The potential energy function for a system is given by U(x) = 3x3 - 2x2 - 6x whe

Question

The potential energy function for a system is given by U(x) = 3x3 - 2x2 - 6x where x is in meters and U is in Joules. Determine the Force Fx as a function of x. For what values of x is the force equal to zero? Plot U(x) versus x and Fx versus x. mid indicate the points of stable and unstable equilibrium. (Use graph paper 3 Points for each correct graph and 2 points for identifying stable and unstable equilibruim.) If a particle moves from x = 2 in to x = 4 m, find the charge in its kinetic energy. Assume that the only force acting on the particle is the force found in part (a). A skier weighing 800 N comes down a frictionless ski run that is circular (R = 30m) at the bottom, as shown in Figure 2. If her speed is 12m/s at point A, what is het speed at the bottom of the hill

Explanation / Answer

   Given potential energy function :       U (x) = 3 x3 - 2x2 - 6x   (a ) The force acting on the system is              given by the formula as               F = -dU(x) / dx                = -d /dx [3 x3 - 2x2 - 6x   ]                = -3 (3) x2  + 2 (2x) + 6               =   - 9x2   + 4x + 6 Thus, force function intermas of x as                F (x ) = [ - 9x2 + 4 x + 6 ] (b)           Force equal to 0 for what value of x = ?             so,   [ - 9x2 + 4 x + 6 ] = 0                                   or                        9x2  - 4 x - 6 = 0                            x1 = 1.0684    and x2 = -0.6239          The posts C and D requires graph papers              please post these as seperately .                                                      

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