A 900-kg roller coaster car is initially at the top of a rise, at point. It then

Question

A 900-kg roller coaster car is initially at the top of a rise, at point. It then moves 165 ft, at an angle of 40.0 degree below the horizontal, to a lower point. Choose the car at point to be the zero configuration for gravitational potential energy of the roller coaster-Earth system. Find the potential energy of the system when the car is at at point at point change in potential energy Repeat part (a), setting the zero configuration with the car at point at point at point change in potential energy The potential energy function for a system of particles is given by U(x) = -8x^3 + 7x^2 + 6x, where x is the position of one particle in the system. Determine the force F_x on the particle as a function of x. For what values of x is the force equal to zero? (Enter your answer from smallest to largest.) Plot U(x) versus x and F_x versus x, and indicate points of stable and unstable equilibrium. (Do this on paper. Your instructor may ask you to turn in this work.)

Explanation / Answer

Considering zero at B

165 ft = 50 m

The potential at A would be

PEA = mg 50 sin (40) = 2892 J

Potential at B = 0 J

Change will be = -2892 J

b) For zero at A

Potential at B = -2892

Potential at A = 0

Change will be -2892 J

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