical height ofyabove 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) f_{k}= -(mv_{b}^2 / 4mgh_{a})

[/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.

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# Validation of a Work/Energy Problem

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