A potential energy function for system 1 is given by U_1 (x) = Cx^2 + Bx^3. The

Question

A potential energy function for system 1 is given by U_1 (x) = Cx^2 + Bx^3. The potential energy function for system 2 is given by U_2 (x) = A + Cx^2 + Bx^3, where A is a positive quantity. How does the force on system 1 relate to the force on system 2 at a given position? The force on the second system will be with greater than the force on the first system. The force on the two systems will be in opposite directions. The force is identical on the two systems. There is no relationship between the forces on the two systems. The force on the second system will be with less than the force on the first system.

Explanation / Answer

F1 = -dU1(x)/dx

=d/dx(Cx^2+bx^3)

= 2cx + 3bx^2

F2 = -d2U(x)/dx

=d/dx(A+Cx^2+Bx^3)

= 2cx + 3bx^2

both forces are equal

option C is the answer

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