1. Potential (20 points total) Mass m is in a potential well given by Urm consta

Question

1. Potential (20 points total) Mass m is in a potential well given by Urm constants, and r is the distance from m to the force center, with r0. where a and b are known positive NOTE Consider this problem as one-dimensional motion in the spherical coordinate r a) (3 points each, 9 ports total): i In terms of m, a, b and r find an expression for Fin, the force acting on the atom ln terms of a and b: find, the distance from the force center to the atom when taat equilibrium. In terms of m, a and b: find an expression for U,- U) the potential of this stom at the equilibrium point. Simplity b) Suppose that, when the atom is at equiibrium, it undergoes a small dispiacement a (where x

Explanation / Answer

a)

force is given as

F = - dU(r)/dr

F = - (d/dr) (m (a/r15 - b/r5))

F = - m ((-15 a/r16 + 5 b/r6)

ii)

at equilibrium , F = 0

- m ((-15 a/r16 + 5 b/r6) = 0

15 a/r16 = 5 b/r6

3a/b = r10

r = (3a/b)1/10

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