**Unformatted text preview: **hysics; see Appendix C.) = = = = = = Section 8-6:
Problem Nonconservative Forces Problem
47. The potential energy associated witH a certain conservative force is given by U = b:t2 i where b is a constant. Show that the force always tends to accelerate a particle toward the origin if b is positive and away from the origfu. .if b is negative. 50. Repeat Problem 20 for the case when the coefficient of kinetic friction on both slopes is 0.11, while the level stretches remain frictionless. Solution
The work done by friction skiing down a straight slope of lengthfis WI -Ike -!-'kNf= -!-'k(mgccs(J)x (h/sitJ.f) = -!-'kmghcotB, where h = isinB is the vertical drop of the slope. The energy principle applied between the start and the first level (see Problem 20) now gives I:!..KAB + I:!..UAB = Wf,AB, or = mg(YA - VB) - !-'kmg(YA - VB) cot 32. Therefore, = = Solution
The conservative force represented by. the one-dimensional potential energy U (x) :::: bx2 is given by Equation 8-8, Fx = -'-dUjdx = -2bx.x is the displacement from the origin, so this is towards t...

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