For the potential energy curve shown in Figure P7....

Question

For the potential energy curve shown in Figure P7.52, (a) determine whether the force F_x is positive, negative, or zero at the five points indicated. (b) Indicate points of stable, unstable, and neutral equilibrium. (c) Sketch the curve for F_x versus x from x = 0 to x = 9.5 m.

Patrick Ford · Accepted Answer

in this problem, we'll apply the relationship between Force, potential, and the change in position.Potential energy:[readmore]∆U=-F∆x(a)The slope of a graph of potential energy versus x is the force. The force is positive when the slope is negative.The force is negative when the slope is positive. The force is zero when the slope is zero.At A, C, and E the slope is zero. The force is zero at A, C, E.The slope is negative at B. The force is positive at B.The slope is positive at D. The force is negative at D.(b)Equilibrium exists when all the forces acting on the object are balanced. At B and D the forces are not balanced. That is, the net force is not zero. B, D - no equilibriumIn a potential energy graph, stable equilibrium occurs in a trough, unstable equilibrium occurs at a maxima (opposite of a trough) while neutral equilibrium occurs at a horizontal stretch. A, E - unstable equilibriumC - stable equilibrium(c)In part (a) we said the force is zero at A, C, and E.We'll determine the magnitude of the force at B and D by drawing a tangent to the curve. Draw a tangent through (1,3) and (2,1).Fx,B = - (U2 - U1)/(x2 - x1) = - (3 - 1)/(1 - 2) = +2 NDraw a tangent through (9,4) and (6,-2)Fx,D = - (U2 - U1)/(x2 - x1) = - (4 - (-2))/(9 - 6) = -2 NWe'll approximate the values of F at B and D to make the plot. B - (1.5,2)D - (7.6,-2)A sketch of the curve for Fx versus x from x = 0 to x = 9.5 m is shown below.

Problem: For the potential energy curve shown in Figure P7.52, (a) determine whether the force Fx is positive, negative, or zero at the five points indicated. (b) Indicate points of stable, unstable, and neutral equilibrium. (c) Sketch the curve for Fx versus x from x = 0 to x = 9.5 m.

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FREE Expert Solution

Problem Details

Problem: For the potential energy curve shown in Figure P7.52, (a) determine whether the force Fx is positive, negative, or zero at the five points indicated. (b) Indicate points of stable, unstable, and neutral equilibrium. (c) Sketch the curve for Fx versus x from x = 0 to x = 9.5 m.

FREE Expert Solution

FREE Expert Solution

Problem Details

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