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Force or equilibrium position from a potential energy function

This type of question, asked 2 times: 14 Jun 2022, 29 Jan 2024. All 2 questions below, oldest first.

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  1. Question 1

    14 Jun 2022

    101
    Potential energy as a function of rr is given by U=Ar10−Br5U =\frac{A}{r^{10}}-\frac{B}{r^{5}}, where rr is the interatomic distance, AA and BB are positive constants. The equilibrium distance between the two atoms will be:

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  2. Question 2

    29 Jan 2024

    7
    The potential energy function (in J) of a particle in a region of space is given as U=(2x2+3y3+2z)U =\left( 2x^{2}+ 3y^{3}+ 2z \right). Here x,yx,y and zz are in meter. The magnitude of xx - component of force (in NN ) acting on the particle at point P(1,2,3)mP(1,2,3)m is:

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